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Representing voting rules in Łukasiewicz’s three-valued logic

Representing voting rules in Łukasiewicz’s three-valued logic We show how voting rules like the simple and the absolute majority rules, unanimity, consensus, etc. can be represented as logical operators in Łukasiewicz’s three-valued logic. First, we prove that the binary simple majority operator can be extended to express the majority choice of groups formed of n voters. Consequently, decisions in larger groups can be represented as more complex decisions in groups formed of pairs of voters. This property is not shared, however, by the consensus and the absolute majority operators. Secondly, we prove that the simple majority operator can be defined in terms of the consensus operator, but that the converse does not hold. Finally, we construct the classes of logical operators definable in terms of the simple majority and of the consensus and point to some more general implications of these results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

Representing voting rules in Łukasiewicz’s three-valued logic

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Representing voting rules in Łukasiewicz’s three-valued logic

Abstract

We show how voting rules like the simple and the absolute majority rules, unanimity, consensus, etc. can be represented as logical operators in Łukasiewicz’s three-valued logic. First, we prove that the binary simple majority operator can be extended to express the majority choice of groups formed of n voters. Consequently, decisions in larger groups can be represented as more complex decisions in groups formed of pairs of voters. This property is not shared, however, by the...
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Publisher
Taylor & Francis
Copyright
© 2022 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.2022.2041351
Publisher site
See Article on Publisher Site

Abstract

We show how voting rules like the simple and the absolute majority rules, unanimity, consensus, etc. can be represented as logical operators in Łukasiewicz’s three-valued logic. First, we prove that the binary simple majority operator can be extended to express the majority choice of groups formed of n voters. Consequently, decisions in larger groups can be represented as more complex decisions in groups formed of pairs of voters. This property is not shared, however, by the consensus and the absolute majority operators. Secondly, we prove that the simple majority operator can be defined in terms of the consensus operator, but that the converse does not hold. Finally, we construct the classes of logical operators definable in terms of the simple majority and of the consensus and point to some more general implications of these results.

Journal

Journal of Applied Non-Classical Logics – Taylor & Francis

Published: Jan 2, 2022

Keywords: Three-valued logic; simple majority; consensus; unanimity; absolute majority

References

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