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Independence of irrelevant alternatives in the theory of voting

Independence of irrelevant alternatives in the theory of voting Abstract In social choice theory there has been, and for some authors there still is, a confusion between Arrow'sIndependence of Irrelevant Alternatives (IIA) and somechoice consistency conditions. In this paper we analyze this confusion. It is often thought that Arrow himself was confused, but we show that this is not so. What happened was that Arrow had in mind a condition we callregularity, which implies IIA, but which he could not state formally in his model because his model was not rich enough to permit certain distinctions that would have been necessary. It is the combination of regularity and IIA that he discusses, and the origin of the confusion lies in the fact that if one uses a model that does not permit a distinction between regularity and IIA, regularity looks like a consistency condition, which it is not. We also show that the famous example that ‘proves’ that Arrow was confused does not prove this at all if it is correctly interpreted. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theory and Decision Springer Journals

Independence of irrelevant alternatives in the theory of voting

Theory and Decision , Volume 30 (2): 24 – Mar 1, 1991

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References (20)

Publisher
Springer Journals
Copyright
1991 Kluwer Academic Publishers
ISSN
0040-5833
eISSN
1573-7187
DOI
10.1007/BF00134122
Publisher site
See Article on Publisher Site

Abstract

Abstract In social choice theory there has been, and for some authors there still is, a confusion between Arrow'sIndependence of Irrelevant Alternatives (IIA) and somechoice consistency conditions. In this paper we analyze this confusion. It is often thought that Arrow himself was confused, but we show that this is not so. What happened was that Arrow had in mind a condition we callregularity, which implies IIA, but which he could not state formally in his model because his model was not rich enough to permit certain distinctions that would have been necessary. It is the combination of regularity and IIA that he discusses, and the origin of the confusion lies in the fact that if one uses a model that does not permit a distinction between regularity and IIA, regularity looks like a consistency condition, which it is not. We also show that the famous example that ‘proves’ that Arrow was confused does not prove this at all if it is correctly interpreted.

Journal

Theory and DecisionSpringer Journals

Published: Mar 1, 1991

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