Forecasting Competitions with Correlated Events

Beginning with Witkowski et al. (2023), recent work on forecasting competitions has addressed incentive problems with the common winner-take-all mechanism. Frongillo et al. (2021) propose a competition mechanism based on Multiplicative Weights, an online learning algorithm. They show that their mechanism selects an epsilon-optimal forecaster with high probability using only O(log(n)/epsilon^2) events. These works, together with all prior work on this problem thus far, assume that events are independent. We prove the first accuracy and approximate truthfulness guarantees for forecasting competitions with correlated events. To quantify correlation, we introduce a notion of block correlation, which allows each event to be strongly correlated with up to b others and weakly correlated with the rest. We show that under distributions with this correlation, the Multiplicative Weights mechanism retains its epsilon-optimal guarantee using O(b^2 log(n)/epsilon^2) events. Our proof involves a novel concentration bound for correlated random variables which may be of broader interest.