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Transitive permutation groups and equipotent voting rules

Packel, Edward W. (1980) Transitive permutation groups and equipotent voting rules. Mathematical Social Sciences, 1 (1). pp. 93-100. ISSN 0165-4896. doi:10.1016/0165-4896(80)90008-6.

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Let F a two-alternative voting rule and G_F the subgroup of permutations of the voters under which F is invariant. Group theoretic properties of G_F provide information about the voting rule F. In particular, sets of imprimitivity of G_F describe the ‘committee decomposition’ structure of F and permutation group transitivity of G_F (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.

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Additional Information:© 1980 North-Holland Publishing Company. Communicated by F. W. Roush. Received 16 September 1979. Revised 8 November 1979. The author is indebted to John A. Ferejohn for suggesting several ideas fundamental to the evolution of this paper. Support from National Science Foundation Grant SOC 790-7366 is gratefully acknowledged. Formerly SSWP 212.
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Subject Keywords:transitive permutation group, equipotent voting rule, majority rule, stable voting rule
Issue or Number:1
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83401
Deposited By: Jacquelyn Bussone
Deposited On:21 Nov 2017 21:52
Last Modified:15 Nov 2021 19:57

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