The Attitudinal Entropy (AE) Framework as a General Theory of Individual Attitudes
The Attitudinal Entropy (AE) Framework as a General Theory of Individual Attitudes
Dalege, Jonas; Borsboom, Denny; van Harreveld, Frenk; van der Maas, Han L. J.
2018-10-02 00:00:00
PSYCHOLOGICAL INQUIRY 2018, VOL. 29, NO. 4, 175–193 https://doi.org/10.1080/1047840X.2018.1537246 TARGET ARTICLE The Attitudinal Entropy (AE) Framework as a General Theory of Individual Attitudes Jonas Dalege, Denny Borsboom, Frenk van Harreveld, and Han L. J. van der Maas Department of Psychology, University of Amsterdam, Amsterdam, The Netherlands KEYWORDS ABSTRACT Attention; attitude; entropy; This article introduces the Attitudinal Entropy (AE) framework, which builds on the Causal Attitude network models; statistical Network model that conceptualizes attitudes as Ising networks. The AE framework rests on three mechanics; thought propositions. First, attitude inconsistency and instability are two related indications of attitudinal entropy, a measure of randomness derived from thermodynamics. Second, energy of attitude con- figurations serves as a local processing strategy to reduce the global entropy of attitude networks. Third, directing attention to and thinking about attitude objects reduces attitudinal entropy. We first discuss several determinants of attitudinal entropy reduction and show that several findings in the attitude literature, such as the mere thought effect on attitude polarization and the effects of heuristic versus systematic processing of arguments, follow from the AE framework. Second, we discuss the AE framework’s implications for ambivalence and cognitive dissonance. A century of research on attitudes has produced an impres- possibility to evaluate the global entropy of an attitude. sive amount of empirical findings and identified an abun- Third, attention and thought directed at the attitude object dance of concepts and processes related to attitudes. An have an analogous effect on the attitudinal representation as important next step toward a thorough understanding of (inverse) temperature has on thermodynamic behavior— attitudes would be a theoretical framework able to explain heightened attention and thought make attitudinal represen- these empirical findings from few first principles. The aim tations low in energy more likely and therefore reduce the of this article is to develop such a framework. To do so, we entropy of the attitude. The structure of this article is as follows. First, we discuss make use of analogical modeling (Haig, 2005): We use stat- istical mechanics as a starting point for our framework the main tenets of the AE framework. Second, we discuss determinants of reduction of attitudinal entropy and show because of its advanced theory and because our earlier ana- lysis has shown that a formalized measurement model of that several findings in the attitude literature, such as indi- vidual vs. group effects of implicitly measured attitudes, the attitudes can be based on statistical mechanics principles (Dalege et al., 2016) and show that an analogous theoretical mere thought effect, and systematic vs. heuristic processing, approach to attitude can explain a wide variety of empir- follow from these determinants. Third, we discuss ambiva- lence (e.g., Priester & Petty, 1996) and cognitive dissonance ical phenomena. Statistical mechanics revolves around three fundamental (Festinger, 1957) from the perspective of the AE framework. properties of a system—entropy (a measure of the system’s Throughout the subsequent sections we model several estab- randomness), energy, and temperature. To investigate lished phenomena in the attitude literature to show that the whether statistical mechanics represents a fruitful starting AE framework indeed holds promise in explaining several point for a general theory of attitudes, we search for analo- phenomena with few first principles. We also identify several gies of these fundamental properties and test whether the predictions that can be derived from the AE framework in consequences of these analogies match empirical findings in each discussion of a given phenomena to illustrate the pre- the attitude literature. Based on this approach we derive the dictive power of the AE framework and to define an empir- Attitudinal Entropy (AE) framework, which rests on three ical agenda for future research. We close by discussing propositions. First, inconsistency and instability of an atti- potential neural substrates of the AE framework’s proposi- tude represents attitudinal entropy and is therefore the nat- tions, the AE framework’s relation to other broad models of ural state of an attitude. Second, the energy of the attitude, and several open questions that need to be attitudinal representation serves as a local processing addressed to further develop the AE framework. CONTACT Jonas Dalege j.dalege@uva.nl Department of Psychology, University of Amsterdam, Nieuwe Achtergracht 129, 1018 WT, Amsterdam, The Netherlands. Color versions of one or more of the figures in this article can be found online at www.tandfonline.com/hpli Temperature, strictly speaking, might not be regarded as a fundamental property, because it can be derived from the relation between entropy and energy. However, for our current purposes it is beneficial to treat temperature as a fundamental property. 2018 Taylor & Francis Group, LLC 176 J. DALEGE ET AL. The AE Framework work, constituting heat loss or entropy. This notion also lies at the heart of the second law of thermodynamics, which In this section, we discuss the meaning of attitudinal states that entropy of an isolated system always increases. entropy and its implications for the dynamics of attitudes. Although the concept of entropy originated in classical We first discuss micro- and macrostates of attitudes and thermodynamics, its application to statistical mechanics then turn to the meaning of attitudinal entropy. Based on resulted in a broader use of entropy as a general measure of these definitions, we derive the AE framework. disorder or uncertainty in a system. The physicist Ludwig Boltzmann (1877) developed the statistical mechanics defin- ition of entropy, which holds that a macrostate that can be Attitudinal Micro- and Macrostates realized by many microstates has higher entropy than a The first question that needs to be addressed before we can macrostate that can be realized by few microstates (see define attitudinal entropy is what constitutes microstates Figure 1a). As an example, take the distribution of oxygen and macrostates of an attitude. In statistical mechanics, a molecules in the room you are sitting in right now. Luckily, microstate refers to the microscopic configuration of a given the macrostate of the oxygen molecules being distributed system (e.g., the position of each oxygen molecule in the evenly throughout the room can be realized by many more room you are sitting in), and a macrostate refers to the microstates (thus having higher entropy) than the macro- macroscopic behavior of a given system (e.g., whether all the state of the oxygen molecules clustering at one position in oxygen molecules are centered in one corner or whether the room. As an intuitive example of why the likelihood of they are evenly dispersed throughout the room). In line with a macrostate depends on its Boltzmann entropy, imagine a several theories on attitudinal structure (e.g., Dalege et al., simple slot machine with three fields that can show a lemon, 2016; Eagly & Chaiken, 2007; Fishbein & Ajzen, 1975; a peach, or a banana. The macrostate “win” (i.e., all fields Rosenberg, Hovland, McGuire, Abelson, & Brehm, 1960), showing the same fruit) can then be realized by three micro- we define the microstate of an attitude as the configuration states (e.g., three lemons). The macrostate “lose” (i.e., the of the relevant beliefs, feelings, and behaviors toward an atti- fields show at least two different fruits), on the other hand, tude object (i.e., attitude elements). As an example take the can be realized by 24 (3 –3) microstates. Although we attitude toward snakes. The microstate of this attitude can already see with this simple example that high-entropy states be represented like this: Attitude Element 1 (e.g., snakes are more likely than low-entropy states, the effect becomes maintain ecological order) is positive, Attitude Element 2 increasingly pronounced with the size of the system increas- (e.g., snakes are scary) is negative, Attitude Element 3 (e.g., ing (up to the point where the high-entropy state is essen- I run away when I see a snake) is negative, and so forth. tially the only possible state as is the case for the The macrostate of an attitude is then defined as the combin- distribution of oxygen molecules in a room). ation of all attitude elements (e.g., how many attitude ele- Applying the Boltzmann entropy to the domain of atti- ments are negative and how many are positive). Based on tudes implies that inconsistent attitudes have higher entropy several theories on the integration of attitude elements into than consistent attitudes. To illustrate this, consider an atti- a global evaluation (e.g., Anderson, 1971; Cacioppo, Petty, & tude consisting of 10 attitude elements. A perfectly univalent Green, 1989; Cunningham & Zelazo, 2007; Fazio, 1995; attitude can be realized only by two different microstates Zanna & Rempel, 1988), we assume that the global evalu- (i.e., all attitude elements being either positive or negative). ation of an attitude object is strongly related to the macro- So the attitude of a snake enthusiast (i.e., judging snakes as state of an attitude, in that it represents a context-depended entirely positive) can be realized only by one microstate. A weighted sum score of the attitude elements. Thus, we pro- perfectly ambivalent or neutral attitude, in contrast, can be pose the following three definitions: realized by 252 microstates. So judging snakes as positive on some aspects and negative on others can be realized by a Definition 1: The configuration of the attitude elements constitutes the microstate of the attitude. large number of microstates. This leads to the following first proposition of the AE framework: Definition 2: The number of positive versus negative attitude elements constitutes the macrostate of an attitude. Proposition I.1: Inconsistency of an attitude is the Boltzmann entropy of the attitude. Definition 3: A situation-depended weighted sum score constitutes the global evaluation of an attitude object. It is important to note here that the Boltzmann entropy concerns the entropy of a single given macrostate (e.g., five attitude elements are in a positive state and five attitude ele- Attitudinal Entropy ments are in a negative state). The entropy of a system, on Entropy is a concept originating from thermodynamics, the other hand, is described by the Gibbs entropy (Jaynes, where it was originally defined as energy that is lost when 1965). Gibbs entropy depends on the likelihood of the dif- energy is transformed (e.g., from chemical to kinetic ferent microstates of a system. As Figure 1b illustrates, energy). Take as an example the situation when you walk up Gibbs entropy is at maximum when all microstates are a steep hill. To do this, your body has to transform chemical energy in the form of calories to kinetic energy so that your Otherwise you might get crushed by all oxygen molecules distributed at the legs move up the hill. However, during this transformation position of the room you are in, or you might suffocate because all oxygen of energy, some energy is inevitably lost that is not put to molecules are at a different position than you. ATTITUDINAL ENTROPY FRAMEWORK 177 Figure 1. Illustrations of the Boltzmann and Gibbs entropies. Note. In (1) W refers to the number of microstates that can realize the given macrostate. In (2) X refers to all possible states of a given system. equally likely—implying that the system’s behavior is com- system, and it is our view that one of the main functions of pletely random—and it is at minimum when only a single focusing our attention on (or thinking about) an attitude configuration is possible, implying that the system’s behavior object is to put such force on the attitude system and obtain (or maintain) a consistent attitude that is low in entropy. is completely ordered. As an example of Gibbs entropy, take Entropy reduction is a crucial aspect of life because a key the movement of water molecules. Under high temperature, characteristic of any living organism is that it must maintain water molecules move randomly (i.e., water is in a gas state); order in their own system (Schrodinger, € 1944). According to this indicates high Gibbs entropy, because the configuration Kauffman (1993), the ability to reduce entropy is the most (i.e., positions) of the water molecules is consistently chang- important selection criterion for evolution. This implies that ing (i.e., all microstates are roughly equally likely). In con- the ability to reduce entropy is one of the central hallmarks trast, under low temperature the water molecules cannot of any living organism. We think that a similar argument move (i.e., water is in a solid state); this reflects low Gibbs can be made for the human mind, so that one of the central entropy, because the configuration of the water molecules is objectives of the human mind is to reduce its entropy (cf. stable (i.e., the current microstate is much more likely than Hirsh, Mar, & Peterson, 2012). It is straightforward that all other microstates). Someone who consistently changes only attitudes low in entropy fulfill the functions typically her attitude toward snakes would therefore have a high- associated with attitudes, such as to organize knowledge, entropy attitude toward snakes, whereas both a snake enthu- increase utility, and express values (Katz, 1960; Smith, siast and phobic have low-entropy attitudes toward snakes. Bruner, & White, 1956). All these functions require attitudes The Gibbs entropy, therefore, measures the inherent stability to be in predictable, stable, and consistent states, and there- of a system, which leads to the following proposition: fore attitudes are much more likely to fulfill their functions Proposition I.2: The Gibbs entropy of the attitude network when they are low in entropy (e.g., only a low-entropy atti- reflects the attitude’s stability. tude toward snakes can clearly imply that you should run From Proposition I.1, it follows that the natural state of when you are near one). Linking the need for entropy an attitude is neutral or ambivalent and that consistent atti- reduction to cognitive consistency also echoes the funda- tudes should be rare. However, this is clearly not the case; mental and widespread assumption in research on attitudes even though individuals are often exposed to ambiguous that individuals have an inherent preference for cognitive information, they often arrive at consistent representations of consistency (e.g., Festinger, 1957; Gawronski & Strack, 2012; Heider, 1946, 1958; Monroe & Read, 2008; Shultz & the information (e.g., Holyoak & Simon, 1999; Simon & Lepper, 1996). Spiller, 2016). So why are attitudes often consistent, whereas playing slot machines generally results in losing your money? The answer to this is that attitude elements are not inde- The Causal Attitude Network Model pendent of one another (to be explained next), and because of this dependency, attitudes can assume low-entropy macro- To formalize the ideas presented here, we build on the Causal states. However, for a system to remain in a low-entropy Attitude Network (CAN) model (Dalege et al., 2016), which state (i.e., low Gibbs entropy), force has to be put on this treats attitude elements as nodes in a network that are 178 J. DALEGE ET AL. connected by pairwise interactions. The complexity of the atti- weights can also vary, and the higher the magnitude, the tudinal representation is reflected by the size of the network stronger the interaction. The CAN model assumes that (i.e., number of nodes). The CAN model is based on psycho- weights between attitude elements generally arise based on inferences that support evaluative consistency. In the Ising metric network models (e.g., Cramer, Waldorp, van der Maas, model shown in Figure 2 all nodes are positively connected & Borsboom, 2010; van der Maas et al., 2006) and on con- straint-satisfaction models of attitudes (e.g., Kunda & Thagard, (indicated by green edges, see the online article for the color 1996; Monroe & Read, 2008; Shultz & Lepper, 1996). The cen- version of the figure). This Ising model thus represents a sim- tral assumption of the CAN model is that dynamics of atti- ple attitude network consisting of, for example, four positive tude networks can be described in an idealized way by the beliefs (e.g., believing that snakes maintain ecological order and are safe, beautiful, and smooth). Note that in the current Ising (1925) model, which originated from statistical mechan- article we focus on the situation in which edges between atti- ics. Although the Ising model is an extremely parsimonious tude elements are already present. How we can model the model, its behavior is exceptionally rich. Due to these qual- development of edges in attitude networks is currently inves- ities, the Ising model has been applied to many different fields tigated in our laboratory. The starting point for this investiga- of research, such as magnetization (e.g., Ising, 1925), kinetic tion is to combine the AE framework with connectionist energy (e.g., Fredrickson & Andersen, 1984), predator–prey models of attitudes, which assume that Hebbian learning dynamics (e.g., Kim, Liu, Um, & Lee, 2005), neuroscience underlies development of attitudinal structures (e.g., Monroe (e.g., Fraiman, Balenzuela, Foss, & Chialvo, 2009), clinical &Read, 2008). psychology (e.g., Cramer et al., 2016), and population dynam- Thresholds and weights determine a given configuration’s ics (e.g.,Galam,Gefen,& Shapir, 1982). energy (denoted by H). It is our view that, in contrast to the The Ising model describes the dynamics of networks by physical application of the Ising model, energy does not using the fact that systems strive toward low-energy configu- reflect an existing physical property. Calculation of energy is rations (see Figure 2 for an illustration of a simple Ising needed because it enables the mental system to arrive at a model). The energy of a configuration is determined by two low-entropy state by evaluating locally which elements need classes of parameters. The first class constitutes the thresh- to be changed. By evaluating several attitude elements in olds of the nodes, which determine the disposition of a turn, the mental system is able to create a global low-entropy given node to be “on” or “off” (denoted as s ). A node with state without evaluating the global state directly (which would a positive (negative) threshold requires less energy when it probably be too complex from a computational point of is “on” (“off”). In the original Ising model, thresholds repre- view). This leads to the following proposition: sent the external field that influences the spins of the mag- net. Similarly, in attitude networks, thresholds represent Proposition II: Energy of the attitudinal representation serves external information regarding the attitude object. These as a local processing possibility to evaluate the global Boltzmann entropy of an attitude. Attitude elements are likely to change thresholds therefore represent the disposition of a given atti- when the opposite state has lower energy. tude element to be endorsed or not. A positive threshold represents a disposition of a given node to be “on” (e.g., a The extent to which a configuration’s energy results in positive thresholds of judging snakes as dangerous indicates the configuration with lower energy being more likely than that one is inclined to judge snakes as dangerous holding all a configuration with higher energy depends on the depend- other information in the attitude network constant). A nega- ence parameter b (representing temperature in the original tive threshold represents