Pivot mechanisms as a link between probability and preference revelation
This paper defines a pivot mechanism for revealing probability judgments and explores a parallel between pivot mechanisms in two Bayesian games: one for probability revelation and the other for preference revelation. The main result is that Bayesian equilibria must satisfy a simple fixed point property (which can be used constructively to find equilibria). The result provides simplification and extension of previous results for the Groves mechanism and kth price auctions. Further, pivot mechanisms generalize proper scoring rules, provide an analytic tool for optimizing research incentives, and under some conditions outperform proper scoring rules.