The uniqueness of the pivotal mechanisms without strategy-proofness

Moulin (J Public Econ 31:53–78, 1986; Theorem 4) characterizes the pivotal mechanisms without imposing strategy-proofness under the assumption of the full domain. In this paper, we provide a domain property that is necessary and sufficient for Moulin’s characterization without strategy-proofness to hold. We also provide examples of domains that do (not) satisfy our domain property.