A characterization of the single-peaked domain |
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Authors: | Miguel A Ballester Guillaume Haeringer |
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Institution: | 1. Departament d??Economia i d??Hist??ria Econ??mica and Barcelona Graduate School of Economics, Universitat Aut??noma de Barcelona, Bellaterra (Barcelona), Spain
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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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