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Are Condorcet procedures so bad according to the reinforcement axiom?

Author

Listed:
  • Sébastien Courtin

    (THEMA, Universite de Cergy-Pontoise)

  • Boniface Mbih

    (University of Caen basse-Normandie)

  • Issofa Moyouwou

    (University of Yaounde I)

Abstract

A Condorcet social choice procedure elects the candidate that beats every other candidate under simple majority when such a candidate exists. The reinforcement axiom roughly states that given two groups of individuals, if these two groups select the same alternative, then this alternative must also be selected by their union. Condorcet social choice procedures are known to violate this axiom. Our goal in this paper is to put this important voting theory result into perspective. We then proceed by evaluating how frequently this phenomenon is susceptible to occur.

Suggested Citation

  • Sébastien Courtin & Boniface Mbih & Issofa Moyouwou, 2012. "Are Condorcet procedures so bad according to the reinforcement axiom?," THEMA Working Papers 2012-37, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2012-37
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    File URL: http://thema.u-cergy.fr/IMG/documents/2012-37.pdf
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    References listed on IDEAS

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    1. Sébastien Courtin & Boniface Mbih & Issofa Moyouwou & Thomas Senné, 2010. "The reinforcement axiom under sequential positional rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 473-500, September.
    2. 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.
    3. Shmuel Nitzan, 1985. "The vulnerability of point-voting schemes to preference variation and strategic manipulation," Public Choice, Springer, vol. 47(2), pages 349-370, January.
    4. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    5. Donald Saari, 2006. "Which is better: the Condorcet or Borda winner?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 107-129, January.
    6. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    7. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    8. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
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    Cited by:

    1. Eric Kamwa, 2017. "Stable Rules for Electing Committees and Divergence on Outcomes," Group Decision and Negotiation, Springer, vol. 26(3), pages 547-564, May.
    2. Kamwa, Eric, 2017. "On stable rules for selecting committees," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 36-44.
    3. Fabrice Barthélémy & Mathieu Martin, 2021. "Dummy Players and the Quota in Weighted Voting Games: Some Further Results," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 299-315, Springer.

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    More about this item

    Keywords

    Condorcet procedures • Reinforcement axiom • Likelihood • Impartial culture • Impartial anonymous culture;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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