An Axiomatic Decomposition of Strategyproofness for Ordinal Mechanism with Indifferences

Abstract: We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three axioms: separation monotonic, separation upper invariant, and separation lower invariant. Each axiom is a natural restriction on how mechanisms can react when agents change their opinion about the relative ranking of any two adjacently ranked groups of alternatives. Our result extends a result from (Mennle and Seuken, 2017), a decomposition of strategyproofness for strict preferences, to the full domain that includes weak preferences.