Bounded response and the equivalence of nonmanipulability and independence of irrelevant alternatives

Abstract

A social welfare function satisfies Bounded Response if the smallest change in the variable (i.e., preference profile) leads to the smallest change, if any, in the value (i.e., social preference). We show that each social welfare function on each connected domain satisfies Bounded Response and a nonmanipulability condition if and only if it satisfies a monotonicity condition and independence of irrelevant alternatives. Moreover, under Bounded Response, we show the equivalence of various notions of nonmanipulability of social welfare functions.