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Transitive Permutation Groups and Equipotent Voting Rules

Packel, Edward W. (1978) Transitive Permutation Groups and Equipotent Voting Rules. Social Science Working Paper, 212. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20171020-154208011

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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.


Item Type:Report or Paper (Working Paper)
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http://resolver.caltech.edu/CaltechAUTHORS:20171121-131202367Related ItemPublished Article
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.
Group:Social Science Working Papers
Subject Keywords:Transitive permutation group, Equipotent voting rule, Majority rule, Stable voting rule
Series Name:Social Science Working Paper
Issue or Number:212
Record Number:CaltechAUTHORS:20171020-154208011
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171020-154208011
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82555
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:20 Oct 2017 23:08
Last Modified:03 Oct 2019 18:55

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