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A general impossibility result on strategy-proof social choice hyperfunctions. (English) Zbl 1165.91365

Summary: A social choice hyperfunction picks a non-empty set of alternatives at each admissible preference profile over sets of alternatives. We analyze the manipulability of social choice hyperfunctions. We identify a domain \(D^\lambda \) of lexicographic orderings which exhibits an impossibility of the Gibbard-Satterthwaite type. Moreover, this impossibility is inherited by all well-known superdomains of \(D^\lambda \). As most of the standard extension axioms induce superdomains of \(D^\lambda \) while social choice correspondences are particular social choice hyperfunctions, we are able to generalize many impossibility results in the literature.

MSC:

91B14 Social choice
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