Quasi-transitive and Suzumura consistent relations

We examine properties of binary relations that complement quasi-transitivity and Suzumura consistency in the sense that they, in conjunction with the original axiom(s), are equivalent to transitivity. In general, the conjunction of quasi-transitivity and Suzumura consistency is weaker than transitivity but in the case of collective choice rules that satisfy further properties, this conjunction implies transitivity of the social relation. We prove this observation by characterizing the Pareto rule as the only collective choice rule such that collective preference relations are quasi-transitive and Suzumura consistent, and standard social choice axioms are satisfied.