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A characterization of the single-peaked domain

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Abstract

We provide in this paper two properties that are both necessary and sufficient to characterize the domain of single-peaked preference profiles. This characterization allows for a definition of single-peaked preference profiles without using an ad hoc underlying order of the alternatives and also sheds light on the structure of single-peaked profiles. Considering the larger domain of value-restricted preference profiles (Sen, Econometrica 34:491–499, 1966) we also provide necessary and sufficient conditions for a preference profile to be single-caved or group-separable. Our results show that for single-peaked, single-caved and group-separable profiles it is sufficient to restrict to profiles containing of either three individuals and three alternatives or two individuals and four alternatives.

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Authors and Affiliations

  1. Departament d’Economia i d’Història Econòmica and Barcelona Graduate School of Economics, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain

    Miguel A. Ballester & Guillaume Haeringer

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  1. Miguel A. Ballester
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  2. Guillaume Haeringer
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Correspondence to Guillaume Haeringer.

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Ballester, M.A., Haeringer, G. A characterization of the single-peaked domain. Soc Choice Welf 36, 305–322 (2011). https://doi.org/10.1007/s00355-010-0476-3

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  • DOI: https://doi.org/10.1007/s00355-010-0476-3

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