a disposition of a given node to be Ising model). The higher the dependence parameter, the “off” (e.g., a negative threshold of judging snakes as beauti- more the probability of a configuration depends on its ful indicates that one is inclined to judge snakes as not energy. Because of this, the dependence parameter directly beautiful). The magnitude of thresholds can also vary and scales the Gibbs entropy of a given Ising model (e.g., the higher the magnitude, the stronger the disposition of the Kindermann & Snell, 1980), implying that increasing the node to be “on” or “off”. In the Ising model shown in dependence parameter results in attitude networks being Figure 2, two nodes have the disposition to be “on” (indi- more ordered and stable. For example, the Ising model with cated by green thresholds, see the online article for the color dependence at 0 at the top of Figure 2 has also maximum version of the figure) and two nodes have the disposition to Gibbs entropy, because all configurations are equally likely. be “off” (indicated by red thresholds, see the online article In contrast, the Ising model with high dependence at the for the color version of the figure). bottom of Figure 2 has lower Gibbs entropy, because the The second class of parameters constitutes weights of completely consistent configurations are much more likely edges between nodes, representing the strength of interaction than the inconsistent configurations. A system low in Gibbs between nodes (denoted as x ). Two nodes that have positive entropy thus creates the possibility of macrostates having weights between them require less (more) energy when they low Boltzmann entropy, but as long as the system is not at assume the same (different) state, representing preference for minimum Gibbs entropy, macrostates with high Boltzmann consistency. A positive weight represents an exhibitory inter- entropy are still possible. action (e.g., feeling afraid of snakes because you also judge The probability formula allows us to calculate the distri- them as dangerous), and a negative weight represents an bution of configurations we would expect if we measure an inhibitory interaction (e.g., not judging snakes as beautiful infinite number of individuals holding an attitude that can because you judge them as dangerous). The magnitude of be described by a given Ising model. For describing the ATTITUDINAL ENTROPY FRAMEWORK 179 Figure 2. Illustration of the Ising model. Note. In (3) HðxÞ represents the Hamiltonian energy of the configuration of k distinct nodes 1, … ,I,j, … .k, that engage in pairwise interactions and the variables x and x represent the states (1, þ1) of nodes i and j, respectively. The parameter s represents the threshold of node i and the parameter x represents the inter- i i action weight between nodes i and j. In (4) PrðX ¼ xÞ represents the probability of a given network configuration and b represents the dependence parameter of the Ising model. In (5) Z represents the standardization factor, which ensures that the probabilities add up to 1. The Distributions part of the figure shows the probability distributions of two Ising models for the sum scores of the nodes (upper distributions) and the individual configurations (lower distributions). The bottom of the figure shows all possible states of the four-node network, with green (red) nodes indicating that the node is “on” (“off”). dynamics of a given individual’s attitude, we can use time- increasing an attitude’s consistency can be described by such dependent dynamics called Glauber dynamics (Glauber, dynamics. For example, if one believes that snakes are safe 1963). The basic workings of Glauber dynamics on Ising while one also feels scared of them and always screams models are that at each iteration we (a) calculate the energy when one sees a snake, the probability that one changes his of the current configuration, (b) pick a random node and or her belief that snakes are safe is high. In the simulations calculate the energy of this neighboring configuration when we describe later, we make use of Glauber dynamics when this node is “flipped” (e.g., when this node changes from on we model individual-level dynamics. to off), (c) determine the probability of the node actually Figure 3 illustrates the reason why the dependence par- flipping by using the difference in energy, and (d) flip the ameter scales the Gibbs entropy of an Ising model. In the node with this probability (see Figure 3 for an illustration network with the dependence parameter at 0.5, the thresh- and formula). For attitude dynamics, this implies that olds and weights have little influence on the network’s 180 J. DALEGE ET AL. Figure 3. Glauber dynamics for two four-node networks under different dependence parameters. Note. In (6) and (7) x and x represent the current state of a given node and its opposite state, respectively. In (6) the probability of a node remaining in its current i j state relative to the probability that it will flip is represented. Each network represents one iteration and the node with a given probability represents a node that was randomly picked to be flipped with the given probability. Implication II: High Gibbs entropy in combination with a high dynamics and the network behaves essentially randomly. dependence parameter indirectly leads to psychological This situation therefore represents an attitude that is discomfort. The Gibbs entropy is indirectly evaluated by the unstable and in which the different attitude elements are temporal stability of the attitude. held with low certainty (e.g., the attitude of a person who does not care at all about snakes). With increases in the Levels of Attitudinal Entropy Reduction dependence parameter, the probability of the network con- figuration becomes increasingly dependent on the thresholds In this section, we discuss different levels of attitudinal and the weights of the network. In the network with the entropy reduction and research supporting these levels. Note dependence parameter at 3, the thresholds and weights have that these levels do not represent distinctive categories but strong influence on the network’s dynamics and the network are assumed to lie on a dimension from weak entropy behaves in accordance with these parameters. This situation reduction to high entropy reduction (just as the dependence therefore represents an attitude that is stable and in which parameter in the Ising model is also a continuous variable). the different attitude elements are held with high certainty It is our view that thinking about an attitude object—or, (e.g., the attitude of a snake phobic or enthusiast). This more generally, paying attention to an attitude object—has underscores the necessity of attitude elements being depend- the default effect of slightly increasing the dependency of ent on one another to reduce attitudinal entropy. In this art- the attitude network; as such, simply focusing attention icle, we argue that the dependence parameter in the Ising on the attitude object represents the most basic level of model constitutes a formalized representation of the effect dependency of the attitude network. Such a situation, for of directing attention and thinking about attitude objects, example, arises when an individual observes an attitude leading to the third proposition of the AE framework: object. The dependence parameter increases when the individual is prompted to think about the attitude object, Proposition III: Focusing attention on the attitude object and which would, for example, be the case when the individual thinking about the attitude object reduces the Gibbs entropy of attitudes by increasing the attitude network’s dependence responds to a questionnaire about an attitude object. parameter. The higher the dependence parameter, the stronger Increased levels of attitudinal entropy reduction may arise the correspondence between energy and probability of a given when individuals are for some reason prompted to think attitude network configuration. more elaborately about an attitude object and dependency of the attitude network is further increased when motivational Based on our argument that individuals are motivated to factors come into play, representing intermediate levels of reduce attitudinal entropy, we expect that a high level of attitudinal entropy reduction. Examples of factors moder- attitudinal entropy causes psychological discomfort. ately increasing motivation to reduce attitudinal entropy are However, because we assume that entropy of attitude net- situations in which individuals are committed to an evalu- works cannot be directly evaluated, this influence is indirect. ation or in which they have to make a relatively unimport- We expect that both measures of attitudinal entropy trans- ant decision. late into psychological discomfort through proxies, which Even more enhanced levels of attitudinal entropy reduc- are easier to evaluate for the mental system. This leads to tion arise when individuals attach personal importance to the following implications: their attitudes. Attitude importance is a widely researched Implication I: High Boltzmann entropy in combination with a topic and is a key determinant of attitude strength (Howe & high dependence parameter indirectly leads to psychological Krosnick, 2017). Factors increasing attitude importance are discomfort. The Boltzmann entropy is indirectly evaluated by the attitude’s relevance to self-interests (e.g., attitude’s rele- the difference in energy of the current and neighboring vance to important decisions), to personal values, and to configurations (i.e., configurations for which only one attitude element has to be flipped). social identification (Boninger, Krosnick, & Berent, 1995). ATTITUDINAL ENTROPY FRAMEWORK 181 Crucially, attitude importance is strongly related to how straightforwardly solved by assuming that implicit measures much attention individuals devote to an attitude object are more likely to tap attitudes in high-entropy (insta- ble) states. (Krosnick, Boninger, Chuang, Berent, & Carnot, 1993), mak- ing it likely that, indeed, attitudes high in personal import- ance represent attitude networks with the highest Simulation 1a: Implicit measures – low temporal stability, dependence and therefore also the lowest entropy attitudes. stable means. For this simulation, we investigated Glauber Furthermore, as we discuss in a later section, strong atti- dynamics on a fully connected 10-node network with all tudes show exactly the dynamics that would be expected edges set to .1. We varied the thresholds uniformly from from high dependence attitude networks. .2 to .7 with steps of .1, resulting in 10 different sets of To summarize, lower levels of attitudinal entropy reduc- thresholds. (We chose these thresholds so that the means tion arise when individuals pay some attention to the attitude differ from 0 and that there is sufficient variance for correla- object or briefly think about it. Intermediate levels represent tions to be meaningful.) The dependence parameter was set situations in which an individual is for some reason to .5 (representing that only some attention is directed at prompted to think about the attitude object in more detail the attitude object) and the network was randomly initial- (e.g., when an argument regarding the attitude object has to ized. We simulated 100 individuals for each set of thresh- be evaluated) and when individuals have to base a decision olds, resulting in the total number of 1,000 individuals. For on their attitude network or are committed to an evaluation. each individual we simulated 1,000 iterations. After 500 and The final levels of attitudinal entropy reduction arise when 1,000 iterations, respectively, we measured the sum score of an individual attaches high personal importance to an atti- the nodes. The resulting scores at the first measurement and tude object. In the remainder of this section, we show that at the second measurement were only weakly correlated several central findings in the attitude literature follow from (r ¼ .24, p < .001). The means of the first measurement the entropy reducing function of attention and thought. (M ¼ 1.91) and the second measurement (M ¼ 2.04), in con- trast, were virtually identical, t(999) ¼ 0.71, p ¼ .479, although the standard deviation at both the first measure- Implicit Measures Are More Likely to Tap Attitudes in ment (r ¼ 4.55) and the second measurement (r ¼ 4.45) High-Entropy States were substantial. Networks under a low dependence param- eter thus show low individual temporal stability but stable The dependence parameter of attitude networks increases means, which precisely matches the known behavior of when attention is directed at the attitude object, which implicit attitude measures. implies that the measurement of attitudes influences the dependence parameter. Implicit measures of attitudes, such Simulation 1b: Implicit measures – low behavior predic- as the Implicit Association Test (IAT; Greenwald, McGhee, tion on individual level, high behavior prediction on & Schwartz, 1998) and the Affective Misattribution Task group level. For this simulation, we used mostly the same (Payne, Cheng, Govorun, & Stewart, 2005), limit attention setup as in Simulation 1a, with the following adjustments. directed at the attitude object by measuring attitudes with- First, we added an 11th node that represented behavior. out directly asking individuals to introspect. These measures This node was also connected with weights of .1 to all other are therefore more likely to tap attitudes in high-entropy nodes but always had a threshold of 0 (so that all systematic states than explicit measures. Attitudes in high-entropy variation in this node is caused by its connection to other states are less internally consistent than attitudes in low- nodes). Second, we ran a total number of 10,000 individuals entropy states, which might contribute to the fact that impli- to be able to create groups of sufficiently large size. Third, cit measures generally show both poor internal reliability we created 10 groups that differed in their mean thresholds and test–retest reliability (e.g., Bar-Anan & Nosek, 2014; (see Table A1 in the appendix). The correlation between the Gawronski, Morrison, Phills, & Galdi, 2017; Hofmann, first 10 nodes and the “behavior” node on an individual Gawronski, Gschwendner, Le, & Schmitt, 2005). In contrast level was relatively weak (r ¼ .23, p < .001). In contrast, the to the low individual temporal stability of scores on implicit correlation on the group level was very strong (r ¼ .80, measures of attitudes, mean effects on implicit measures are p ¼ .006). These patterns fit the finding that individual-level substantially more robust (Payne, Vuletich, & Lundberg, correlations between implicit measures of attitudes and 2017). For example, children show similar scores on the IAT behavior are relatively low and that group level correlations as adults (Baron & Banaji, 2006), and the IAT predicts are considerably stronger. behavior much better on a global level (e.g., police shootings The implication of the AE framework that implicit meas- of Blacks is strongly associated with prejudice assessed with ures are more likely to tap attitudes in high-entropy states the IAT on a regional level; Hehman, Flake, and Calanchini, than explicit measures has fundamental implications for the 2018) than on an individual level, which is generally rather research on implicit measures of attitudes. Although research- low (e.g., Oswald, Mitchell, Blanton, Jaccard, & Tetlock, ers in this domain have long acknowledged that implicit 2013). A recent review identified these patterns as important measures show low internal consistency, they have generally puzzles in the literature on implicit measures of attitudes interpreted this as a measurement problem (e.g., Fazio & (Payne, Vuletich, & Lundberg, 2017). With the following Olson, 2003b; Gawronski, LeBel, & Peters, 2007; LeBel & simulations we show that these puzzles can be Paunonen, 2011; Nosek & Banaji, 2001). However, the AE 182 J. DALEGE ET AL. framework implies that the construct measured by implicit can be seen in Figure 4b, increasing the dependence param- measures is itself more internally inconsistent than the con- eter for such a small-size network does not lead to a sub- struct measured by explicit measures because the former by stantial increase in extreme sum scores, mimicking the their very nature direct less attention toward the attitude finding that complex cognitive schemas are necessary for the object than the latter. One consequence of this is that often mere thought effect to manifest itself. the only way to make implicit measures more reliable is to make them more explicit, leading to the counterintuitive con- Simulation 2c: Magnitude of edge weights as a formaliza- clusion that a valid measurement of attitudes (or any system tion of dependence between evaluative dimensions. Edge for that matter) in high-entropy states must be unreliable. weights in Ising networks are a straightforward formaliza- tion of interdependence between evaluative dimensions. To Prediction 1a. Manipulating the dependency in attitude investigate whether decreasing edge weights leads to lower networks (e.g., letting individuals think for some time about the increase in extreme scores, we adapted Simulation 2a by set- attitude object) is expected to increase internal consistency and stability of implicit measures. ting all edge weights to .05. As can be seen in Figure 4c, increasing the dependence parameter for such a weakly con- Prediction 1b. Scores on implicit measures assessing attitudes individuals regularly think about are expected to have higher nected network does not lead to a substantial increase in internal consistency and stability than scores on implicit extreme sum scores, mimicking the finding that inter- measures assessing attitudes individuals think only dependence of complex schemas is necessary for the mere infrequently about. thought effect to manifest itself. Prediction 1c: Implicit and explicit measures should show the Further support for the proposition that merely thinking lowest convergence when the dependence of the attitude about an attitude object represents an intermediate level of network is generally low. attitudinal entropy reduction comes from research on the coherence effect in judgment and decision making (e.g., Holyoak & Simon, 1999; Simon, Krawczyk, & Holyoak, The Mere Thought Effect as an Initial Level of 2004; Simon, Pham, Le, & Holyoak, 2001; Simon, Snow, & Heightened Attitudinal Entropy Reduction Read, 2004; Simon, Stenstrom, & Read, 2015). The coher- The mere thought effect on attitude polarization refers to the ence effect represents the general finding that when individ- classic finding that briefly thinking about an attitude object uals are presented with ambiguous information about a without receiving external information results in more given scenario (e.g., a legal case), individuals interpret this extreme evaluation of the attitude object (e.g., Tesser, 1978; information in such a way that it allows for a coherent judg- Tesser & Conlee, 1975). Based on several studies on the mere ment or decision about the scenario. Of interest, such coher- thought effect, Tesser, Martin, and Mendola (1995) argued ence shifts are also observed for dependency between that (a) sufficiently complex cognitive schemas (defined as emotions and beliefs regarding an attitude object (Simon the number of dimensions an attitude object is rated on) are et al., 2015) and in the complete absence of making a deci- necessary (Tesser & Leone, 1977) and (b) the evaluative sion (Simon et al., 2001). However, there are some indica- dimensions, on which the cognitive schema is based, need to tions that having to make a decision heightens the be sufficiently interdependent for the mere thought effect to coherence shift effect (Simon et al., 2001, 2004). manifest itself (Millar & Tesser, 1986). In the following simu- Prediction 2: Sizes of edge weights and size of attitude network lations, we show that the mere thought effect and its modera- predict the strength of the mere thought effect. tors