Strictly Proper Contract Functions Can Be Arbitrage-Free

TL;DR

This paper introduces a class of contract functions for eliciting expert predictions that are both strictly proper and arbitrage-free, preventing collusive misreporting and ensuring truthful reporting.

Contribution

It provides the first construction of strictly proper, arbitrage-free contract functions that discourage collusion among experts.

Findings

The proposed contract functions depend only on the average report of experts.

Changing the average report can decrease experts' rewards under some outcomes.

The class of functions guarantees truthful reporting and prevents arbitrage.

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. Chun and Shachter (2011) termed any such collusion "arbitrage" and asked whether there is any truthful elicitation mechanism that makes 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.