Strictly Proper Contract Functions Can Be Arbitrage-Free

Abstract

We consider mechanisms for truthfully eliciting probabilistic predictions from a group of experts. The standard approach --- using a proper scoring rule to separately reward each expert --- is not robust to collusion: experts may collude to misreport their beliefs in a way that guarantees them a larger total reward no matter the eventual outcome. It is a long-standing open question whether there is a truthful elicitation mechanism that makes any such collusion (also called "arbitrage") impossible. We resolve this question positively, exhibiting a class of strictly proper arbitrage-free contract functions. These contract functions have two parts: one ensures that the total reward of a coalition of experts depends only on the average of their reports; the other ensures that changing this average report hurts the experts under at least one outcome.