Consistent Probabilistic Social Choice
Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic social choice, these axioms are incompatible with each other. We show that in the c...
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Zusammenfassung: | Two fundamental axioms in social choice theory are consistency with respect
to a variable electorate and consistency with respect to components of similar
alternatives. In the context of traditional non-probabilistic social choice,
these axioms are incompatible with each other. We show that in the context of
probabilistic social choice, these axioms uniquely characterize a function
proposed by Fishburn (Rev. Econ. Stud., 51(4), 683--692, 1984). Fishburn's
function returns so-called maximal lotteries, i.e., lotteries that correspond
to optimal mixed strategies of the underlying plurality game. Maximal lotteries
are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always
unique, and can be efficiently computed using linear programming. |
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DOI: | 10.48550/arxiv.1503.00694 |