Strategy-proof social choice with exogenous indifference classes

There are many situations where the indifference classes of the agents’ preferences are exogenously given. We present a framework for dealing with such situations and find that the cardinality of the set S, which consists of alternatives that every agent ranks strictly, is critical to the construction of a strategyproof social choice function; if |S| ≥ 3, then strategy-proofness implies dictatorship, if |S| = 2, then strategy-proofness and efficiency imply dictatorship, and if |S| < 2, then strategyproofness and efficiency do not necessarily imply dictatorship. © 2008 Elsevier B.V. All rights reserved.