naturally follow from the AE framework. Prediction 3: Because the AE framework assumes that increasing dependency of attitude networks is a continuous process, the AE framework predicts that an opposite mere Simulation 2a: Basic mere thought effect. We calculated thought effect also exists, in the sense that when individuals are the probabilities of the sum scores of a fully connected 10- asked to very quickly answer attitude questions, attitudes are node network with the dependence parameter set to either 1 expected to be less polarized than when individuals are given (representing merely asking individuals about their attitudes) more time to answer the questions. Note that the AE framework or 1.5 (representing mere thought). All edge weights were predicts that this would constitute a small effect. set to .1 and all thresholds were set to 0. As can be seen in Figure 4a, increasing the dependence parameter leads to an Attitude Strength increase in extreme sum scores, mimicking the basic mere thought effect. The highest levels of attitudinal entropy reduction have implications for attitude strength. The macrobehavior of Simulation 2b: Network size as formalization of a complex Ising networks is governed by the dependence of the net- cognitive schema. As stated in the section on the CAN work and can be described by the cusp catastrophe model model, the size of networks reflects the complexity of the (Sitnov, Sharma, Papadopoulos, & Vassiliadis, 2001). The cognitive schema of the attitude object. We therefore expect cusp catastrophe model describes sudden versus smooth that a network with few nodes will not show a strong changes in a variable depending on two control variables, increase in extreme sum scores when the dependence par- referred to as the normal variable and splitting variable, ameter is increased. To investigate this, we adapted respectively (Gilmore, 1981; Thom, 1972; Zeeman, 1976). Simulation 2a by decreasing the number of nodes to 4. As Depending on the value of the splitting factor, the influence ATTITUDINAL ENTROPY FRAMEWORK 183 Figure 4. The mere thought effect on polarization modeled by the Attitudinal Entropy framework. Note. Implied distributions of sum scores are shown under different independence parameters for (a) a 10-node network with all edge weights equal to .1, (b) a four-node network with all edge weights equal to .1, and (c) a 10-node network with edge weights equal to .05. of the normal variable on the dependent variable is either gradual or discrete, implying that the so-called bifurcation area, in which sudden transitions happen in the dependent variable, is larger when the splitting factor is high (see Figure 5). As an illustration, take the freezing of water. In this case, temperature represents the normal variable and pressure represents the splitting variable: Under low pres- sure, water freezes and melts at the same temperature, whereas under high pressure, frozen water melts at a higher temperature than when liquid water freezes (and the other way around). In Ising networks the average of the thresholds functions as normal control variable, the dependence of the network as splitting variable, and the macrobehavior of the network as dependent variable (Sitnov et al., 2001). Because of this, networks high in dependency are stable and Figure 5. The cusp catastrophe model from the perspective of the Attitudinal ordered and change happens suddenly, whereas networks Entropy framework. low in dependency are fluctuating and random and change happens gradually. These observations link the AE frame- 1976). In the catastrophe model of attitudes, valenced infor- work to the catastrophe model of attitudes, which assumes mation functions as the normal variable, attitude involve- that attitude change can be described by the cusp catastro- ment or attitude importance functions as the splitting phe model (Flay, 1978; Latane & Nowak, 1994; Zeeman, variable, and the global evaluation functions as the 184 J. DALEGE ET AL. Prediction 4: The mere thought effect extends to the stability dependent variable (see Figure 5). Several studies support and resistance of attitudes. Thinking briefly about attitude the catastrophe model of attitudes by showing that import- objects is predicted to (temporally) increase the stability and ant attitudes are more extreme than unimportant attitudes resistance of attitudes. (e.g., Latane & Nowak, 1994; Liu & Latane, 1998) and by Prediction 5: Persuasion is more effective for strong attitudes directly fitting the catastrophe model to data on attitudes when the dependence parameter is lowered (e.g., by reducing (van der Maas, Kolstein, & van der Pligt, 2003). The CAN attention directed at the attitude object) before the persuasion is model can easily integrate the catastrophe model of attitudes employed, because lowering the dependence parameter reduces and also provides a micro-level explanation of the postulates the hysteresis effect. of the catastrophe model (Dalege et al., 2016). Thresholds in Prediction 6: Whether an attitude changes continuously or the CAN model directly relate to the valenced information a discretely depends on the dependence parameter of the person receives regarding an attitude object and the macro- attitude network. behavior of an attitude is strongly related to global evalua- Prediction 7: Reducing the dependence parameter of networks tions of the attitude object. These similarities lead to the (e.g., by limiting cognitive capacity) results in less stable and conclusion that important attitudes are based on attitude less resistant attitudes. networks high in dependence. Linking attitude importance to the dependence of attitude Heuristic-Based versus Argument-Based Persuasion as networks also has broader implications for attitude strength. Global versus Specific Threshold Changes As attitude importance is a central determinant of attitude strength (Howe & Krosnick, 2017), it becomes likely that The elaboration likelihood model (Petty & Cacioppo, 1986) strong attitudes represent high-dependence attitude networks. and the Heuristic Systematic Model (Chaiken, Liberman, & Indeed, the dynamics of strong attitudes are highly similar to Eagly, 1989) are two hallmark dual process theories assum- the dynamics of strongly connected networks (Dalege et al., ing that persuasion can be accomplished via two routes— 2016), which in turn are similar to the behavior of low- one in which individuals change their attitudes based on dependence networks. Similar to strong attitudes (Krosnick heuristic cues (e.g., whether the source of the message is an & Petty, 1995), high-dependence networks are more stable expert) and one in which individuals change their attitudes and resistant (Kindermann & Snell, 1980). Increasing the based on a deeper processing of the quality of the persuasive dependence of attitude networks likely results in information arguments. Several studies have supported this idea and being processed in accordance with the attitude, which repre- showed that individuals low in involvement are more likely sents another central feature of attitude strength. to change their attitudes according to heuristic cues, whereas Biased information processing is related to the phenom- individuals high in involvement are more likely to change enon of hysteresis in the cusp catastrophe model. Hysteresis their attitudes according to argument quality (e.g., Petty & implies that the point at which a system moves to the Cacioppo, 1984; Petty, Cacioppo, & Goldman, 1981; Petty, opposite state depends on the direction of change (just as is Cacioppo, & Schumann, 1983). From the perspective of the the case for the melting and freezing of water under high AE framework, heuristic-based persuasion represents a mod- pressure). The strength of the hysteresis effect in the cusp erate global change in the attitude network’s thresholds (i.e., catastrophe model depends on the splitting variable—imply- change in the magnetic field in the language of the original ing that attitude networks under high dependence should Ising model), whereas argument-based persuasion represents show strong hysteresis effects (i.e., the bifurcation area a strong change of few specific thresholds, implying that becomes broader). Changing such an attitude thus requires moderate global change is more influential under low a disproportionate amount of persuasion compared to the dependence and strong specific change is more influential amount of information the individual already received. In under high dependence. We tested this hypothesis in the fol- such a situation it would probably be more effective to first lowing simulation. reduce the dependence parameter of the attitude network so that the individual is more “open” to change. Attitude-behavior consistency, which represents the final Simulation 3: Global versus specific threshold changes. For this simulation, we again used a fully connected 10- central feature of attitude strength, is also more likely in node network with all edge weights set to .1. We investi- high dependence attitude networks, because attitude ele- gated Glauber dynamics of this network using 1,000 itera- ments are more dependent on one another. As the CAN model treats behavior as part of the attitude network, tions. In the first 500 iterations, all simulated individuals’ increasing dependence of attitude networks also increases thresholds were set to .2 (thus representing a positive initial the dependence of behavior on beliefs and feelings regarding attitude) and the network was randomly initialized. In the second 500 iterations, (a) thresholds remained at .2 (repre- the attitude object, and vice versa, implying higher attitude- behavior consistency (Dalege, Borsboom, van Harreveld, senting the no heuristic cue/weak arguments condition), (b) Waldorp, & van der Maas, 2017). This hypothesis is sup- all thresholds changed to .12 (representing the heuristic ported by findings indicating that attitude-behavior consist- cue/weak arguments condition), (c) the first four thresholds ency depends on the stability of attitudes (Glasman & changed to .6 and the other thresholds remained at .2 Albarrac ın, 2006), which represents a proxy of the depend- (representing the no heuristic cue/strong arguments condi- ence of the attitude network. tion), or (d) the first four thresholds changed to .72 and ATTITUDINAL ENTROPY FRAMEWORK 185 (a) (b) Global threshold change Specific threshold change Global change Specific change no no yes yes 13 13 β β Figure 6. Effects of global (a) and specific threshold change (b) under moderate and high b. Note. Error bars represent ±2 SDs around the mean. the other thresholds changed to .12 (representing the Aversiveness of Attitudinal Entropy: Ambivalence heuristic cue/strong arguments condition). The thresholds and Cognitive Dissonance from the Perspective of were chosen this way so that the mean change in the heuris- the AE Framework tic cue/weak arguments condition and the no heuristic cue/ The first proposition of the AE framework holds that incon- strong arguments condition was equal. Half of the simulated sistency of an attitude is attitudinal entropy. Research on individuals’ bs was set to 1 (representing low involvement) ambivalence and cognitive dissonance underscores that con- and the other half of the simulated individuals’ bs was set to sistency is a fundamental human need and that violations of 3 (representing high involvement). We simulated 100 indi- this need cause psychological discomfort. Cognitive disson- viduals for each experimental cell, resulting in 600 simulated ance refers to aversive feelings caused by incongruent beliefs individuals in total. The results showed a pattern reminis- and behaviors vis-a-vis an attitude object, with most cent of the typical findings in the heuristic-based versus research on cognitive dissonance focusing on the effects of argument-based persuasion literature (e.g., Petty et al., carrying out a behavior inconsistent with the beliefs an indi- 1981). The three-way interaction on the sum score of the vidual holds. A crucial distinction in the research on attitude elements at the 1,000th iteration was significant, ambivalence is that between potential (or objective) and felt F(1, 792) ¼ 16.40, p ¼ .001, g ¼ .02, and the pattern of the (or subjective) ambivalence (e.g., Newby-Clark, McGregor, results was in line with the hypotheses (see Figure 6). & Zanna, 2002; Priester & Petty, 1996; van Harreveld, van Conceptualizing heuristic cues as global moderate threshold der Pligt, & de Liver, 2009). Potential ambivalence refers to change and strong arguments as specific strong thresholds the number of incongruent attitude elements, and felt change thus explains the basic result in the heuristic versus ambivalence refers to the aversive feelings caused by these argument-based persuasion literature. incongruent attitude elements. Crucially, the distinction Prediction 8a: Sufficiently strong heuristic cues lead to attitude between potential and felt ambivalence is made, because change under both low and high involvement. potential ambivalence can, but not necessarily does, result in Prediction 8b: A large number of strong arguments lead to felt ambivalence. In other words: Ambivalence can, but does attitude change under both low and high involvement. not have to be, unpleasant. From the perspective of the AE framework, the question when potential ambivalence results Prediction 9: As can be seen in Figure 6b, specific threshold change also affected networks with low b to a meaningful in felt ambivalence becomes the question when attitudinal extent. This leads to the prediction that, given sufficient power entropy results in psychological discomfort. In this section (e.g., in a meta-analysis), an effect of strong arguments should we discuss two possibilities of how the mental system indir- also be detected under low involvement. ectly evaluates attitudinal entropy and under which circum- stances this results in psychological discomfort. This We want to emphasize that although in all the other simulations presented discussion is based on Implications I and II of the AE here the findings are highly robust to changes in parameters, for the current framework. Implication I holds that Boltzmann entropy is simulation specific parameters had to be chosen to find the reported pattern of the results (e.g., when global threshold changes are chosen that are too indirectly evaluated through the energies of neighboring high or when too many specific thresholds are targeted, differences between the b conditions become less meaningful). The AE framework therefore predicts that the effect of argument versus persuasion-based persuasion is We use the terms potential and felt ambivalence throughout the article limited to a specific range of stimuli (i.e., not too strong heuristic cues or not because these terms fit our framework better than the recently more too many strong arguments). commonly used terms objective (or structural) and subjective ambivalence. Sum score −10 −5 0 5 10 Sum score −10 −5 05 10 186 J. DALEGE ET AL. configurations. In the following subsection we show that scores for each of the possible configurations and varied the this implication integrates the gradual threshold (GT) model power function parameter between .3, .5, and .7. of ambivalence (Priester & Petty, 1996) into the AE frame- Using Equation 6, we then calculated the mean prefer- work. Second, Implication II holds that Gibbs entropy is ence of each node to remain in its current state for each indirectly evaluated by the temporal stability of the attitude configuration. We then averaged these scores for each con- network’s configuration. figuration with the same number of conflicting attitude ele- ments (e.g., for each configurations in which all but one Boltzmann Entropy as Ambivalence attitude elements are in the positive state). We calculated the distribution of preference scores with the dependence An influential account of how potential ambivalence trans- parameter set to 1, 1.5, and 2.5. As can be seen in Figure 7, lates into felt ambivalence is the GT model (Priester & varying the dependence parameter has an analogous effect Petty, 1996). This model assumes a curvilinear relation as varying the power function of the GT model. Based on between the number of conflicting evaluations (treated here this finding, the AE framework implies that the dependence as attitude elements) and felt ambivalence, in which felt parameter determines to what degree potential ambivalence ambivalence increases less as the number of conflicting atti- translates into felt ambivalence. tude elements increases (e.g., the difference between holding Based on the finding that preferences of nodes to remain no conflicting attitude element and holding one conflicting in their current states are faster decelerating under a high attitude element is larger than the difference between hold- dependence parameter, we expect that factors increasing the ing three conflicting attitude elements and holding four con- dependence parameter also increase felt ambivalence. This flicting attitude elements). The specific formula of the GT hypothesis is indirectly supported by the finding that having model is the following: to make a decision increases felt ambivalence (e.g., Armitage p 1=C Ambivalence ¼ 5ðÞ C þ 1 ðÞ D þ 1 ; (8) & Arden, 2007; van Harreveld, Rutjens, Rotteveel, Nordgren, & van der Pligt, 2009; van Harreveld, van der Pligt, et al., where C refers to conflicting attitude elements (i.e., attitude 2009). The AE framework holds that basing a decision on elements that are incongruent to the majority of attitude ele- an attitude increases the dependence parameter of the atti- ments) and D refers to the number of dominant attitude ele- tude network, which results in lower (relative) preference of ments (i.e., attitude element that is consistent with the nodes to remain in their current state if the current config- majority of attitude elements). The p determines the power uration is ambivalent. function and was estimated by Priester and Petty (1996)to lie somewhere between .4 and .5. Although Priester and Prediction 10: Dependence of attitude networks moderates the relation between potential and felt ambivalence. The higher the Petty explicitly stated that these specific values are exogen- dependence, the stronger the impact of the first incongruent ous to the GT model, most research based on the GT model attitude elements. uses a value between .4 and .5 to calculate expected felt ambivalence scores (e.g., Clark, Wegener, & Fabrigar, 2008; Prediction 11: The AE framework assumes that dependence is increased when a decision has to be made. After the decision is Refling, Calnan, Fabrigar, MacDonald, Johnson, & Smith, made, dependence drops again. This implies that before a 2013). Clearly, a better understanding of the power function decision is contemplated and after a decision, correspondence would provide us with more knowledge on when and why between potential and felt ambivalence is expected to be lower potential ambivalence results in felt ambivalence (high p val- than while contemplating the decision. The same holds for the ues would indicate an almost linear relation, whereas low p stability and resistance of the attitude. values would indicate a steep relation). From the perspective of the AE framework, the number of conflicting attitude ele- Gibbs Entropy as Ambivalence ments is given by the configuration of the attitude network. We therefore expect that felt ambivalence as modeled by the In our view, it is likely that felt ambivalence, if caused by GT model indirectly reflects Boltzmann entropy of the con- low preference of nodes to remain in their current state, figuration of the attitude network. As stated in Implication I generally represents a situation-dependent process (e.g., hav- of the AE framework, Boltzmann entropy is indirectly eval- ing to make a decision based on an ambivalent attitude). In uated by the energy difference between the current configur- contrast, felt ambivalence caused by Gibbs entropy reflects a ation and its neighboring configurations and that the more chronic state of felt