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Theory and Decision
Published in: Theory and Decision 1/2017

05-08-2016

Resolute majority rules

Authors: Hyewon Jeong, Biung-Ghi Ju

Published in: Theory and Decision | Issue 1/2017

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Abstract

We investigate resolute voting rules that always rank two alternatives strictly and avoid social indecision. Resolute majority rules differ from the standard majority rule in that whenever both alternatives win the same number of votes, a tie-breaking function is used to determine the outcome. We provide axiomatic characterizations of resolute majority rules or resolute majority rules with a quorum. Resoluteness axiom is used in all these results. The other axioms are weaker than those considered in the characterization of the majority rule by May (1952 Econometrica, 20:680–684). In particular, instead of May’s positive responsiveness, we consider a much weaker monotonicity axiom.
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Footnotes
1
See also Llamazares (2006) for some related characterization results. Pauly (2013) considers a different quorum constraint introduced by García-Lapresta and Llamazares (2001), which requires at least as many positive votes as the quorum. Majority rules with this quorum constraint are characterized by Pauly (2013) using “strategy-proofness”.
 
2
In a related work, Quesada (2013) defines “relative” majority rules with a tie-breaking chairperson and provides an axiomatic characterization. A similar type of modification of the plurality rule in a different model is considered by Ju (2005), who provides a characterization result.
 
Literature
Fishburn, P. C., & Gehrlein, W. V. (1977). Collective rationality versus distribution of power for binary social choice functions. Journal of Economic Theory, 15, 72–91.CrossRef
García-Lapresta, J. L., & Llamazares, B. (2001). Majority decisions based on difference of votes. Journal of Mathematical Economics, 35(3), 463–481.CrossRef
Houy, N. (2007). Some further characterizations for the forgotten voting rules. Mathematical Social Sciences, 53, 111–121.CrossRef
Houy, N. (2009). A characterization of majority voting rules with quorums. Theory and decision, 67, 295–301.CrossRef
Ju, B.-G. (2005). A characterization of plurality-like decision based on non-manipulability, restricted efficiency, and anonymity. International Journal of Game Theory, 33, 335–354.CrossRef
Karotkin, D. (1996). Justification of the simple majority and chairman rules. Social Choice and Welfare, 13, 479–486.CrossRef
Llamazares, B. (2006). The forgotten decision rules: Majority rules based on difference of votes. Mathematical Social Science, 51, 311–326.CrossRef
May, K. O. (1952). A set of independent necessary and sufficient conditions for simple majority decision. Econometrica, 20, 680–684.CrossRef
Nitzan, S., & Paroush, J. (1981). The characterization of decisive weighted majority rules. Economics Letters, 7(2), 119–124.CrossRef
Nitzan, S., & Paroush, J. (1982). Optimal decision rules in uncertain dichotomous choice situations. International Economic Review, 23, 289–297.CrossRef
Pauly, M. (2013). Characterizing referenda with quorums via strategy-proofness. Theory and Decision, 75, 581–597.CrossRef
Quesada, A. (2013). The majority rule with a chairman. Social Choice and Welfare, 40, 679–691.CrossRef
Metadata
Title
Resolute majority rules
Authors
Hyewon Jeong
Biung-Ghi Ju
Publication date
05-08-2016
Publisher
Springer US
Published in
Theory and Decision / Issue 1/2017
Print ISSN: 0040-5833
Electronic ISSN: 1573-7187
DOI
https://doi.org/10.1007/s11238-016-9563-y

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