Arrow's Possibility Theorem for one-dimensional single-peaked preferences |
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Authors: | Lars Ehlers Ton Storcken |
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Institution: | aDépartement de Sciences Économiques and CIREQ, Université de Montréal, CP 6128, Succ. Centre Ville, Montréal, PQ H3C 3J7, Canada;bDepartment of Quantitative Economics, Maastricht University, PO Box 616, 6200 MD Maastricht, The Netherlands |
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Abstract: | In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow's requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. |
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Keywords: | Arrovian social choice One-dimensional continuum Single-peaked preferences |
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