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Plurality rule and Condorcet criterion over restricted domains

Author

Listed:
  • Thérèse Embigne Killanga

    (Ecole Nationale Supérieure Polytechnique)

  • Issofa Moyouwou

    (Ecole Normale Supérieure)

  • Boniface Mbih

    (Université de Caen Normandie, Unicaen, CREM, UMR CNRS 6211)

Abstract

Given a nonempty set of voters and a nonempty set of candidates, we provide a characterization of preference domains over which the plurality rule is Condorcet consistent; these are preference domains over which it is possible to design a social choice function that always chooses a plurality winner and also respects the Condorcet criterion. We take into account the possibility that some voters abstain and that some candidates withdraw freely from the competition, just as in real elections. In the general case with at least five potential voters and at least three potential candidates, we show that being defined on a quasi-cyclic permutation domain is a necessary and sufficient condition for the plurality rule to be Condorcet consistent. As points of discussion, we also investigate on the probability that a Condorcet winner exists in an admissible profile over a cyclic permutation domain as well as the existence of an ideal preference domain on which all scoring rules are Condorcet consistent. On this latter issue, it turns out that only essentially top-trivial domains are left.

Suggested Citation

  • Thérèse Embigne Killanga & Issofa Moyouwou & Boniface Mbih, 2025. "Plurality rule and Condorcet criterion over restricted domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 64(3), pages 633-663, May.
  • Handle: RePEc:spr:sochwe:v:64:y:2025:i:3:d:10.1007_s00355-024-01553-y
    DOI: 10.1007/s00355-024-01553-y
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    References listed on IDEAS

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    1. William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 503-512.
    2. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
    3. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    4. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, Enero-Abr.
    5. William Gehrlein & Dominique Lepelley & Issofa Moyouwou, 2015. "Voters’ preference diversity, concepts of agreement and Condorcet’s paradox," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2345-2368, November.
    6. William V. Gehrlein & Dominique Lepelley, 2017. "Elections, Voting Rules and Paradoxical Outcomes," Studies in Choice and Welfare, Springer, number 978-3-319-64659-6, June.
    7. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    8. Gehrlein, William V., 1982. "Condorcet efficiency and constant scoring rules," Mathematical Social Sciences, Elsevier, vol. 2(2), pages 123-130, March.
    9. 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.
    10. Gehrlein, William V., 2001. "Condorcet winners on four candidates with anonymous voters," Economics Letters, Elsevier, vol. 71(3), pages 335-340, June.
    11. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    12. 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.
    13. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    14. Gehrlein, William V. & Fishburn, Peter C., 1976. "The probability of the paradox of voting: A computable solution," Journal of Economic Theory, Elsevier, vol. 13(1), pages 14-25, August.
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