What majority decisions are possible |
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| Authors: | Saharon Shelah |
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| Institution: | The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA |
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| Abstract: | Suppose we are given a family of choice functions on pairs from a given finite set (with at least three elements) closed under permutations of the given set. The set is considered the set of alternatives (say candidates for an office). The question is, what are the choice functions c on pairs of this set of the following form: for some (finite) family of “voters”, each having a preference, i.e. a choice from each pair from the given family,  is chosen by the preference of the majority of voters. We give full characterization. |
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| Keywords: | Choice function Majority decision Condorcet&rsquo s paradox Tournament |
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