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La démocratie : oui, mais laquelle?

  • Truchon, Michel

    (CRÉFA, Université Laval)

This paper uses the results of a poll held at Université Laval to illustrate the difficulty in aggregating individual preferences. In this poll, voters were asked to rank four candidates for a position of dean. The paper provides a brief survey of the literature on the theory of social choice, from which it borrows heavily. It first shows how apparently clear results, from the perspective of the plurality rule, may violate the Condorcet principle according to which a candidate who is ranked ahead of another candidate by a majority of voters should also come ahead in the collective ranking. Next, it presents weighted majority procedures, or positional rules, among which the plurality rule and the Borda count. It discusses manipulation of these rules as a function of the weighting scheme. Going back to the Condorcet principle, it is well known that its application to all pairs of candidates may yield a cycle. This is the famous Condorcet paradox. Many procedures have been proposed to break these cycles while retaining the Condorcet principle whenever possible. This paper advocates for the maximum likelihood procedure as the more natural way out of these cycles. Many examples are provided. Cet article illustre les difficultés inhérentes au processus démocratique à partir des résultats d’une consultation tenue à l’Université Laval, dans le cadre de la nomination d’un doyen. Lors de ce scrutin, les votants devaient en principe ordonner tous les candidats, au nombre de quatre. La compilation des résultats s’avérait donc un exercice d’agrégation des ordres (préférences) individuels en ordre (préférence) collectif. L’article emprunte abondamment à la littérature sur la théorie des choix sociaux et constitue en quelque sorte un survol partiel de cette dernière. Il montre d’abord comment des résultats, en apparence si clairs selon la règle de la pluralité, peuvent venir en contradiction avec le principe de la majorité préconisé par Condorcet. Ce dernier veut qu’un candidat, que la majorité des votants placent avant un autre, se retrouve également avant ce dernier dans l’ordre collectif. L’article présente ensuite les procédures de vote pondéré, les plus connues étant celles de la pluralité et de Borda. Il discute des possibilités de manipulation de ces procédures selon le système de pondération choisi. Pour revenir au principe de Condorcet, son application à toutes les paires de candidats peut malheureusement donner des cycles dans les préférences collectives. C’est le fameux paradoxe de Condorcet. Plusieurs méthodes ont été proposées pour briser ces cycles. L’article présente la méthode dite du maximum de vraisemblance comme celle qui se rapproche davantage de l’esprit du principe de Condorcet. Plusieurs exemples sont fournis tout au long de l’article.

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Article provided by Société Canadienne de Science Economique in its journal L'Actualité économique.

Volume (Year): 75 (1999)
Issue (Month): 1 (mars-juin-septembre)
Pages: 189-214

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Handle: RePEc:ris:actuec:v:75:y:1999:i:1:p:189-214
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  1. Truchon, Michel, 1998. "An Extension of the Concordet Criterion and Kemeny Orders," Cahiers de recherche 9813, Université Laval - Département d'économique.
  2. Yves Balasko & Hervé Crès, 1995. "The Probability of Condorcet Cycles and Super Majority Rules," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 95.01, Institut d'Economie et Econométrie, Université de Genève.
  3. Truchon, M., 1993. "Voting Games and Acyclic Collective Choice Rules," Papers 9315, Laval - Recherche en Politique Economique.
  4. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
  5. Saari, Donald G, 1990. " Susceptibility to Manipulation," Public Choice, Springer, vol. 64(1), pages 21-41, January.
  6. Donald G. Saari, 1985. "The Optimal Ranking Method is the Borda Count," Discussion Papers 638, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Robert J. Weber, 1995. "Approval Voting," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 39-49, Winter.
  8. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, June.
  9. Le Breton, M. & Truchon, M., 1993. "Acyclicity and the Dispersion of the Veto Power," Papers 9317, Laval - Recherche en Politique Economique.
  10. Le Breton, Michel & Truchon, Michel, 1997. "A Borda measure for social choice functions," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 249-272, October.
  11. Jonathan Levin & Barry Nalebuff, 1995. "An Introduction to Vote-Counting Schemes," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 3-26, Winter.
  12. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
  13. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
  14. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  15. Simpson, Paul B, 1969. "On Defining Areas of Voter Choice: Professor Tullock on Stable Voting," The Quarterly Journal of Economics, MIT Press, vol. 83(3), pages 478-90, August.
  16. 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.
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