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Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom

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  • McMorris, F.R.
  • Mulder, Henry Martyn
  • Novick, Beth
  • Powers, Robert C.

Abstract

This paper considers voting rules for two alternatives, viz. the simple majority rule of K.O. May, the majority rule with bias of Fishburn and others, and the majority rule by difference of votes of Goodin and List, and of Llamazares. These all have been characterized axiomatically for profiles of fixed length, that is, for a fixed population. The aim of this paper is to study analogs of these results in the situation where various populations are considered and disjoint populations can be combined into one population. The effect of this shift of focus is that now the domain of the rule consists of all finite nonempty sequences of votes. Young (1974) introduced the axiom of consistency, by which two populations can be combined into one as long as they agree on the output of the voting rule. We use a version of this axiom as given by Roberts (1991). Our paper can be seen as making a strong case for this simple, and natural axiom.

Suggested Citation

  • McMorris, F.R. & Mulder, Henry Martyn & Novick, Beth & Powers, Robert C., 2021. "Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 164-174.
    • Handle: RePEc:eee:matsoc:v:109:y:2021:i:c:p:164-174
    DOI: 10.1016/j.mathsocsci.2020.12.001
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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. Ron Holzman, 1990. "An Axiomatic Approach to Location on Networks," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 553-563, August.
    3. Goodin, Robert E. & List, Christian, 2006. "Special Majorities Rationalized," British Journal of Political Science, Cambridge University Press, vol. 36(2), pages 213-241, April.
    4. Vohra, Rakesh, 1996. "An axiomatic characterization of some locations in trees," European Journal of Operational Research, Elsevier, vol. 90(1), pages 78-84, April.
    5. Bubboloni, Daniela & Gori, Michele, 2016. "Resolute refinements of social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 37-49.
    6. B. Fine & K. Fine, 1974. "Social Choice and Individual Rankings II," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(4), pages 459-475.
    7. Bubboloni, Daniela & Gori, Michele, 2015. "Symmetric majority rules," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 73-86.
    8. Duddy, Conal & Piggins, Ashley, 2013. "Collective approval," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 190-194.
    9. Quesada, Antonio, 2010. "Monotonicity + efficiency + continuity = majority," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 149-153, September.
    10. Campbell, Donald E., 1988. "A characterization of simple majority rule for restricted domains," Economics Letters, Elsevier, vol. 28(4), pages 307-310.
    11. B. Fine & K. Fine, 1974. "Social Choice and Individual Ranking I," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(3), pages 303-322.
    12. Yi, Jianxin, 2005. "A complete characterization of majority rules," Economics Letters, Elsevier, vol. 87(1), pages 109-112, April.
    13. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    14. Hyewon Jeong & Biung-Ghi Ju, 2017. "Resolute majority rules," Theory and Decision, Springer, vol. 82(1), pages 31-39, January.
    15. 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.
    16. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    17. Roberts, Fred S., 1991. "Characterizations of the plurality function," Mathematical Social Sciences, Elsevier, vol. 21(2), pages 101-127, April.
    18. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    19. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    20. J. Woeginger, Gerhard, 2003. "A new characterization of the majority rule," Economics Letters, Elsevier, vol. 81(1), pages 89-94, October.
    21. Llamazares, Bonifacio, 2006. "The forgotten decision rules: Majority rules based on difference of votes," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 311-326, May.
    22. Asan, Goksel & Sanver, M. Remzi, 2002. "Another characterization of the majority rule," Economics Letters, Elsevier, vol. 75(3), pages 409-413, May.
    23. Duggan, John, 2016. "Limits of acyclic voting," Journal of Economic Theory, Elsevier, vol. 163(C), pages 658-683.
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