ambivalence. Implication II of the psychological discomfort caused by the energy difference is AE framework holds that the Gibbs entropy of an attitude amplified by the dependence parameter. Based on this rea- network is indirectly evaluated by the stability of the atti- soning, we expect the dependence parameter to determine tude. Based on this implication, we expect that unstable atti- the steepness of the relation between potential and felt tude networks in combination with a high dependence ambivalence. parameter cause strong feelings of ambivalence. To investi- gate under which circumstances low stability and a high Simulation 4: Felt ambivalence as Boltzmann entropy. For this simulation we again used a fully connected 10-node net- Note that with an increasing dependence parameter, the preference scores of work with all edge weights set to .1 and all thresholds set to almost all configurations increase. It therefore seems likely that the preference 0. We first calculated the GT model’s implied ambivalence scores are evaluated relative to the dependence parameter. ATTITUDINAL ENTROPY FRAMEWORK 187 Figure 7. Similarity of ambivalence calculated by the gradual threshold (GT) model and mean preference scores of nodes in Ising networks. dependence parameter can co-occur, we set up the follow- which an individual receives weak mixed information about ing simulation. an attitude object), (c) half of the thresholds were set to .5 and the other half were set to .5 (representing a situation Simulation 5: Felt ambivalence as Gibbs entropy. For this in which an individual receives strong mixed information simulation we again used a fully connected 10-node network about an attitude object), (d) all thresholds were set to .1 with all edge weights set to .1. We varied the thresholds in (representing a situation in which the external information the following way: (a) all thresholds were set to 0 (represent- points in a weak positive direction), and (e) all thresholds ing a situation in which the external information points in were set to .5 (representing a situation in which the external no direction), (b) half of the thresholds were set to .1 and information points in a strong positive direction). In add- the other half were set to .1 (representing a situation in ition, we varied the dependence parameter between 1, 1.5, 188 J. DALEGE ET AL. and 2.5 (mirroring Simulation 4). For each combination of relevant to research on cognitive dissonance. Similarities thresholds and dependence parameter, we simulated 100 between cognitive dissonance and felt ambivalence have individuals, resulting in the total number of 1,500 simulated been noted by several researchers (e.g., Jonas, Broemer, & individuals. For each individual, we simulated 500 iterations Diehl, 2000; McGregor, Newby-Clark, & Zanna, 1999); both based on Glauber dynamics (the network was again initial- concepts describe aversive feelings caused by being aware of ized randomly). To evaluate the stability of the attitude net- incongruence of one’s beliefs regarding an attitude object. work, we calculated the percentage of flipped states for the The main difference between these two concepts concerns last 100 iterations. the situations by which they are caused (van Harreveld, van The results indicated that for b ¼ 1, only the highly posi- der Pligt, et al., 2009). Whereas felt ambivalence arises in tive thresholds resulted in a relatively stable attitude network situations in which attention is directed at an ambivalent (see Figure 8). For b ¼ 1.5, attitude networks were more sta- attitude, cognitive dissonance arises in situation in which a ble overall, with the strong positive thresholds resulting in univalent attitude is disturbed (e.g., by inducing behavior almost perfect stability. The highly mixed thresholds net- incongruent with an individual’s attitude; Festinger and works remained relatively unstable. For b ¼ 2.5, only highly Carlsmith, 1959). However, the consequences of felt ambiva- mixed thresholds networks did not approach perfect stability. lence and cognitive dissonance are similar. This point is It is our view that such a situation results in the strongest illustrated by the similarities of two experiments focused on feelings of ambivalence, because stability remains rather low the role of arousal in dissonance reduction (Zanna & while the dependence parameter is already at a high value. Cooper, 1974) and on biased information processing serving Based on the results of the simulation, we conclude that ambivalence reduction (Study 1; Nordgren, van Harreveld, high felt ambivalence arises when individuals receive highly & van der Pligt, 2006), respectively. In both experiments, mixed information. Felt ambivalence is then amplified by participants were first administered a sugar pill but were the motivation to reduce attitudinal entropy. Such a situ- told that the pill would make them feel either aroused or ation would arise when individuals hold important attitudes relaxed. The results in both experiments were similar: When for which they receive mixed information, for instance, participants were told that the pill would be relaxing, they when individuals are disposed to a given evaluation (e.g., showed dissonance reduction and biased information proc- holding liberal values because you work at a liberal univer- essing. In contrast, when they were told that the pill was sity), whereas significant others endorse a different evalu- arousing, participants showed neither dissonance reduction ation (e.g., having parents who hold conservative values). nor biased information processing. Both Zanna and Cooper Such a situation has been shown to cause strong feelings of (1974) and Nordgren et al. (2006) argued that the reason for ambivalence (Priester & Petty, 2001). Further support for this pattern of results is that participants attributed their the relation between stability of an attitude and feelings on negative feelings caused by cognitive dissonance or ambiva- ambivalence comes from the finding that ambivalent indi- lence to the effects of the pill. We take the results of these viduals show physical signs of instability (i.e., moving from experiments as indication that negative feelings caused by one side to the other; Schneider et al., 2013). cognitive dissonance and ambivalence in fact result from Prediction 12: Highly mixed information and high attitude attitudinal entropy; the difference is that in cognitive disson- importance result in strong felt ambivalence. ance paradigms entropy is induced and in ambivalence para- digms attention to high entropy attitudes is induced. Cognitive Dissonance and Ambivalence Reflect Prediction 13: Given that the AE framework assumes that felt Attitudinal Entropy ambivalence and cognitive dissonance are caused by aversive configurations of the attitude network in combination with high Apart from research on ambivalence, the implication that dependence, felt ambivalence and cognitive dissonance are attitudinal entropy causes psychological discomfort is also predicted to have similar consequences. Figure 8. Stability of attitude networks based on different thresholds and dependence parameters. ATTITUDINAL ENTROPY FRAMEWORK 189 Future Study of the AE Framework The AE Framework’s Relation to Other Models of Attitude In the remainder of this article, we address some important opportunities for future study of the AE framework. Apart Although it is beyond the scope of our article to discuss the AE framework’s relation to all prominent models of attitude, from the empirical predictions that follow from the AE we discuss the framework’s relation to three models that are framework, we highlight the possibility of finding neural in our view especially relevant: the Iterative Reprocessing substrates of the AE framework’s propositions and possibil- (IR) model (Cunningham & Zelazo, 2007), the Attitude as ities for further theoretical integration, and we discuss open Constraint Satisfaction (ACS) model (Monroe & Read, questions raised by the AE framework. 2008) as an exemplar of constraint-satisfaction based con- nectionist models, and the Associative Propositional Possible Neural Substrates of the AE Framework Evaluation (APE) model (Gawronski & Bodenhausen, 2006). These models are especially relevant, because they are simi- Affective neuroscience has identified several neural sub- lar in focus as the AE framework. The basic assumption of strates of attitude dynamics. Much of this research has the APE model is that evaluations tapped by implicit meas- focused on finding neural substrates of the reaction to ures result from associative processes, whereas evaluations valenced stimuli. This research has identified that the amyg- tapped by explicit measures result from propositional proc- dala plays a central role in processing valenced stimuli (e.g., esses. The APE model further assumes that cognitive con- Morris et al., 1996; Phelps, 2006; Zald, 2003). Important to sistency is relevant only to propositional processes. note, the amygdala seems to integrate information from Similarly, the AE framework holds that attitudinal entropy throughout the brain (Cunningham & Zelazo, 2007), which reduction, which is mostly pronounced during explicit proc- makes it likely that global evaluations are formed in this essing of the attitude object, results in heightened cognitive neural structure. Another neural structure that plays a cen- consistency. However, the models diverge in the assumption tral role in attitude dynamics seems to be the anterior cin- that heightened cognitive consistency during explicit proc- gulate cortex (ACC). The ACC plays an important role in essing of the attitude object results from a process that is the detection of potential conflict (Carter et al., 1998), and it qualitatively different from implicit processing of the atti- was shown that the ACC is active during the experience of tude. In this sense, the AE framework is more in line with cognitive dissonance (van Veen, Krug, Schooler, & Carter, the IR model and the ACS model, which both assume that 2009) and when ambivalent stimuli are processed implicit and explicit evaluations are based on the (Cunningham, Raye, & Johnson, 2004). This makes the same processes. ACC a likely candidate for the neural structure involved in As we mention in the introduction of the AE framework, translating entropy of attitudes under high dependence into the process by which complex attitudinal representations are aversive feelings (note that also other neural substrates are reduced to a single global evaluation is partly based on the likely to be involved in the processing of ambivalent stimuli, IR model, which assumes that global evaluations are the such as the insula, the temporal parietal junction, and the result of iterative reprocessing of the attitude object, serving posterior cingulate cortex; see Nohlen, van Harreveld, the reduction of entropy (Cunningham, Dunfield, & Rotteveel, Lelieveld, & Crone, 2014). Stillman, 2013). The AE framework has several similarities Because the AE framework proposes that directing atten- to the ACS model, as both models assume that the main tion to and thinking about attitude objects serves the func- driving factor in attitude dynamics is the drive for cognitive tion of reducing attitudinal entropy, research on the neural consistency. The ACS model and the AE framework also substrates of consciousness is relevant to the AE framework. share a more technical similarity, because the ACS model is A recent influential theory of the neural underpinnings of based on Hopfield (1982, 1984) neural networks, which in consciousness posits that conscious experience results from turn are based on Ising models. In our view, the ACS model neurons engaging in recurrent processing of stimuli, which and the AE framework are therefore likely to complement enables information exchange between several low-level and each other and have different weaknesses and strengths. A high-level areas of the brain (Block, 2005, 2007; Lamme, strong feature of the ACS model is that it provides a formal- 2003, 2006). It thus seems likely that conscious processing ized account of evaluative learning, whereas the AE frame- of attitude objects results from integrating different kinds of work is more parsimonious than the ACS model, which in information regarding the attitude object. This idea is also our view has two advantages: First, parsimony aids the in line with the information integration theory of conscious- objective of “understanding by building,” in the sense that ness (Tononi, 2004; Tononi & Edelman, 1998), which holds the more parsimonious the model, the more likely it is that that the level of a system’s consciousness depends on the we can come to an understanding of the modeled construct. amount of information this system integrates. This again Second, parsimony also aids the development of predictions, underscores the importance of conscious thought in infor- because parsimony of a model makes it also less variable. mation integration. Information integration in turn is an Ultimately, we think that important knowledge can be important requirement for entropy reduction, thus further gained by integrating these different models of attitudes. supporting the AE framework’s assumption that a central Based on the similarities between the IR model, the ACS function of conscious thought is to reduce attitu- model, and the AE framework, we are optimistic that such dinal entropy. integration is possible (for an integration of the IR model 190 J. DALEGE ET AL. and the ACS model, see Ehret, Monroe, and Read, 2015). As Lehman, 1997; Hoshino-Browne et al., 2005; Kitayama, discussed in the introduction of the AE framework, we are Snibbe, Markus, & Suzuki, 2004). currently working on such integration. Open Question 6c: Combining Open Questions 6a and 6b leads to the question of whether individuals might even differ qualitatively in attitudinal entropy reduction: Are Open Questions there individuals who do not engage in attitudinal entropy reduction? The AE framework fosters subsequent research on attitudes Open Question 7: In the current article we focused on in two ways. First, as we discuss throughout this article, sev- single attitudes. Attitudes, however, do not exist in inde- eral predictions can be straightforwardly derived from the pendence from one another, and future study of the AE AE framework. Second, the AE framework also identifies framework should explore whether its principles also extend several open questions, which we discuss next. to interattitudinal processes. Open Question 1: The exact nature of attitude elements needs to be further investigated. In our earlier work on atti- tude networks (Dalege et al., 2016; Dalege, Borsboom, van Conclusion Harreveld, van der Maas, 2017, 2018; Dalege et al., 2017)we In this article, we introduced the AE framework, which treated rather general beliefs (e.g., judging a presidential holds that (a) attitude inconsistency is entropy, (b) energy candidate as honest) and feelings (feeling anger toward a of attitude configurations serves as a local processing strat- presidential candidate), as well as concrete behaviors (voting egy to reduce the global entropy of attitude networks, and for a presidential candidate) as attitude elements. However, (c) directing attention to and thinking about attitude objects it might also be possible that more low-level beliefs (e.g., reduces attitudinal entropy by increasing the dependence episodic memories of a person acting in a specific way) and parameter of attitude networks. The level of attitudinal feelings (e.g., recalling situations in which a person made entropy reduction depends on several factors, with merely one feel in a given way) are alternative operationalizations directing attention to and thinking shortly about the attitude of attitude elements. object representing the initial levels. Thinking more elabor- Open Question 2: Although we have focused on determi- ately about an attitude object and commitment to an evalu- nants of entropy reduction, it is also relevant to investigate ation and relevance to decisions of the attitude represent the determinants that make individuals more tolerant to attitu- intermediate levels and high attitude importance represents dinal entropy. A possible such determinant might be that the final level in attitudinal entropy reduction. We discussed individuals are highly motivated to be accurate. the AE framework’s relevance to research on ambivalence, Open Question 3: Can one level of attitudinal entropy the mere thought effect on attitude polarization, attitude reduction substitute for the other (e.g., is commitment to a strength, heuristic versus systematic persuasion, and implicit given evaluation always necessary to reach higher levels of versus explicit measurements of attitude, thereby underscor- attitudinal entropy reduction or would something like rele- ing the integrative power of the AE framework. We also dis- vance of the attitude to a decision be sufficient)? cussed several predictions that follow from the AE Open Question 4: The AE framework assumes that atti- framework and several open questions identified by the AE tudinal entropy is evaluated through two processes—the framework. It is our view that because of its abilities in inte- energy of a given attitudinal configuration and the instability gration and spurring novel research questions, the AE of an attitude. However, the extent to which these processes framework represents a significant advancement in the the- are linked is a matter for future research. oretical understanding of attitudes. Furthermore, the AE Open Question 5: Although we discussed attitudinal framework places attitude dynamics into a broader dynam- entropy reduction mostly as an intrapersonal process, it is ical systems context, further underscoring that reduction of certainly also possible that there are interpersonal effects on entropy is the defining feature of living systems—both in a attitudinal entropy reduction. A question needs to be biological and a psychological sense. Ultimately, this might addressed: How often individuals spontaneously reduce atti- help to answer the question why it is that we think: to tudinal entropy compared to how often this is reduce the entropy of our mental representations. socially instigated? Open Question 6a: How pronounced are individual dif- ferences in attitudinal entropy reduction? Indirect evidence References points to the existence of substantial differences, as individu- Anderson, N. H. (1971). Integration theory and attitude change. als differ in their preference for consistency (Cialdini, Trost, Psychological Review, 78(3), 171–206. & Newsom, 1995). Armitage, C. J., & Arden, M. A. (2007). Felt and potential ambivalence Open Question 6b: How pronounced are cultural differ- across the stages of change. Journal of Health Psychology, 12(1), ences in attitudinal entropy reduction? Similar to Open 149–158. Bar-Anan, Y., & Nosek, B. A. (2014). 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The Attitudinal Entropy (AE) Framework as a General Theory of Individual Attitudes
The Attitudinal Entropy (AE) Framework as a General Theory of Individual Attitudes
Abstract
AbstractThis article introduces the Attitudinal Entropy (AE) framework, which builds on the Causal Attitude Network model that conceptualizes attitudes as Ising networks. The AE framework rests on three propositions. First, attitude inconsistency and instability are two related indications of attitudinal entropy, a measure of randomness derived from thermodynamics. Second, energy of attitude configurations serves as a local processing strategy to reduce the global entropy of attitude networks. Third, directing attention to and thinking about attitude objects reduces attitudinal entropy. We first discuss several determinants of attitudinal entropy reduction and show that several findings in the attitude literature, such as the mere thought effect on attitude polarization and the effects of heuristic versus systematic processing of arguments, follow from the AE framework. Second, we discuss the AE framework’s implications for ambivalence and cognitive dissonance.
