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Characterization of tie-breaking plurality rules

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  • Hiroki Saitoh

    (Meiji Gakuin University)

Abstract

We introduce a new condition for social choice functions, called “equal treatment of congruent distributions.” It requires some invariance between two preference profiles that share a type of congruity property with respect to the associated distributions of votes. It also implies two equal treatment conditions: one is a natural weakening of anonymity, which is the most standard equal treatment condition for individuals, and the other is a natural weakening of neutrality, which is the most standard equal treatment one for alternatives. Thus, equal treatment of congruent distributions plays the role of weak equal treatment conditions both for individuals and for alternatives. As our main results, we characterize a class of social choice functions that satisfy equal treatment of congruent distributions and some mild positive responsiveness conditions, and it is shown to coincide with the class of tie-breaking plurality rules, which are selections of the well-known plurality rule.

Suggested Citation

  • Hiroki Saitoh, 2022. "Characterization of tie-breaking plurality rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(1), pages 139-173, July.
    • Handle: RePEc:spr:sochwe:v:59:y:2022:i:1:d:10.1007_s00355-021-01382-3
    DOI: 10.1007/s00355-021-01382-3
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    1. Sekiguchi, Yohei, 2012. "A characterization of the plurality rule," Economics Letters, Elsevier, vol. 116(3), pages 330-332.
    2. Michele Gori, 2014. "Selecting anonymous, neutral and reversal symmetric minimal majority rules," Working Papers - Mathematical Economics 2014-04, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    3. Daniela Bubboloni & Michele Gori, 2014. "Anonymous and neutral majority rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 377-401, August.
    4. Daniela Bubboloni & Michele Gori, 2021. "Breaking ties in collective decision-making," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 411-457, June.
    5. Eyal Baharad & Shmuel Nitzan, 2005. "The inverse plurality rule—an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 173-178, October.
    6. Ali I. Ozkes & M. Remzi Sanver, 2021. "Anonymous, neutral, and resolute social choice revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 97-113, July.
    7. Laslier, Jean-Francois, 1996. "Rank-based choice correspondences," Economics Letters, Elsevier, vol. 52(3), pages 279-286, September.
    8. Campbell, Donald E. & Kelly, Jerry S., 2015. "The finer structure of resolute, neutral, and anonymous social choice correspondences," Economics Letters, Elsevier, vol. 132(C), pages 109-111.
    9. Kelly, Jerry S. & Qi, Shaofang, 2016. "Characterizing plurality rule on a fixed population," Economics Letters, Elsevier, vol. 146(C), pages 39-41.
    10. Yeh, Chun-Hsien, 2006. "Reduction-consistency in collective choice problems," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 637-652, September.
    11. Moulin, Herve, 1980. "Implementing efficient, anonymous and neutral social choice functions," Journal of Mathematical Economics, Elsevier, vol. 7(3), pages 249-269, December.
    12. Markus Schulze, 2011. "A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 267-303, February.
    13. Donald E. Campbell & Jerry S. Kelly, 2016. "A Strategy-Proofness Characterization of Plurality Rule," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(4), pages 610-623, August.
    14. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    15. Ching, Stephen, 1996. "A Simple Characterization of Plurality Rule," Journal of Economic Theory, Elsevier, vol. 71(1), pages 298-302, October.
    16. Campbell, Donald E. & Kelly, Jerry S., 2013. "Anonymity, monotonicity, and limited neutrality: Selecting a single alternative from a binary agenda," Economics Letters, Elsevier, vol. 118(1), pages 10-12.
    17. Nitzan, Shmuel & Paroush, Jacob, 1981. "The characterization of decisive weighted majority rules," Economics Letters, Elsevier, vol. 7(2), pages 119-124.
    18. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-1151, November.
    19. Jean-FranÚois Laslier, 2000. "Aggregation of preferences with a variable set of alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 269-282.
    20. Elisha A. Pazner & Eugene Wesley, 1978. "Cheatproofness Properties of the Plurality Rule in Large Societies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(1), pages 85-91.
    21. Hyewon Jeong & Biung-Ghi Ju, 2017. "Resolute majority rules," Theory and Decision, Springer, vol. 82(1), pages 31-39, January.
    22. Yohei Sekiguchi, 2012. "A Characterization of the Plurality Rule," CIRJE F-Series CIRJE-F-833, CIRJE, Faculty of Economics, University of Tokyo.
    23. Fishburn, Peter C. & Gehrlein, William V., 1977. "Collective rationality versus distribution of power for binary social choice functions," Journal of Economic Theory, Elsevier, vol. 15(1), pages 72-91, June.
    24. M. Sanver, 2009. "Strategy-proofness of the plurality rule over restricted domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 461-471, June.
    25. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    26. Chun-Hsien Yeh, 2008. "An efficiency characterization of plurality rule in collective choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 575-583, March.
    27. Peleg, Bezalel, 1978. "Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 153-161, January.
    28. Ali I. Ozkes & M. Remzi Sanver, 2021. "Correction to: Anonymous, neutral, and resolute social choice revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 115-115, July.
    29. Gilbert Laffond & Jean Lainé & Jean-François Laslier, 1996. "Composition-consistent tournament solutions and social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 75-93, January.
    30. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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