A general impossibility result on strategy-proof social choice hyperfunctions

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 Dλ of lexicographic orderings which exhibits an impossibility of the Gibbard-Satterthwaite type. Moreover, this impossibility is inherited by all well-known superdomains of Dλ. As most of the standard extension axioms induce superdomains of Dλ while social choice correspondences are particular social choice hyperfunctions, we are able to generalize many impossibility results in the literature.