Strictly Proper Scoring Mechanisms Without Expected Arbitrage

Abstract

When eliciting forecasts from a group of experts, it is important to reward predictions so that market participants are incentivized to tell the truth. Existing mechanisms partially accomplish this but remain susceptible to groups of experts colluding to increase their expected reward, meaning that no aggregation of predictions can be fully trusted to represent the true beliefs of forecasters. This paper presents two novel scoring mechanisms which elicit truthful forecasts from any group of experts, even if they can collude or access each other's predictions. The key insight of this approach is a randomization component which maintains strict properness but prevents experts from coordinating dishonest reports in advance. These mechanisms are strictly proper and do not admit expected arbitrage, resolving an open question in the field.