PSYCHOLOGICAL INQUIRY 2018, VOL. 29, NO. 4, 175–193 https://doi.org/10.1080/1047840X.2018.1537246 TARGET ARTICLE The Attitudinal Entropy (AE) Framework as a General Theory of Individual Attitudes Jonas Dalege, Denny Borsboom, Frenk van Harreveld, and Han L. J. van der Maas Department of Psychology, University of Amsterdam, Amsterdam, The Netherlands KEYWORDS ABSTRACT Attention; attitude; entropy; This article introduces the Attitudinal Entropy (AE) framework, which builds on the Causal Attitude network models; statistical Network model that conceptualizes attitudes as Ising networks. The AE framework rests on three mechanics; thought propositions. First, attitude inconsistency and instability are two related indications of attitudinal entropy, a measure of randomness derived from thermodynamics. Second, energy of attitude con- figurations serves as a local processing strategy to reduce the global entropy of attitude networks. Third, directing attention to and thinking about attitude objects reduces attitudinal entropy. We first discuss several determinants of attitudinal entropy reduction and show that several findings in the attitude literature, such as the mere thought effect on attitude polarization and the effects of heuristic versus systematic processing of arguments, follow from the AE framework. Second, we discuss the AE framework’s implications for ambivalence and cognitive dissonance. A century of research on attitudes has produced an impres- possibility to evaluate the global entropy of an attitude. sive amount of empirical findings and identified an abun- Third, attention and thought directed at the attitude object dance of concepts and processes related to attitudes. An have an analogous effect on the attitudinal representation as important next step toward a thorough understanding of (inverse) temperature has on thermodynamic behavior— attitudes would be a theoretical framework able to explain heightened attention and thought make attitudinal represen- these empirical findings from few first principles. The aim tations low in energy more likely and therefore reduce the of this article is to develop such a framework. To do so, we entropy of the attitude. The structure of this article is as follows. First, we discuss make use of analogical modeling (Haig, 2005): We use stat- istical mechanics as a starting point for our framework the main tenets of the AE framework. Second, we discuss determinants of reduction of attitudinal entropy and show because of its advanced theory and because our earlier ana- lysis has shown that a formalized measurement model of that several findings in the attitude literature, such as indi- vidual vs. group effects of implicitly measured attitudes, the attitudes can be based on statistical mechanics principles (Dalege et al., 2016) and show that an analogous theoretical mere thought effect, and systematic vs. heuristic processing, approach to attitude can explain a wide variety of empir- follow from these determinants. Third, we discuss ambiva- lence (e.g., Priester & Petty, 1996) and cognitive dissonance ical phenomena. Statistical mechanics revolves around three fundamental (Festinger, 1957) from the perspective of the AE framework. properties of a system—entropy (a measure of the system’s Throughout the subsequent sections we model several estab- randomness), energy, and temperature. To investigate lished phenomena in the attitude literature to show that the whether statistical mechanics represents a fruitful starting AE framework indeed holds promise in explaining several point for a general theory of attitudes, we search for analo- phenomena with few first principles. We also identify several gies of these fundamental properties and test whether the predictions that can be derived from the AE framework in consequences of these analogies match empirical findings in each discussion of a given phenomena to illustrate the pre- the attitude literature. Based on this approach we derive the dictive power of the AE framework and to define an empir- Attitudinal Entropy (AE) framework, which rests on three ical agenda for future research. We close by discussing propositions. First, inconsistency and instability of an atti- potential neural substrates of the AE framework’s proposi- tude represents attitudinal entropy and is therefore the nat- tions, the AE framework’s relation to other broad models of ural state of an attitude. Second, the energy of the attitude, and several open questions that need to be attitudinal representation serves as a local processing addressed to further develop the AE framework. CONTACT Jonas Dalege j.dalege@uva.nl Department of Psychology, University of Amsterdam, Nieuwe Achtergracht 129, 1018 WT, Amsterdam, The Netherlands. Color versions of one or more of the figures in this article can be found online at www.tandfonline.com/hpli Temperature, strictly speaking, might not be regarded as a fundamental property, because it can be derived from the relation between entropy and energy. However, for our current purposes it is beneficial to treat temperature as a fundamental property. 2018 Taylor & Francis Group, LLC 176 J. DALEGE ET AL. The AE Framework work, constituting heat loss or entropy. This notion also lies at the heart of the second law of thermodynamics, which In this section, we discuss the meaning of attitudinal states that entropy of an isolated system always increases. entropy and its implications for the dynamics of attitudes. Although the concept of entropy originated in classical We first discuss micro- and macrostates of attitudes and thermodynamics, its application to statistical mechanics then turn to the meaning of attitudinal entropy. Based on resulted in a broader use of entropy as a general measure of these definitions, we derive the AE framework. disorder or uncertainty in a system. The physicist Ludwig Boltzmann (1877) developed the statistical mechanics defin- ition of entropy, which holds that a macrostate that can be Attitudinal Micro- and Macrostates realized by many microstates has higher entropy than a The first question that needs to be addressed before we can macrostate that can be realized by few microstates (see define attitudinal entropy is what constitutes microstates Figure 1a). As an example, take the distribution of oxygen and macrostates of an attitude. In statistical mechanics, a molecules in the room you are sitting in right now. Luckily, microstate refers to the microscopic configuration of a given the macrostate of the oxygen molecules being distributed system (e.g., the position of each oxygen molecule in the evenly throughout the room can be realized by many more room you are sitting in), and a macrostate refers to the microstates (thus having higher entropy) than the macro- macroscopic behavior of a given system (e.g., whether all the state of the oxygen molecules clustering at one position in oxygen molecules are centered in one corner or whether the room. As an intuitive example of why the likelihood of they are evenly dispersed throughout the room). In line with a macrostate depends on its Boltzmann entropy, imagine a several theories on attitudinal structure (e.g., Dalege et al., simple slot machine with three fields that can show a lemon, 2016; Eagly & Chaiken, 2007; Fishbein & Ajzen, 1975; a peach, or a banana. The macrostate “win” (i.e., all fields Rosenberg, Hovland, McGuire, Abelson, & Brehm, 1960), showing the same fruit) can then be realized by three micro- we define the microstate of an attitude as the configuration states (e.g., three lemons). The macrostate “lose” (i.e., the of the relevant beliefs, feelings, and behaviors toward an atti- fields show at least two different fruits), on the other hand, tude object (i.e., attitude elements). As an example take the can be realized by 24 (3 –3) microstates. Although we attitude toward snakes. The microstate of this attitude can already see with this simple example that high-entropy states be represented like this: Attitude Element 1 (e.g., snakes are more likely than low-entropy states, the effect becomes maintain ecological order) is positive, Attitude Element 2 increasingly pronounced with the size of the system increas- (e.g., snakes are scary) is negative, Attitude Element 3 (e.g., ing (up to the point where the high-entropy state is essen- I run away when I see a snake) is negative, and so forth. tially the only possible state as is the case for the The macrostate of an attitude is then defined as the combin- distribution of oxygen molecules in a room). ation of all attitude elements (e.g., how many attitude ele- Applying the Boltzmann entropy to the domain of atti- ments are negative and how many are positive). Based on tudes implies that inconsistent attitudes have higher entropy several theories on the integration of attitude elements into than consistent attitudes. To illustrate this, consider an atti- a global evaluation (e.g., Anderson, 1971; Cacioppo, Petty, & tude consisting of 10 attitude elements. A perfectly univalent Green, 1989; Cunningham & Zelazo, 2007; Fazio, 1995; attitude can be realized only by two different microstates Zanna & Rempel, 1988), we assume that the global evalu- (i.e., all attitude elements being either positive or negative). ation of an attitude object is strongly related to the macro- So the attitude of a snake enthusiast (i.e., judging snakes as state of an attitude, in that it represents a context-depended entirely positive) can be realized only by one microstate. A weighted sum score of the attitude elements. Thus, we pro- perfectly ambivalent or neutral attitude, in contrast, can be pose the following three definitions: realized by 252 microstates. So judging snakes as positive on some aspects and negative on others can be realized by a Definition 1: The configuration of the attitude elements constitutes the microstate of the attitude. large number of microstates. This leads to the following first proposition of the AE framework: Definition 2: The number of positive versus negative attitude elements constitutes the macrostate of an attitude. Proposition I.1: Inconsistency of an attitude is the Boltzmann entropy of the attitude. Definition 3: A situation-depended weighted sum score constitutes the global evaluation of an attitude object. It is important to note here that the Boltzmann entropy concerns the entropy of a single given macrostate (e.g., five attitude elements are in a positive state and five attitude ele- Attitudinal Entropy ments are in a negative state). The entropy of a system, on Entropy is a concept originating from thermodynamics, the other hand, is described by the Gibbs entropy (Jaynes, where it was originally defined as energy that is lost when 1965). Gibbs entropy depends on the likelihood of the dif- energy is transformed (e.g., from chemical to kinetic ferent microstates of a system. As Figure 1b illustrates, energy). Take as an example the situation when you walk up Gibbs entropy is at maximum when all microstates are a steep hill. To do this, your body has to transform chemical energy in the form of calories to kinetic energy so that your Otherwise you might get crushed by all oxygen molecules distributed at the legs move up the hill. However, during this transformation position of the room you are in, or you might suffocate because all oxygen of energy, some energy is inevitably lost that is not put to molecules are at a different position than you. ATTITUDINAL ENTROPY FRAMEWORK 177 Figure 1. Illustrations of the Boltzmann and Gibbs entropies. Note. In (1) W refers to the number of microstates that can realize the given macrostate. In (2) X refers to all possible states of a given system. equally likely—implying that the system’s behavior is com- system, and it is our view that one of the main functions of pletely random—and it is at minimum when only a single focusing our attention on (or thinking about) an attitude configuration is possible, implying that the system’s behavior object is to put such force on the attitude system and obtain (or maintain) a consistent attitude that is low in entropy. is completely ordered. As an example of Gibbs entropy, take Entropy reduction is a crucial aspect of life because a key the movement of water molecules. Under high temperature, characteristic of any living organism is that it must maintain water molecules move randomly (i.e., water is in a gas state); order in their own system (Schrodinger, € 1944). According to this indicates high Gibbs entropy, because the configuration Kauffman (1993), the ability to reduce entropy is the most (i.e., positions) of the water molecules is consistently chang- important selection criterion for evolution. This implies that ing (i.e., all microstates are roughly equally likely). In con- the ability to reduce entropy is one of the central hallmarks trast, under low temperature the water molecules cannot of any living organism. We think that a similar argument move (i.e., water is in a solid state); this reflects low Gibbs can be made for the human mind, so that one of the central entropy, because the configuration of the water molecules is objectives of the human mind is to reduce its entropy (cf. stable (i.e., the current microstate is much more likely than Hirsh, Mar, & Peterson, 2012). It is straightforward that all other microstates). Someone who consistently changes only attitudes low in entropy fulfill the functions typically her attitude toward snakes would therefore have a high- associated with attitudes, such as to organize knowledge, entropy attitude toward snakes, whereas both a snake enthu- increase utility, and express values (Katz, 1960; Smith, siast and phobic have low-entropy attitudes toward snakes. Bruner, & White, 1956). All these functions require attitudes The Gibbs entropy, therefore, measures the inherent stability to be in predictable, stable, and consistent states, and there- of a system, which leads to the following proposition: fore attitudes are much more likely to fulfill their functions Proposition I.2: The Gibbs entropy of the attitude network when they are low in entropy (e.g., only a low-entropy atti- reflects the attitude’s stability. tude toward snakes can clearly imply that you should run From Proposition I.1, it follows that the natural state of when you are near one). Linking the need for entropy an attitude is neutral or ambivalent and that consistent atti- reduction to cognitive consistency also echoes the funda- tudes should be rare. However, this is clearly not the case; mental and widespread assumption in research on attitudes even though individuals are often exposed to ambiguous that individuals have an inherent preference for cognitive information, they often arrive at consistent representations of consistency (e.g., Festinger, 1957; Gawronski & Strack, 2012; Heider, 1946, 1958; Monroe & Read, 2008; Shultz & the information (e.g., Holyoak & Simon, 1999; Simon & Lepper, 1996). Spiller, 2016). So why are attitudes often consistent, whereas playing slot machines generally results in losing your money? The answer to this is that attitude elements are not inde- The Causal Attitude Network Model pendent of one another (to be explained next), and because of this dependency, attitudes can assume low-entropy macro- To formalize the ideas presented here, we build on the Causal states. However, for a system to remain in a low-entropy Attitude Network (CAN) model (Dalege et al., 2016), which state (i.e., low Gibbs entropy), force has to be put on this treats attitude elements as nodes in a network that are 178 J. DALEGE ET AL. connected by pairwise interactions. The complexity of the atti- weights can also vary, and the higher the magnitude, the tudinal representation is reflected by the size of the network stronger the interaction. The CAN model assumes that (i.e., number of nodes). The CAN model is based on psycho- weights between attitude elements generally arise based on inferences that support evaluative consistency. In the Ising metric network models (e.g., Cramer, Waldorp, van der Maas, model shown in Figure 2 all nodes are positively connected & Borsboom, 2010; van der Maas et al., 2006) and on con- straint-satisfaction models of attitudes (e.g., Kunda & Thagard, (indicated by green edges, see the online article for the color 1996; Monroe & Read, 2008; Shultz & Lepper, 1996). The cen- version of the figure). This Ising model thus represents a sim- tral assumption of the CAN model is that dynamics of atti- ple attitude network consisting of, for example, four positive tude networks can be described in an idealized way by the beliefs (e.g., believing that snakes maintain ecological order and are safe, beautiful, and smooth). Note that in the current Ising (1925) model, which originated from statistical mechan- article we focus on the situation in which edges between atti- ics. Although the Ising model is an extremely parsimonious tude elements are already present. How we can model the model, its behavior is exceptionally rich. Due to these qual- development of edges in attitude networks is currently inves- ities, the Ising model has been applied to many different fields tigated in our laboratory. The starting point for this investiga- of research, such as magnetization (e.g., Ising, 1925), kinetic tion is to combine the AE framework with connectionist energy (e.g., Fredrickson & Andersen, 1984), predator–prey models of attitudes, which assume that Hebbian learning dynamics (e.g., Kim, Liu, Um, & Lee, 2005), neuroscience underlies development of attitudinal structures (e.g., Monroe (e.g., Fraiman, Balenzuela, Foss, & Chialvo, 2009), clinical &Read, 2008). psychology (e.g., Cramer et al., 2016), and population dynam- Thresholds and weights determine a given configuration’s ics (e.g.,Galam,Gefen,& Shapir, 1982). energy (denoted by H). It is our view that, in contrast to the The Ising model describes the dynamics of networks by physical application of the Ising model, energy does not using the fact that systems strive toward low-energy configu- reflect an existing physical property. Calculation of energy is rations (see Figure 2 for an illustration of a simple Ising needed because it enables the mental system to arrive at a model). The energy of a configuration is determined by two low-entropy state by evaluating locally which elements need classes of parameters. The first class constitutes the thresh- to be changed. By evaluating several attitude elements in olds of the nodes, which determine the disposition of a turn, the mental system is able to create a global low-entropy given node to be “on” or “off” (denoted as s ). A node with state without evaluating the global state directly (which would a positive (negative) threshold requires less energy when it probably be too complex from a computational point of is “on” (“off”). In the original Ising model, thresholds repre- view). This leads to the following proposition: sent the external field that influences the spins of the mag- net. Similarly, in attitude networks, thresholds represent Proposition II: Energy of the attitudinal representation serves external information regarding the attitude object. These as a local processing possibility to evaluate the global Boltzmann entropy of an attitude. Attitude elements are likely to change thresholds therefore represent the disposition of a given atti- when the opposite state has lower energy. tude element to be endorsed or not. A positive threshold represents a disposition of a given node to be “on” (e.g., a The extent to which a configuration’s energy results in positive thresholds of judging snakes as dangerous indicates the configuration with lower energy being more likely than that one is inclined to judge snakes as dangerous holding all a configuration with higher energy depends on the depend- other information in the attitude network constant). A nega- ence parameter b (representing temperature in