Free Triples, Large Indifference Classes and the Majority Rule
AbstractWe present a new domain of preferences under which the majority relation is always quasi-transitive and thus Condorcet winners always exist. We model situations where a set of individuals must choose one individual in the group. Agents are connected through some relationship that can be interpreted as expressing neighborhood, and which is formalized by a graph. Our restriction on preferences is as follows: each agent can freely rank his immediate neighbors, but then he is indifferent between each neighbor and all other agents that this neighbor "leads to". Hence, agents can be highly perceptive regarding their neighbors, while being insensitive to the differences between these and other agents which are further removed from them. We show quasi-transitivity of the majority relation when the graph expressing the neighborhood relation is a tree. We also discuss a further restriction allowing to extend the result for more general graphs. Finally, we compare the proposed restriction with others in the literature, to conclude that it is independent of any previously discussed domain restriction.
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Bibliographic InfoPaper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 512.02.
Date of creation: 15 May 2002
Date of revision:
Voting; Tree; Majority Rule;
Other versions of this item:
- Salvador Barberà & Lars Ehlers, 2011. "Free triples, large indifference classes and the majority rule," Social Choice and Welfare, Springer, vol. 37(4), pages 559-574, October.
- EHLERS, Lars & BARBERÀ, Salvador, 2007. "Free Triples, Large Indifference Classes and the Majority Rule," Cahiers de recherche 2007-02, Universite de Montreal, Departement de sciences economiques.
- 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.
- Salvador Barberà & Lars Ehlers, 2003. "Free Triples, Large Indifference Classes and the Majority Rule," UFAE and IAE Working Papers 599.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Feb 2007.
- Salvador Barberà & Lars Ehlers, 2003. "Free Triples, Large Indifference Classes and the Majority Rule," Working Papers 15, Barcelona Graduate School of Economics.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-06-13 (All new papers)
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