An Axiomatic Characterization of Strategyproof Ordinal Mechanisms with Indifferences

An ordinal mechanism is a mechanism that takes as input ordinal preference orderings over outcomes and selects a lottery over the outcomes, e.g., most matching mechanisms. In (Mennle and Seuken, 2014) we have given an axiomatic characterization of strategyproof ordinal mechanisms when the agent is not indifferent between outcomes: a mechanism is strategyproof if and only if it is swap monotonic, upper invariant, and lower invariant. In this note, we extend the axioms the the case of indifferences. We then show that the extended axioms characterize strategyproof ordinal mechanisms in this larger domain. Our axioms separation monotonicity, separation upper invariance, and separation lower invariance coincide with the original axioms in the domain without indifferences. 1 Model We consider a set of outcomes M . An agent’s weak ordinal preference order over these outcomes is denoted by ¡: for some partition pMkqkPt1,...,Ku of M the preference order M1 ¡ . . . ¡Mk ¡ . . . ¡MK represents the preferences, where the agent • is indifferent between the outcomes j, j1 PMk from the same subset, denoted j j1, • prefers outcome j PMk to outcome j1 PMk1 where k k1, denoted j ¡ j1. We would like to thank Baharak Rastegari for insightful discussions. Department of Informatics, University of Zurich, 8050 Zurich, Switzerland, {mennle, seuken}@ifi.uzh.ch.