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Free Triples, Large Indifference Classes and the Majority Rule

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  • EHLERS, Lars
  • BARBERÀ, Salvador

Abstract

We consider situations in which agents are notable to completely distinguish between all alternatives. Preferences respect individual objective indifferences if any two alternatives are indifferent whenever an agent cannot distinguish between them. We present necessary and sufficient conditions of such a domain of preferences under which majority rule is quasi-transitive and thus Condorcet winner sexist for any set of alternatives. Finally, we compare our proposed restrictions with others in the literature, to conclude that they are independent of any previously discussed domain restriction.

Suggested Citation

  • EHLERS, Lars & BARBERÀ, Salvador, 2007. "Free Triples, Large Indifference Classes and the Majority Rule," Cahiers de recherche 02-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  • Handle: RePEc:mtl:montec:02-2007
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    References listed on IDEAS

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    1. David Pérez-Castrillo & David Wettstein, 2002. "Choosing Wisely: A Multibidding Approach," American Economic Review, American Economic Association, vol. 92(5), pages 1577-1587, December.
    2. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    3. 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.
    4. Salles, Maurice, 1976. "Characterization of Transitive Individual Preferences for Quasi-Transitive Collective Preference under Simple Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 308-318, June.
    5. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, December.
    6. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
    7. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, pages 1013-1037.
    8. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, pages 165-184.
    9. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    10. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    11. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
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    Cited by:

    1. repec:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1075-3 is not listed on IDEAS
    2. Anup Pramanik & Arunava Sen, 2016. "Pairwise partition graphs and strategy-proof social choice in the exogenous indifference class model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 1-24, June.
    3. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.

    More about this item

    Keywords

    Quasi-Transitivity; Majority Rule;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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