the original tive threshold represents a disposition of a given node to be Ising model). The higher the dependence parameter, the “off” (e.g., a negative threshold of judging snakes as beauti- more the probability of a configuration depends on its ful indicates that one is inclined to judge snakes as not energy. Because of this, the dependence parameter directly beautiful). The magnitude of thresholds can also vary and scales the Gibbs entropy of a given Ising model (e.g., the higher the magnitude, the stronger the disposition of the Kindermann & Snell, 1980), implying that increasing the node to be “on” or “off”. In the Ising model shown in dependence parameter results in attitude networks being Figure 2, two nodes have the disposition to be “on” (indi- more ordered and stable. For example, the Ising model with cated by green thresholds, see the online article for the color dependence at 0 at the top of Figure 2 has also maximum version of the figure) and two nodes have the disposition to Gibbs entropy, because all configurations are equally likely. be “off” (indicated by red thresholds, see the online article In contrast, the Ising model with high dependence at the for the color version of the figure). bottom of Figure 2 has lower Gibbs entropy, because the The second class of parameters constitutes weights of completely consistent configurations are much more likely edges between nodes, representing the strength of interaction than the inconsistent configurations. A system low in Gibbs between nodes (denoted as x ). Two nodes that have positive entropy thus creates the possibility of macrostates having weights between them require less (more) energy when they low Boltzmann entropy, but as long as the system is not at assume the same (different) state, representing preference for minimum Gibbs entropy, macrostates with high Boltzmann consistency. A positive weight represents an exhibitory inter- entropy are still possible. action (e.g., feeling afraid of snakes because you also judge The probability formula allows us to calculate the distri- them as dangerous), and a negative weight represents an bution of configurations we would expect if we measure an inhibitory interaction (e.g., not judging snakes as beautiful infinite number of individuals holding an attitude that can because you judge them as dangerous). The magnitude of be described by a given Ising model. For describing the ATTITUDINAL ENTROPY FRAMEWORK 179 Figure 2. Illustration of the Ising model. Note. In (3) HðxÞ represents the Hamiltonian energy of the configuration of k distinct nodes 1, … ,I,j, … .k, that engage in pairwise interactions and the variables x and x represent the states (1, þ1) of nodes i and j, respectively. The parameter s represents the threshold of node i and the parameter x represents the inter- i i action weight between nodes i and j. In (4) PrðX ¼ xÞ represents the probability of a given network configuration and b represents the dependence parameter of the Ising model. In (5) Z represents the standardization factor, which ensures that the probabilities add up to 1. The Distributions part of the figure shows the probability distributions of two Ising models for the sum scores of the nodes (upper distributions) and the individual configurations (lower distributions). The bottom of the figure shows all possible states of the four-node network, with green (red) nodes indicating that the node is “on” (“off”). dynamics of a given individual’s attitude, we can use time- increasing an attitude’s consistency can be described by such dependent dynamics called Glauber dynamics (Glauber, dynamics. For example, if one believes that snakes are safe 1963). The basic workings of Glauber dynamics on Ising while one also feels scared of them and always screams models are that at each iteration we (a) calculate the energy when one sees a snake, the probability that one changes his of the current configuration, (b) pick a random node and or her belief that snakes are safe is high. In the simulations calculate the energy of this neighboring configuration when we describe later, we make use of Glauber dynamics when this node is “flipped” (e.g., when this node changes from on we model individual-level dynamics. to off), (c) determine the probability of the node actually Figure 3 illustrates the reason why the dependence par- flipping by using the difference in energy, and (d) flip the ameter scales the Gibbs entropy of an Ising model. In the node with this probability (see Figure 3 for an illustration network with the dependence parameter at 0.5, the thresh- and formula). For attitude dynamics, this implies that olds and weights have little influence on the network’s 180 J. DALEGE ET AL. Figure 3. Glauber dynamics for two four-node networks under different dependence parameters. Note. In (6) and (7) x and x represent the current state of a given node and its opposite state, respectively. In (6) the probability of a node remaining in its current i j state relative to the probability that it will flip is represented. Each network represents one iteration and the node with a given probability represents a node that was randomly picked to be flipped with the given probability. Implication II: High Gibbs entropy in combination with a high dynamics and the network behaves essentially randomly. dependence parameter indirectly leads to psychological This situation therefore represents an attitude that is discomfort. The Gibbs entropy is indirectly evaluated by the unstable and in which the different attitude elements are temporal stability of the attitude. held with low certainty (e.g., the attitude of a person who does not care at all about snakes). With increases in the Levels of Attitudinal Entropy Reduction dependence parameter, the probability of the network con- figuration becomes increasingly dependent on the thresholds In this section, we discuss different levels of attitudinal and the weights of the network. In the network with the entropy reduction and research supporting these levels. Note dependence parameter at 3, the thresholds and weights have that these levels do not represent distinctive categories but strong influence on the network’s dynamics and the network are assumed to lie on a dimension from weak entropy behaves in accordance with these parameters. This situation reduction to high entropy reduction (just as the dependence therefore represents an attitude that is stable and in which parameter in the Ising model is also a continuous variable). the different attitude elements are held with high certainty It is our view that thinking about an attitude object—or, (e.g., the attitude of a snake phobic or enthusiast). This more generally, paying attention to an attitude object—has underscores the necessity of attitude elements being depend- the default effect of slightly increasing the dependency of ent on one another to reduce attitudinal entropy. In this art- the attitude network; as such, simply focusing attention icle, we argue that the dependence parameter in the Ising on the attitude object represents the most basic level of model constitutes a formalized representation of the effect dependency of the attitude network. Such a situation, for of directing attention and thinking about attitude objects, example, arises when an individual observes an attitude leading to the third proposition of the AE framework: object. The dependence parameter increases when the individual is prompted to think about the attitude object, Proposition III: Focusing attention on the attitude object and which would, for example, be the case when the individual thinking about the attitude object reduces the Gibbs entropy of attitudes by increasing the attitude network’s dependence responds to a questionnaire about an attitude object. parameter. The higher the dependence parameter, the stronger Increased levels of attitudinal entropy reduction may arise the correspondence between energy and probability of a given when individuals are for some reason prompted to think attitude network configuration. more elaborately about an attitude object and dependency of the attitude network is further increased when motivational Based on our argument that individuals are motivated to factors come into play, representing intermediate levels of reduce attitudinal entropy, we expect that a high level of attitudinal entropy reduction. Examples of factors moder- attitudinal entropy causes psychological discomfort. ately increasing motivation to reduce attitudinal entropy are However, because we assume that entropy of attitude net- situations in which individuals are committed to an evalu- works cannot be directly evaluated, this influence is indirect. ation or in which they have to make a relatively unimport- We expect that both measures of attitudinal entropy trans- ant decision. late into psychological discomfort through proxies, which Even more enhanced levels of attitudinal entropy reduc- are easier to evaluate for the mental system. This leads to tion arise when individuals attach personal importance to the following implications: their attitudes. Attitude importance is a widely researched Implication I: High Boltzmann entropy in combination with a topic and is a key determinant of attitude strength (Howe & high dependence parameter indirectly leads to psychological Krosnick, 2017). Factors increasing attitude importance are discomfort. The Boltzmann entropy is indirectly evaluated by the attitude’s relevance to self-interests (e.g., attitude’s rele- the difference in energy of the current and neighboring vance to important decisions), to personal values, and to configurations (i.e., configurations for which only one attitude element has to be flipped). social identification (Boninger, Krosnick, & Berent, 1995). ATTITUDINAL ENTROPY FRAMEWORK 181 Crucially, attitude importance is strongly related to how straightforwardly solved by assuming that implicit measures much attention individuals devote to an attitude object are more likely to tap attitudes in high-entropy (insta- ble) states. (Krosnick, Boninger, Chuang, Berent, & Carnot, 1993), mak- ing it likely that, indeed, attitudes high in personal import- ance represent attitude networks with the highest Simulation 1a: Implicit measures – low temporal stability, dependence and therefore also the lowest entropy attitudes. stable means. For this simulation, we investigated Glauber Furthermore, as we discuss in a later section, strong atti- dynamics on a fully connected 10-node network with all tudes show exactly the dynamics that would be expected edges set to .1. We varied the thresholds uniformly from from high dependence attitude networks. .2 to .7 with steps of .1, resulting in 10 different sets of To summarize, lower levels of attitudinal entropy reduc- thresholds. (We chose these thresholds so that the means tion arise when individuals pay some attention to the attitude differ from 0 and that there is sufficient variance for correla- object or briefly think about it. Intermediate levels represent tions to be meaningful.) The dependence parameter was set situations in which an individual is for some reason to .5 (representing that only some attention is directed at prompted to think about the attitude object in more detail the attitude object) and the network was randomly initial- (e.g., when an argument regarding the attitude object has to ized. We simulated 100 individuals for each set of thresh- be evaluated) and when individuals have to base a decision olds, resulting in the total number of 1,000 individuals. For on their attitude network or are committed to an evaluation. each individual we simulated 1,000 iterations. After 500 and The final levels of attitudinal entropy reduction arise when 1,000 iterations, respectively, we measured the sum score of an individual attaches high personal importance to an atti- the nodes. The resulting scores at the first measurement and tude object. In the remainder of this section, we show that at the second measurement were only weakly correlated several central findings in the attitude literature follow from (r ¼ .24, p < .001). The means of the first measurement the entropy reducing function of attention and thought. (M ¼ 1.91) and the second measurement (M ¼ 2.04), in con- trast, were virtually identical, t(999) ¼ 0.71, p ¼ .479, although the standard deviation at both the first measure- Implicit Measures Are More Likely to Tap Attitudes in ment (r ¼ 4.55) and the second measurement (r ¼ 4.45) High-Entropy States were substantial. Networks under a low dependence param- eter thus show low individual temporal stability but stable The dependence parameter of attitude networks increases means, which precisely matches the known behavior of when attention is directed at the attitude object, which implicit attitude measures. implies that the measurement of attitudes influences the dependence parameter. Implicit measures of attitudes, such Simulation 1b: Implicit measures – low behavior predic- as the Implicit Association Test (IAT; Greenwald, McGhee, tion on individual level, high behavior prediction on & Schwartz, 1998) and the Affective Misattribution Task group level. For this simulation, we used mostly the same (Payne, Cheng, Govorun, & Stewart, 2005), limit attention setup as in Simulation 1a, with the following adjustments. directed at the attitude object by measuring attitudes with- First, we added an 11th node that represented behavior. out directly asking individuals to introspect. These measures This node was also connected with weights of .1 to all other are therefore more likely to tap attitudes in high-entropy nodes but always had a threshold of 0 (so that all systematic states than explicit measures. Attitudes in high-entropy variation in this node is caused by its connection to other states are less internally consistent than attitudes in low- nodes). Second, we ran a total number of 10,000 individuals entropy states, which might contribute to the fact that impli- to be able to create groups of sufficiently large size. Third, cit measures generally show both poor internal reliability we created 10 groups that differed in their mean thresholds and test–retest reliability (e.g., Bar-Anan & Nosek, 2014; (see Table A1 in the appendix). The correlation between the Gawronski, Morrison, Phills, & Galdi, 2017; Hofmann, first 10 nodes and the “behavior” node on an individual Gawronski, Gschwendner, Le, & Schmitt, 2005). In contrast level was relatively weak (r ¼ .23, p < .001). In contrast, the to the low individual temporal stability of scores on implicit correlation on the group level was very strong (r ¼ .80, measures of attitudes, mean effects on implicit measures are p ¼ .006). These patterns fit the finding that individual-level substantially more robust (Payne, Vuletich, & Lundberg, correlations between implicit measures of attitudes and 2017). For example, children show similar scores on the IAT behavior are relatively low and that group level correlations as adults (Baron & Banaji, 2006), and the IAT predicts are considerably stronger. behavior much better on a global level (e.g., police shootings The implication of the AE framework that implicit meas- of Blacks is strongly associated with prejudice assessed with ures are more likely to tap attitudes in high-entropy states the IAT on a regional level; Hehman, Flake, and Calanchini, than explicit measures has fundamental implications for the 2018) than on an individual level, which is generally rather research on implicit measures of attitudes. Although research- low (e.g., Oswald, Mitchell, Blanton, Jaccard, & Tetlock, ers in this domain have long acknowledged that implicit 2013). A recent review identified these patterns as important measures show low internal consistency, they have generally puzzles in the literature on implicit measures of attitudes interpreted this as a measurement problem (e.g., Fazio & (Payne, Vuletich, & Lundberg, 2017). With the following Olson, 2003b; Gawronski, LeBel, & Peters, 2007; LeBel & simulations we show that these puzzles can be Paunonen, 2011; Nosek & Banaji, 2001). However, the AE 182 J. DALEGE ET AL. framework implies that the construct measured by implicit can be seen in Figure 4b, increasing the dependence param- measures is itself more internally inconsistent than the con- eter for such a small-size network does not lead to a sub- struct measured by explicit measures because the former by stantial increase in extreme sum scores, mimicking the their very nature direct less attention toward the attitude finding that complex cognitive schemas are necessary for the object than the latter. One consequence of this is that often mere thought effect to manifest itself. the only way to make implicit measures more reliable is to make them more explicit, leading to the counterintuitive con- Simulation 2c: Magnitude of edge weights as a formaliza- clusion that a valid measurement of attitudes (or any system tion of dependence between evaluative dimensions. Edge for that matter) in high-entropy states must be unreliable. weights in Ising networks are a straightforward formaliza- tion of interdependence between evaluative dimensions. To Prediction 1a. Manipulating the dependency in attitude investigate whether decreasing edge weights leads to lower networks (e.g., letting individuals think for some time about the increase in extreme scores, we adapted Simulation 2a by set- attitude object) is expected to increase internal consistency and stability of implicit measures. ting all edge weights to .05. As can be seen in Figure 4c, increasing the dependence parameter for such a weakly con- Prediction 1b. Scores on implicit measures assessing attitudes individuals regularly think about are expected to have higher nected network does not lead to a substantial increase in internal consistency and stability than scores on implicit extreme sum scores, mimicking the finding that inter- measures assessing attitudes individuals think only dependence of complex schemas is necessary for the mere infrequently about. thought effect to manifest itself. Prediction 1c: Implicit and explicit measures should show the Further support for the proposition that merely thinking lowest convergence when the dependence of the attitude about an attitude object represents an intermediate level of network is generally low. attitudinal entropy reduction comes from research on the coherence effect in judgment and decision making (e.g., Holyoak & Simon, 1999; Simon, Krawczyk, & Holyoak, The Mere Thought Effect as an Initial Level of 2004; Simon, Pham, Le, & Holyoak, 2001; Simon, Snow, & Heightened Attitudinal Entropy Reduction Read, 2004; Simon, Stenstrom, & Read, 2015). The coher- The mere thought effect on attitude polarization refers to the ence effect represents the general finding that when individ- classic finding that briefly thinking about an attitude object uals are presented with ambiguous information about a without receiving external information results in more given scenario (e.g., a legal case), individuals interpret this extreme evaluation of the attitude object (e.g., Tesser, 1978; information in such a way that it allows for a coherent judg- Tesser & Conlee, 1975). Based on several studies on the mere ment or decision about the scenario. Of interest, such coher- thought effect, Tesser, Martin, and Mendola (1995) argued ence shifts are also observed for dependency between that (a) sufficiently complex cognitive schemas (defined as emotions and beliefs regarding an attitude object (Simon the number of dimensions an attitude object is rated on) are et al., 2015) and in the complete absence of making a deci- necessary (Tesser & Leone, 1977) and (b) the evaluative sion (Simon et al., 2001). However, there are some indica- dimensions, on which the cognitive schema is based, need to tions that having to make a decision heightens the be sufficiently