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Majority Voting and Higher-Order Societies

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  • Adrian Miroiu

    (National University of Political Studies and Public Administration (SNSPA))

Abstract

The aim of this paper is to study the applications of social choice functions (scfs) like for example the simple majority rule μ and the consensus rule κ to higher-order societies (i.e., societies that have other societies as members). The focus is on the reducibility property of a scf: its capacity to mimic the behavior of other scfs. It is proved that although κ is not reducible to μ, conversely μ can be reduced to κ. A characterization of the class of scfs reducible to κ is given. Finally, it is proved that some scfs can be extended, in the sense that the application of the scf to a society formed of a large number of members is reducible to iterate applications of that scf to (higher-order) societies formed of only two members.

Suggested Citation

  • Adrian Miroiu, 2021. "Majority Voting and Higher-Order Societies," Group Decision and Negotiation, Springer, vol. 30(5), pages 983-999, October.
  • Handle: RePEc:spr:grdene:v:30:y:2021:i:5:d:10.1007_s10726-021-09744-z
    DOI: 10.1007/s10726-021-09744-z
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    References listed on IDEAS

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    1. Jerry S. Kelly & Donald E. Campbell, 2000. "A simple characterization of majority rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 689-700.
    2. Fine, Kit, 1972. "Some Necessary and Sufficient Conditions for Representative Decision on Two Alternatives," Econometrica, Econometric Society, vol. 40(6), pages 1083-1090, November.
    3. Fred McMorris & Robert Powers, 2008. "A Characterization of Majority Rule for Hierarchies," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 153-158, November.
    4. Adrian Miroiu & Catalin Partenie, 2019. "Collective choice in Aristotle," Constitutional Political Economy, Springer, vol. 30(3), pages 261-281, September.
    5. Batra, Raveendra N & Pattanaik, Prasanta K, 1972. "Transitive Multi-Stage Majority Decisions with Quasi-Transitive Individual Preferences," Econometrica, Econometric Society, vol. 40(6), pages 1121-1135, November.
    6. Fishburn, Peter C, 1971. "The Theory of Representative Majority Decision," Econometrica, Econometric Society, vol. 39(2), pages 273-284, March.
    7. Asan, Goksel & Sanver, M. Remzi, 2002. "Another characterization of the majority rule," Economics Letters, Elsevier, vol. 75(3), pages 409-413, May.
    8. Xu, Yongsheng & Zhong, Zhen, 2010. "Single profile of preferences with variable societies: A characterization of simple majority rule," Economics Letters, Elsevier, vol. 107(2), pages 119-121, May.
    9. José Carlos R. Alcantud, 2020. "Simple Majorities with Voice but No Vote," Group Decision and Negotiation, Springer, vol. 29(5), pages 803-822, October.
    10. Antonio Quesada, 2013. "To Majority through the Search for Unanimity," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(5), pages 729-735, October.
    11. Antonio Quesada, 2013. "The majority rule with a chairman," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 679-691, March.
    12. J. Woeginger, Gerhard, 2003. "A new characterization of the majority rule," Economics Letters, Elsevier, vol. 81(1), pages 89-94, October.
    13. M. Sanver, 2009. "Characterizations of majoritarianism: a unified approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 159-171, June.
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