Abstract
We study classes of voting situations where agents may exhibit a systematic inability to distinguish between the elements of certain sets of alternatives. These sets of alternatives may differ from voter to voter, thus resulting in personalized families of preferences. We study the properties of the majority relation when defined on restricted domains that are the cartesian product of preference families, each one reflecting the corresponding agent’s objective indifferences, and otherwise allowing for all possible (strict) preference relations among alternatives. We present necessary and sufficient conditions on the preference domains of this type, guaranteeing that majority rule is quasi-transitive and thus the existence of Condorcet winners at any profile in the domain, and for any finite subset 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.
Similar content being viewed by others
References
Black D (1948) On the rationale of group decision-making. J Polit Econ 56: 23–34
Demange G (1982) Single-peaked orders on a tree. Math Soc Sci 3: 389–396
Demange G (2004) On group stability in hierarchies and networks. J Polit Econ 112: 754–778
Dutta B, Jackson MO, Le Breton M (2001) Strategic candidacy and voting procedures. Econometrica 69: 1013–1037
Gaertner W (2001) Domain conditions in social choice theory. Cambridge University Press, Cambridge
Grandmont J-M (1978) Intermediate preferences and the majority rule. Econometrica 46: 317–330
Inada K-I (1964) A note on the simple majority decision rule. Econometrica 32: 525–531
Inada K-I (1969) The simple majority decision rule. Econometrica 37: 490–506
Pérez-Castrillo JD, Wettstein David (2002) Choosing wisely: a multi-bidding approach. Am Econ Rev 92: 1577–1587
Plott CR (1973) Path independence, rationality, and social choice. Econometrica 41: 1075–1091
Salles M (1976) Characterization of transitive individual preferences for quasi-transitive collective preference for simple games. Int Econ Rev 17: 308–318
Sen A, Pattanaik PK (1969) Necessary and sufficient conditions for rational choice under majority decision. J Econ Theory 1: 178–202
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Barberà, S., Ehlers, L. Free triples, large indifference classes and the majority rule. Soc Choice Welf 37, 559–574 (2011). https://doi.org/10.1007/s00355-011-0584-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-011-0584-8