interdependent for the mere thought effect to coherence shift effect (Simon et al., 2001, 2004). manifest itself (Millar & Tesser, 1986). In the following simu- Prediction 2: Sizes of edge weights and size of attitude network lations, we show that the mere thought effect and its modera- predict the strength of the mere thought effect. tors naturally follow from the AE framework. Prediction 3: Because the AE framework assumes that increasing dependency of attitude networks is a continuous process, the AE framework predicts that an opposite mere Simulation 2a: Basic mere thought effect. We calculated thought effect also exists, in the sense that when individuals are the probabilities of the sum scores of a fully connected 10- asked to very quickly answer attitude questions, attitudes are node network with the dependence parameter set to either 1 expected to be less polarized than when individuals are given (representing merely asking individuals about their attitudes) more time to answer the questions. Note that the AE framework or 1.5 (representing mere thought). All edge weights were predicts that this would constitute a small effect. set to .1 and all thresholds were set to 0. As can be seen in Figure 4a, increasing the dependence parameter leads to an Attitude Strength increase in extreme sum scores, mimicking the basic mere thought effect. The highest levels of attitudinal entropy reduction have implications for attitude strength. The macrobehavior of Simulation 2b: Network size as formalization of a complex Ising networks is governed by the dependence of the net- cognitive schema. As stated in the section on the CAN work and can be described by the cusp catastrophe model model, the size of networks reflects the complexity of the (Sitnov, Sharma, Papadopoulos, & Vassiliadis, 2001). The cognitive schema of the attitude object. We therefore expect cusp catastrophe model describes sudden versus smooth that a network with few nodes will not show a strong changes in a variable depending on two control variables, increase in extreme sum scores when the dependence par- referred to as the normal variable and splitting variable, ameter is increased. To investigate this, we adapted respectively (Gilmore, 1981; Thom, 1972; Zeeman, 1976). Simulation 2a by decreasing the number of nodes to 4. As Depending on the value of the splitting factor, the influence ATTITUDINAL ENTROPY FRAMEWORK 183 Figure 4. The mere thought effect on polarization modeled by the Attitudinal Entropy framework. Note. Implied distributions of sum scores are shown under different independence parameters for (a) a 10-node network with all edge weights equal to .1, (b) a four-node network with all edge weights equal to .1, and (c) a 10-node network with edge weights equal to .05. of the normal variable on the dependent variable is either gradual or discrete, implying that the so-called bifurcation area, in which sudden transitions happen in the dependent variable, is larger when the splitting factor is high (see Figure 5). As an illustration, take the freezing of water. In this case, temperature represents the normal variable and pressure represents the splitting variable: Under low pres- sure, water freezes and melts at the same temperature, whereas under high pressure, frozen water melts at a higher temperature than when liquid water freezes (and the other way around). In Ising networks the average of the thresholds functions as normal control variable, the dependence of the network as splitting variable, and the macrobehavior of the network as dependent variable (Sitnov et al., 2001). Because of this, networks high in dependency are stable and Figure 5. The cusp catastrophe model from the perspective of the Attitudinal ordered and change happens suddenly, whereas networks Entropy framework. low in dependency are fluctuating and random and change happens gradually. These observations link the AE frame- 1976). In the catastrophe model of attitudes, valenced infor- work to the catastrophe model of attitudes, which assumes mation functions as the normal variable, attitude involve- that attitude change can be described by the cusp catastro- ment or attitude importance functions as the splitting phe model (Flay, 1978; Latane & Nowak, 1994; Zeeman, variable, and the global evaluation functions as the 184 J. DALEGE ET AL. Prediction 4: The mere thought effect extends to the stability dependent variable (see Figure 5). Several studies support and resistance of attitudes. Thinking briefly about attitude the catastrophe model of attitudes by showing that import- objects is predicted to (temporally) increase the stability and ant attitudes are more extreme than unimportant attitudes resistance of attitudes. (e.g., Latane & Nowak, 1994; Liu & Latane, 1998) and by Prediction 5: Persuasion is more effective for strong attitudes directly fitting the catastrophe model to data on attitudes when the dependence parameter is lowered (e.g., by reducing (van der Maas, Kolstein, & van der Pligt, 2003). The CAN attention directed at the attitude object) before the persuasion is model can easily integrate the catastrophe model of attitudes employed, because lowering the dependence parameter reduces and also provides a micro-level explanation of the postulates the hysteresis effect. of the catastrophe model (Dalege et al., 2016). Thresholds in Prediction 6: Whether an attitude changes continuously or the CAN model directly relate to the valenced information a discretely depends on the dependence parameter of the person receives regarding an attitude object and the macro- attitude network. behavior of an attitude is strongly related to global evalua- Prediction 7: Reducing the dependence parameter of networks tions of the attitude object. These similarities lead to the (e.g., by limiting cognitive capacity) results in less stable and conclusion that important attitudes are based on attitude less resistant attitudes. networks high in dependence. Linking attitude importance to the dependence of attitude Heuristic-Based versus Argument-Based Persuasion as networks also has broader implications for attitude strength. Global versus Specific Threshold Changes As attitude importance is a central determinant of attitude strength (Howe & Krosnick, 2017), it becomes likely that The elaboration likelihood model (Petty & Cacioppo, 1986) strong attitudes represent high-dependence attitude networks. and the Heuristic Systematic Model (Chaiken, Liberman, & Indeed, the dynamics of strong attitudes are highly similar to Eagly, 1989) are two hallmark dual process theories assum- the dynamics of strongly connected networks (Dalege et al., ing that persuasion can be accomplished via two routes— 2016), which in turn are similar to the behavior of low- one in which individuals change their attitudes based on dependence networks. Similar to strong attitudes (Krosnick heuristic cues (e.g., whether the source of the message is an & Petty, 1995), high-dependence networks are more stable expert) and one in which individuals change their attitudes and resistant (Kindermann & Snell, 1980). Increasing the based on a deeper processing of the quality of the persuasive dependence of attitude networks likely results in information arguments. Several studies have supported this idea and being processed in accordance with the attitude, which repre- showed that individuals low in involvement are more likely sents another central feature of attitude strength. to change their attitudes according to heuristic cues, whereas Biased information processing is related to the phenom- individuals high in involvement are more likely to change enon of hysteresis in the cusp catastrophe model. Hysteresis their attitudes according to argument quality (e.g., Petty & implies that the point at which a system moves to the Cacioppo, 1984; Petty, Cacioppo, & Goldman, 1981; Petty, opposite state depends on the direction of change (just as is Cacioppo, & Schumann, 1983). From the perspective of the the case for the melting and freezing of water under high AE framework, heuristic-based persuasion represents a mod- pressure). The strength of the hysteresis effect in the cusp erate global change in the attitude network’s thresholds (i.e., catastrophe model depends on the splitting variable—imply- change in the magnetic field in the language of the original ing that attitude networks under high dependence should Ising model), whereas argument-based persuasion represents show strong hysteresis effects (i.e., the bifurcation area a strong change of few specific thresholds, implying that becomes broader). Changing such an attitude thus requires moderate global change is more influential under low a disproportionate amount of persuasion compared to the dependence and strong specific change is more influential amount of information the individual already received. In under high dependence. We tested this hypothesis in the fol- such a situation it would probably be more effective to first lowing simulation. reduce the dependence parameter of the attitude network so that the individual is more “open” to change. Attitude-behavior consistency, which represents the final Simulation 3: Global versus specific threshold changes. For this simulation, we again used a fully connected 10- central feature of attitude strength, is also more likely in node network with all edge weights set to .1. We investi- high dependence attitude networks, because attitude ele- gated Glauber dynamics of this network using 1,000 itera- ments are more dependent on one another. As the CAN model treats behavior as part of the attitude network, tions. In the first 500 iterations, all simulated individuals’ increasing dependence of attitude networks also increases thresholds were set to .2 (thus representing a positive initial the dependence of behavior on beliefs and feelings regarding attitude) and the network was randomly initialized. In the second 500 iterations, (a) thresholds remained at .2 (repre- the attitude object, and vice versa, implying higher attitude- behavior consistency (Dalege, Borsboom, van Harreveld, senting the no heuristic cue/weak arguments condition), (b) Waldorp, & van der Maas, 2017). This hypothesis is sup- all thresholds changed to .12 (representing the heuristic ported by findings indicating that attitude-behavior consist- cue/weak arguments condition), (c) the first four thresholds ency depends on the stability of attitudes (Glasman & changed to .6 and the other thresholds remained at .2 Albarrac ın, 2006), which represents a proxy of the depend- (representing the no heuristic cue/strong arguments condi- ence of the attitude network. tion), or (d) the first four thresholds changed to .72 and ATTITUDINAL ENTROPY FRAMEWORK 185 (a) (b) Global threshold change Specific threshold change Global change Specific change no no yes yes 13 13 β β Figure 6. Effects of global (a) and specific threshold change (b) under moderate and high b. Note. Error bars represent ±2 SDs around the mean. the other thresholds changed to .12 (representing the Aversiveness of Attitudinal Entropy: Ambivalence heuristic cue/strong arguments condition). The thresholds and Cognitive Dissonance from the Perspective of were chosen this way so that the mean change in the heuris- the AE Framework tic cue/weak arguments condition and the no heuristic cue/ The first proposition of the AE framework holds that incon- strong arguments condition was equal. Half of the simulated sistency of an attitude is attitudinal entropy. Research on individuals’ bs was set to 1 (representing low involvement) ambivalence and cognitive dissonance underscores that con- and the other half of the simulated individuals’ bs was set to sistency is a fundamental human need and that violations of 3 (representing high involvement). We simulated 100 indi- this need cause psychological discomfort. Cognitive disson- viduals for each experimental cell, resulting in 600 simulated ance refers to aversive feelings caused by incongruent beliefs individuals in total. The results showed a pattern reminis- and behaviors vis-a-vis an attitude object, with most cent of the typical findings in the heuristic-based versus research on cognitive dissonance focusing on the effects of argument-based persuasion literature (e.g., Petty et al., carrying out a behavior inconsistent with the beliefs an indi- 1981). The three-way interaction on the sum score of the vidual holds. A crucial distinction in the research on attitude elements at the 1,000th iteration was significant, ambivalence is that between potential (or objective) and felt F(1, 792) ¼ 16.40, p ¼ .001, g ¼ .02, and the pattern of the (or subjective) ambivalence (e.g., Newby-Clark, McGregor, results was in line with the hypotheses (see Figure 6). & Zanna, 2002; Priester & Petty, 1996; van Harreveld, van Conceptualizing heuristic cues as global moderate threshold der Pligt, & de Liver, 2009). Potential ambivalence refers to change and strong arguments as specific strong thresholds the number of incongruent attitude elements, and felt change thus explains the basic result in the heuristic versus ambivalence refers to the aversive feelings caused by these argument-based persuasion literature. incongruent attitude elements. Crucially, the distinction Prediction 8a: Sufficiently strong heuristic cues lead to attitude between potential and felt ambivalence is made, because change under both low and high involvement. potential ambivalence can, but not necessarily does, result in Prediction 8b: A large number of strong arguments lead to felt ambivalence. In other words: Ambivalence can, but does attitude change under both low and high involvement. not have to be, unpleasant. From the perspective of the AE framework, the question when potential ambivalence results Prediction 9: As can be seen in Figure 6b, specific threshold change also affected networks with low b to a meaningful in felt ambivalence becomes the question when attitudinal extent. This leads to the prediction that, given sufficient power entropy results in psychological discomfort. In this section (e.g., in a meta-analysis), an effect of strong arguments should we discuss two possibilities of how the mental system indir- also be detected under low involvement. ectly evaluates attitudinal entropy and under which circum- stances this results in psychological discomfort. This We want to emphasize that although in all the other simulations presented discussion is based on Implications I and II of the AE here the findings are highly robust to changes in parameters, for the current framework. Implication I holds that Boltzmann entropy is simulation specific parameters had to be chosen to find the reported pattern of the results (e.g., when global threshold changes are chosen that are too indirectly evaluated through the energies of neighboring high or when too many specific thresholds are targeted, differences between the b conditions become less meaningful). The AE framework therefore predicts that the effect of argument versus persuasion-based persuasion is We use the terms potential and felt ambivalence throughout the article limited to a specific range of stimuli (i.e., not too strong heuristic cues or not because these terms fit our framework better than the recently more too many strong arguments). commonly used terms objective (or structural) and subjective ambivalence. Sum score −10 −5 0 5 10 Sum score −10 −5 05 10 186 J. DALEGE ET AL. configurations. In the following subsection we show that scores for each of the possible configurations and varied the this implication integrates the gradual threshold (GT) model power function parameter between .3, .5, and .7. of ambivalence (Priester & Petty, 1996) into the AE frame- Using Equation 6, we then calculated the mean prefer- work. Second, Implication II holds that Gibbs entropy is ence of each node to remain in its current state for each indirectly evaluated by the temporal stability of the attitude configuration. We then averaged these scores for each con- network’s configuration. figuration with the same number of conflicting attitude ele- ments (e.g., for each configurations in which all but one Boltzmann Entropy as Ambivalence attitude elements are in the positive state). We calculated the distribution of preference scores with the dependence An influential account of how potential ambivalence trans- parameter set to 1, 1.5, and 2.5. As can be seen in Figure 7, lates into felt ambivalence is the GT model (Priester & varying the dependence parameter has an analogous effect Petty, 1996). This model assumes a curvilinear relation as varying the power function of the GT model. Based on between the number of conflicting evaluations (treated here this finding, the AE framework implies that the dependence as attitude elements) and felt ambivalence, in which felt parameter determines to what degree potential ambivalence ambivalence increases less as the number of conflicting atti- translates into felt ambivalence. tude elements increases (e.g., the difference between holding Based on the finding that preferences of nodes to remain no conflicting attitude element and holding one conflicting in their current states are faster decelerating under a high attitude element is larger than the difference between hold- dependence parameter, we expect that factors increasing the ing three conflicting attitude elements and holding four con- dependence parameter also increase felt ambivalence. This flicting attitude elements). The specific formula of the GT hypothesis is indirectly supported by the finding that having model is the following: to make a decision increases felt ambivalence (e.g., Armitage p 1=C Ambivalence ¼ 5ðÞ C þ 1 ðÞ D þ 1 ; (8) & Arden, 2007; van Harreveld, Rutjens, Rotteveel, Nordgren, & van der Pligt, 2009; van Harreveld, van der Pligt, et al., where C refers to conflicting attitude elements (i.e., attitude 2009). The AE framework holds that basing a decision on elements that are incongruent to the majority of attitude ele- an attitude increases the dependence parameter of the atti- ments) and D refers to the number of dominant attitude ele- tude network, which results in lower (relative) preference of ments (i.e., attitude element that is consistent with the nodes to remain in their current state if the current config- majority of attitude elements). The p determines the power uration is ambivalent. function and was estimated by Priester and Petty (1996)to lie somewhere between .4 and .5. Although Priester and Prediction 10: Dependence of attitude networks moderates the relation between potential and felt ambivalence. The higher the Petty explicitly stated that these specific values are exogen- dependence, the stronger the impact of the first incongruent ous to the GT model, most research based on the GT model attitude elements. uses a value between .4 and .5 to calculate expected felt ambivalence scores (e.g., Clark, Wegener, & Fabrigar, 2008; Prediction 11: The AE framework assumes that dependence is increased when a decision has to be made. After the decision is Refling, Calnan, Fabrigar, MacDonald, Johnson, & Smith, made, dependence drops again. This implies that before a 2013). Clearly, a better understanding of the power function decision is contemplated and after a decision, correspondence would provide us with more knowledge on when and why between potential and felt ambivalence is expected to be lower potential ambivalence results in felt ambivalence (high p val- than while contemplating the decision. The same holds for the ues would indicate an almost linear relation, whereas low p stability and resistance of the attitude. values would indicate a steep relation). From the perspective of the AE framework, the number of conflicting attitude ele- Gibbs Entropy as Ambivalence ments is given by the configuration of the attitude network. We therefore expect that felt ambivalence as modeled by the