We study one-sided matching mechanisms where agents have vNM utility functions and report ordinal preferences. We first show that in this domain strategyproof mechanisms are characterized by three intuitive axioms: swap consistency, weak invariance, and lower invariance. Our second result is that dropping lower invariance leads to an interesting new relaxation of strategyproofness, which we call partial strategyproofness.
In particular, we show that mechanisms are swap consistent and weakly invariant if and only if they are strategyproof on a restricted domain where agents have sufficiently different valuations for different objects. Furthermore, we show that this domain restriction is maximal and use it to define a single-parameter measure for the degree of strategyproofness of a mechanism. We also provide an algorithm that computes this measure. Our new partial strategyproofness concept finds applications in the incentive analysis of non-strategyproof mechanisms, such as the Probabilistic Serial mechanism, different variants of the Boston mechanism, and the construction of new hybrid mechanisms. [pdf]