For a society that consists of at least three individuals, we show that a social choice rule is Maskin monotonic if and only if it is Nash implementable by means of a mechanism that is stochastic or a mechanism that contains (arbitrary) awards. In equilibrium, the mechanisms do not have any...

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...

In many, if not most, elections, several different seats must be filled, so that a group of candidates, or an assembly, is selected. Typically in these elections, voters cast their ballots on a seat-by-seat basis. We show that these seat-by-seat procedures are efficient only under extreme...