In our view, it is likely that felt ambivalence, if caused by GT model indirectly reflects Boltzmann entropy of the con- low preference of nodes to remain in their current state, figuration of the attitude network. As stated in Implication I generally represents a situation-dependent process (e.g., hav- of the AE framework, Boltzmann entropy is indirectly eval- ing to make a decision based on an ambivalent attitude). In uated by the energy difference between the current configur- contrast, felt ambivalence caused by Gibbs entropy reflects a ation and its neighboring configurations and that the more chronic state of felt ambivalence. Implication II of the psychological discomfort caused by the energy difference is AE framework holds that the Gibbs entropy of an attitude amplified by the dependence parameter. Based on this rea- network is indirectly evaluated by the stability of the atti- soning, we expect the dependence parameter to determine tude. Based on this implication, we expect that unstable atti- the steepness of the relation between potential and felt tude networks in combination with a high dependence ambivalence. parameter cause strong feelings of ambivalence. To investi- gate under which circumstances low stability and a high Simulation 4: Felt ambivalence as Boltzmann entropy. For this simulation we again used a fully connected 10-node net- Note that with an increasing dependence parameter, the preference scores of work with all edge weights set to .1 and all thresholds set to almost all configurations increase. It therefore seems likely that the preference 0. We first calculated the GT model’s implied ambivalence scores are evaluated relative to the dependence parameter. ATTITUDINAL ENTROPY FRAMEWORK 187 Figure 7. Similarity of ambivalence calculated by the gradual threshold (GT) model and mean preference scores of nodes in Ising networks. dependence parameter can co-occur, we set up the follow- which an individual receives weak mixed information about ing simulation. an attitude object), (c) half of the thresholds were set to .5 and the other half were set to .5 (representing a situation Simulation 5: Felt ambivalence as Gibbs entropy. For this in which an individual receives strong mixed information simulation we again used a fully connected 10-node network about an attitude object), (d) all thresholds were set to .1 with all edge weights set to .1. We varied the thresholds in (representing a situation in which the external information the following way: (a) all thresholds were set to 0 (represent- points in a weak positive direction), and (e) all thresholds ing a situation in which the external information points in were set to .5 (representing a situation in which the external no direction), (b) half of the thresholds were set to .1 and information points in a strong positive direction). In add- the other half were set to .1 (representing a situation in ition, we varied the dependence parameter between 1, 1.5, 188 J. DALEGE ET AL. and 2.5 (mirroring Simulation 4). For each combination of relevant to research on cognitive dissonance. Similarities thresholds and dependence parameter, we simulated 100 between cognitive dissonance and felt ambivalence have individuals, resulting in the total number of 1,500 simulated been noted by several researchers (e.g., Jonas, Broemer, & individuals. For each individual, we simulated 500 iterations Diehl, 2000; McGregor, Newby-Clark, & Zanna, 1999); both based on Glauber dynamics (the network was again initial- concepts describe aversive feelings caused by being aware of ized randomly). To evaluate the stability of the attitude net- incongruence of one’s beliefs regarding an attitude object. work, we calculated the percentage of flipped states for the The main difference between these two concepts concerns last 100 iterations. the situations by which they are caused (van Harreveld, van The results indicated that for b ¼ 1, only the highly posi- der Pligt, et al., 2009). Whereas felt ambivalence arises in tive thresholds resulted in a relatively stable attitude network situations in which attention is directed at an ambivalent (see Figure 8). For b ¼ 1.5, attitude networks were more sta- attitude, cognitive dissonance arises in situation in which a ble overall, with the strong positive thresholds resulting in univalent attitude is disturbed (e.g., by inducing behavior almost perfect stability. The highly mixed thresholds net- incongruent with an individual’s attitude; Festinger and works remained relatively unstable. For b ¼ 2.5, only highly Carlsmith, 1959). However, the consequences of felt ambiva- mixed thresholds networks did not approach perfect stability. lence and cognitive dissonance are similar. This point is It is our view that such a situation results in the strongest illustrated by the similarities of two experiments focused on feelings of ambivalence, because stability remains rather low the role of arousal in dissonance reduction (Zanna & while the dependence parameter is already at a high value. Cooper, 1974) and on biased information processing serving Based on the results of the simulation, we conclude that ambivalence reduction (Study 1; Nordgren, van Harreveld, high felt ambivalence arises when individuals receive highly & van der Pligt, 2006), respectively. In both experiments, mixed information. Felt ambivalence is then amplified by participants were first administered a sugar pill but were the motivation to reduce attitudinal entropy. Such a situ- told that the pill would make them feel either aroused or ation would arise when individuals hold important attitudes relaxed. The results in both experiments were similar: When for which they receive mixed information, for instance, participants were told that the pill would be relaxing, they when individuals are disposed to a given evaluation (e.g., showed dissonance reduction and biased information proc- holding liberal values because you work at a liberal univer- essing. In contrast, when they were told that the pill was sity), whereas significant others endorse a different evalu- arousing, participants showed neither dissonance reduction ation (e.g., having parents who hold conservative values). nor biased information processing. Both Zanna and Cooper Such a situation has been shown to cause strong feelings of (1974) and Nordgren et al. (2006) argued that the reason for ambivalence (Priester & Petty, 2001). Further support for this pattern of results is that participants attributed their the relation between stability of an attitude and feelings on negative feelings caused by cognitive dissonance or ambiva- ambivalence comes from the finding that ambivalent indi- lence to the effects of the pill. We take the results of these viduals show physical signs of instability (i.e., moving from experiments as indication that negative feelings caused by one side to the other; Schneider et al., 2013). cognitive dissonance and ambivalence in fact result from Prediction 12: Highly mixed information and high attitude attitudinal entropy; the difference is that in cognitive disson- importance result in strong felt ambivalence. ance paradigms entropy is induced and in ambivalence para- digms attention to high entropy attitudes is induced. Cognitive Dissonance and Ambivalence Reflect Prediction 13: Given that the AE framework assumes that felt Attitudinal Entropy ambivalence and cognitive dissonance are caused by aversive configurations of the attitude network in combination with high Apart from research on ambivalence, the implication that dependence, felt ambivalence and cognitive dissonance are attitudinal entropy causes psychological discomfort is also predicted to have similar consequences. Figure 8. Stability of attitude networks based on different thresholds and dependence parameters. ATTITUDINAL ENTROPY FRAMEWORK 189 Future Study of the AE Framework The AE Framework’s Relation to Other Models of Attitude In the remainder of this article, we address some important opportunities for future study of the AE framework. Apart Although it is beyond the scope of our article to discuss the AE framework’s relation to all prominent models of attitude, from the empirical predictions that follow from the AE we discuss the framework’s relation to three models that are framework, we highlight the possibility of finding neural in our view especially relevant: the Iterative Reprocessing substrates of the AE framework’s propositions and possibil- (IR) model (Cunningham & Zelazo, 2007), the Attitude as ities for further theoretical integration, and we discuss open Constraint Satisfaction (ACS) model (Monroe & Read, questions raised by the AE framework. 2008) as an exemplar of constraint-satisfaction based con- nectionist models, and the Associative Propositional Possible Neural Substrates of the AE Framework Evaluation (APE) model (Gawronski & Bodenhausen, 2006). These models are especially relevant, because they are simi- Affective neuroscience has identified several neural sub- lar in focus as the AE framework. The basic assumption of strates of attitude dynamics. Much of this research has the APE model is that evaluations tapped by implicit meas- focused on finding neural substrates of the reaction to ures result from associative processes, whereas evaluations valenced stimuli. This research has identified that the amyg- tapped by explicit measures result from propositional proc- dala plays a central role in processing valenced stimuli (e.g., esses. The APE model further assumes that cognitive con- Morris et al., 1996; Phelps, 2006; Zald, 2003). Important to sistency is relevant only to propositional processes. note, the amygdala seems to integrate information from Similarly, the AE framework holds that attitudinal entropy throughout the brain (Cunningham & Zelazo, 2007), which reduction, which is mostly pronounced during explicit proc- makes it likely that global evaluations are formed in this essing of the attitude object, results in heightened cognitive neural structure. Another neural structure that plays a cen- consistency. However, the models diverge in the assumption tral role in attitude dynamics seems to be the anterior cin- that heightened cognitive consistency during explicit proc- gulate cortex (ACC). The ACC plays an important role in essing of the attitude object results from a process that is the detection of potential conflict (Carter et al., 1998), and it qualitatively different from implicit processing of the atti- was shown that the ACC is active during the experience of tude. In this sense, the AE framework is more in line with cognitive dissonance (van Veen, Krug, Schooler, & Carter, the IR model and the ACS model, which both assume that 2009) and when ambivalent stimuli are processed implicit and explicit evaluations are based on the (Cunningham, Raye, & Johnson, 2004). This makes the same processes. ACC a likely candidate for the neural structure involved in As we mention in the introduction of the AE framework, translating entropy of attitudes under high dependence into the process by which complex attitudinal representations are aversive feelings (note that also other neural substrates are reduced to a single global evaluation is partly based on the likely to be involved in the processing of ambivalent stimuli, IR model, which assumes that global evaluations are the such as the insula, the temporal parietal junction, and the result of iterative reprocessing of the attitude object, serving posterior cingulate cortex; see Nohlen, van Harreveld, the reduction of entropy (Cunningham, Dunfield, & Rotteveel, Lelieveld, & Crone, 2014). Stillman, 2013). The AE framework has several similarities Because the AE framework proposes that directing atten- to the ACS model, as both models assume that the main tion to and thinking about attitude objects serves the func- driving factor in attitude dynamics is the drive for cognitive tion of reducing attitudinal entropy, research on the neural consistency. The ACS model and the AE framework also substrates of consciousness is relevant to the AE framework. share a more technical similarity, because the ACS model is A recent influential theory of the neural underpinnings of based on Hopfield (1982, 1984) neural networks, which in consciousness posits that conscious experience results from turn are based on Ising models. In our view, the ACS model neurons engaging in recurrent processing of stimuli, which and the AE framework are therefore likely to complement enables information exchange between several low-level and each other and have different weaknesses and strengths. A high-level areas of the brain (Block, 2005, 2007; Lamme, strong feature of the ACS model is that it provides a formal- 2003, 2006). It thus seems likely that conscious processing ized account of evaluative learning, whereas the AE frame- of attitude objects results from integrating different kinds of work is more parsimonious than the ACS model, which in information regarding the attitude object. This idea is also our view has two advantages: First, parsimony aids the in line with the information integration theory of conscious- objective of “understanding by building,” in the sense that ness (Tononi, 2004; Tononi & Edelman, 1998), which holds the more parsimonious the model, the more likely it is that that the level of a system’s consciousness depends on the we can come to an understanding of the modeled construct. amount of information this system integrates. This again Second, parsimony also aids the development of predictions, underscores the importance of conscious thought in infor- because parsimony of a model makes it also less variable. mation integration. Information integration in turn is an Ultimately, we think that important knowledge can be important requirement for entropy reduction, thus further gained by integrating these different models of attitudes. supporting the AE framework’s assumption that a central Based on the similarities between the IR model, the ACS function of conscious thought is to reduce attitu- model, and the AE framework, we are optimistic that such dinal entropy. integration is possible (for an integration of the IR model 190 J. DALEGE ET AL. and the ACS model, see Ehret, Monroe, and Read, 2015). As Lehman, 1997; Hoshino-Browne et al., 2005; Kitayama, discussed in the introduction of the AE framework, we are Snibbe, Markus, & Suzuki, 2004). currently working on such integration. Open Question 6c: Combining Open Questions 6a and 6b leads to the question of whether individuals might even differ qualitatively in attitudinal entropy reduction: Are Open Questions there individuals who do not engage in attitudinal entropy reduction? The AE framework fosters subsequent research on attitudes Open Question 7: In the current article we focused on in two ways. First, as we discuss throughout this article, sev- single attitudes. Attitudes, however, do not exist in inde- eral predictions can be straightforwardly derived from the pendence from one another, and future study of the AE AE framework. Second, the AE framework also identifies framework should explore whether its principles also extend several open questions, which we discuss next. to interattitudinal processes. Open Question 1: The exact nature of attitude elements needs to be further investigated. In our earlier work on atti- tude networks (Dalege et al., 2016; Dalege, Borsboom, van Conclusion Harreveld, van der Maas, 2017, 2018; Dalege et al., 2017)we In this article, we introduced the AE framework, which treated rather general beliefs (e.g., judging a presidential holds that (a) attitude inconsistency is entropy, (b) energy candidate as honest) and feelings (feeling anger toward a of attitude configurations serves as a local processing strat- presidential candidate), as well as concrete behaviors (voting egy to reduce the global entropy of attitude networks, and for a presidential candidate) as attitude elements. However, (c) directing attention to and thinking about attitude objects it might also be possible that more low-level beliefs (e.g., reduces attitudinal entropy by increasing the dependence episodic memories of a person acting in a specific way) and parameter of attitude networks. The level of attitudinal feelings (e.g., recalling situations in which a person made entropy reduction depends on several factors, with merely one feel in a given way) are alternative operationalizations directing attention to and thinking shortly about the attitude of attitude elements. object representing the initial levels. Thinking more elabor- Open Question 2: Although we have focused on determi- ately about an attitude object and commitment to an evalu- nants of entropy reduction, it is also relevant to investigate ation and relevance to decisions of the attitude represent the determinants that make individuals more tolerant to attitu- intermediate levels and high attitude importance represents dinal entropy. A possible such determinant might be that the final level in attitudinal entropy reduction. We discussed individuals are highly motivated to be accurate. the AE framework’s relevance to research on ambivalence, Open Question 3: Can one level of attitudinal entropy the mere thought effect on attitude polarization, attitude reduction substitute for the other (e.g., is commitment to a strength, heuristic versus systematic persuasion, and implicit given evaluation always necessary to reach higher levels of versus explicit measurements of attitude, thereby underscor- attitudinal entropy reduction or would something like rele- ing the integrative power of the AE framework. We also dis- vance of the attitude to a decision be sufficient)? cussed several predictions that follow from the AE Open Question 4: The AE framework assumes that atti- framework and several open questions identified by the AE tudinal entropy is evaluated through two processes—the framework. It is our view that because of its abilities in inte- energy of a given attitudinal configuration and the instability gration and spurring novel research questions, the AE of an attitude. However, the extent to which these processes framework represents a significant advancement in the the- are linked is a matter for future research. oretical understanding of attitudes. Furthermore, the AE Open Question 5: Although we discussed attitudinal framework places attitude dynamics into a broader dynam- entropy reduction mostly as an intrapersonal process, it is ical systems context, further underscoring that reduction of certainly also possible that there are interpersonal effects on entropy is the defining feature of living systems—both in a attitudinal entropy reduction. A question needs to be biological and a psychological sense. Ultimately, this might addressed: How often individuals spontaneously reduce atti- help to answer the question why it is that we think: to tudinal entropy compared to how often this is reduce the entropy of our mental representations. socially instigated? Open Question 6a: How pronounced are individual dif- ferences in attitudinal entropy reduction? Indirect evidence References points to the existence of substantial differences, as individu- Anderson, N. H. (1971). Integration theory and attitude change. als differ in their preference for consistency (Cialdini, Trost, Psychological Review, 78(3), 171–206. & Newsom, 1995). Armitage, C. J., & Arden, M. A. (2007). Felt and potential ambivalence Open Question 6b: How pronounced are cultural differ- across the stages of change. Journal of Health Psychology, 12(1), ences in attitudinal entropy reduction? Similar to Open 149–158. Bar-Anan, Y., & Nosek, B. A. (2014). 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Journal
Psychological Inquiry
– Taylor & Francis
Published: Oct 2, 2018
Keywords: Attention; attitude; entropy; network models; statistical mechanics; thought
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