  Strategyproof mechanisms provide robust equilibrium with minimal assumptions
about knowledge and rationality but can be unachievable in combination with
other desirable properties such as budget-balance, stability against deviations
by coalitions, and computational tractability. In the search for
maximally-strategyproof mechanisms that simultaneously satisfy other desirable
properties, we introduce a new metric to quantify the strategyproofness of a
mechanism, based on comparing the payoff distribution, given truthful reports,
against that of a strategyproof "reference" mechanism that solves a problem
relaxation. Focusing on combinatorial exchanges, we demonstrate that the metric
is informative about the eventual equilibrium, where simple regretbased metrics
are not, and can be used for online selection of an effective mechanism.
