Robust forecast aggregation via additional queries
Rafael Frongillo, Mary Monroe, Eric Neyman, Bo Waggoner
TL;DR
This paper addresses robust forecast aggregation by enriching expert reports with structured, DAG-elicitable queries, enabling near-optimal aggregation under worst-case information structures. It introduces three complexity measures—query, order, and agent complexity—and proves that optimal error can be achieved with at most n queries. When the query budget is limited to d, the best achievable error scales as 1 − d/n, with tighter bounds under restrictions on agent/order complexity, including 1 − Θ(d^2/n) or exponential decay for larger d. The results demonstrate that modest, incentive-compatible query extensions dramatically enhance robustness and open avenues for further research in elicitation and information-theoretic analysis of aggregation.
Abstract
We study the problem of robust forecast aggregation: combining expert forecasts with provable accuracy guarantees compared to the best possible aggregation of the underlying information. Prior work shows strong impossibility results, e.g. that even under natural assumptions, no aggregation of the experts' individual forecasts can outperform simply following a random expert (Neyman and Roughgarden, 2022). In this paper, we introduce a more general framework that allows the principal to elicit richer information from experts through structured queries. Our framework ensures that experts will truthfully report their underlying beliefs, and also enables us to define notions of complexity over the difficulty of asking these queries. Under a general model of independent but overlapping expert signals, we show that optimal aggregation is achievable in the worst case with each complexity measure bounded above by the number of agents $n$. We further establish tight tradeoffs between accuracy and query complexity: aggregation error decreases linearly with the number of queries, and vanishes when the "order of reasoning" and number of agents relevant to a query is $ω(\sqrt{n})$. These results demonstrate that modest extensions to the space of expert queries dramatically strengthen the power of robust forecast aggregation. We therefore expect that our new query framework will open up a fruitful line of research in this area.