Monotone Strategyproofness

We propose a way to compare the extent of preference misrepresentation between two strategies. We define a mechanism to be monotone strategyproof when declaring a "more truthful" preference ordering in the mechanism dominates - with respect to the true preferences - declaring a less truthful preference ordering. Our main result states that a mechanism is strategyproof if, and only if, it is monotone strategyproof. This result holds for any deterministic social choice function on any domain; for probabilistic social choice functions it holds under a mild assumption on the domain.