On Strategy-Proofness and Semilattice Single-Peakedness

Abstract

We study social choice rules defined on the domain of semilattice singlepeaked preferences. Semilattice single-peakedness has been identified as the necessary condition that a set of preferences must satisfy so that the set can be the domain of a strategy-proof, tops-only, anonymous and unanimous rule. We characterize the class of all such rules on that domain and show that they are deeply related to the supremum of the underlying semilattice structure.