A Borda measure for social choice functions
AbstractThe question addressed in this paper is the order of magnitude of the difference between the Borda rule and any given social choice function. A social choice function is a mapping that associates a subset of alternatives to any profile of individual preferences. The Borda rule consists in asking voters to order all alternatives, knowing that the last one in their ranking will receive a score of zero, the second lowest a score of 1, the third a score of 2 and so on. These scores are then weighted by the number of voters that support them to give the Borda score of each alternative. The rule then selects the alternatives with the highest Borda score. In this paper, a simple measure of the difference between the Borda rule and any given social choice function is proposed. It is given by the ratio of the best Borda score achieved by the social choice function under scrutiny over the Borda score of a Borda winner. More precisely, it is the minimum of this ratio over all possible profiles of preferences that is used. This "Borda measure" or at least bounds for this measure is also computed for well known social choice functions. Cet article se penche sur la distance entre la rÃ¨gle de Borda et n'importe quelle autre fonction de choix social. Ces derniÃ¨res associent un sous-ensemble d'options possibles Ã tout profil ou configuration de prÃ©fÃ©rences individuelles. La rÃ¨gle de Borda consiste Ã demander aux votants d'ordonner les options possibles, en leur disant que la derniÃ¨re dans leur ordre recevra un score nul, l'avant-derniÃ¨re un score Ã©gal Ã 1, celle qui vient au troisiÃ¨me pire rang un score Ã©gal Ã 2 et ainsi de suite. Ces scores sont ensuite pondÃ©rÃ©s par le nombre de votants qui les supportent pour donner le score de Borda de chaque option. La rÃ¨gle choisit les options qui ont reÃ§u le score le plus Ã©levÃ©. Dans cet article, une mesure simple de la diffÃ©rence entre la rÃ¨gle de Borda et n'importe quelle autre fonction de choix social est pro
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Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 34 (1997)
Issue (Month): 3 (October)
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Web page: http://www.elsevier.com/locate/inca/505565
Other versions of this item:
- Le Breton, Michel & Truchon, Michel, 1996. "A Borda Measure for Social Choice Functions," Cahiers de recherche 9602, Université Laval - Département d'économique, revised Jun 1997.
- Le Breton, M. & Truchon, M., 1996. "A Borda Measure for Social Choice Functions," Papers 9602, Laval - Recherche en Politique Economique.
- D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Saari, Donald G, 1990. " Susceptibility to Manipulation," Public Choice, Springer, vol. 64(1), pages 21-41, January.
- Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
- Saari, Donald G., 1989. "A dictionary for voting paradoxes," Journal of Economic Theory, Elsevier, vol. 48(2), pages 443-475, August.
- I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
- 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.
- Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
- 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.
- Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
- Truchon, Michel, 1999.
"La démocratie : oui, mais laquelle?,"
Société Canadienne de Science Economique, vol. 75(1), pages 189-214, mars-juin.
- Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
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