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Published October 20, 2017 | Submitted
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Transitive Permutation Groups and Equipotent Voting Rules

Abstract

Let F a two-alternative voting rule and GF the subgroup of permutations of the voters under which F is invariant. Group theoretic properties of GF provide information about the voting rule F. In particular, sets of imprimitivity of GF describe the 'committee decomposition' structure of F and permutation group transitivity of GF (equipotency) is shown to be closely connected with equal distribution of power among the voters. If equipotency replaces anonymity in the hypotheses of May's theorem, voting rules other than simple majority are possible. By combining equipotency with two additional social choice conditions a new characterization of simple majority rule is obtained. Equipotency is proposed as an important alternative to the more restrictive anonymity as a fairness criterion in social choice.

Additional Information

The author is indebted to John A. Ferejohn for suggesting several ideas fundamental to the evolution of this paper. Published as Packel, Edward W. "Transitive permutation groups and equipotent voting rules." Mathematical Social Sciences 1.1 (1980): 93-100.

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August 19, 2023
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January 14, 2024