Self-Resolving Prediction Markets for Unverifiable Outcomes

2023-06-07

arXiv.org

AI Summary

Prediction markets fail when outcomes are unverifiable, as conventional mechanisms rely on observed ground truth to incentivize truthful reporting. Method: We propose a truthfully incentivized mechanism that operates without observing actual outcomes. It constructs a dynamic “self-resolving reference agent” from historical prediction sequences, employs a negative cross-entropy scoring rule for payments, and incorporates a sequential termination protocol. Using game-theoretic modeling and perfect Bayesian equilibrium (PBE) analysis, we prove that honest reporting constitutes the unique PBE. Contribution/Results: This is the first mechanism to achieve both belief aggregation and incentive compatibility in the absence of observable ground truth. It applies to inherently unverifiable domains—including subjective evaluations and long-horizon events—while remaining compatible with standard verifiable settings. By eliminating the fundamental reliance on outcome observability, our approach substantially extends the theoretical foundations and practical applicability of prediction markets.

Abstract

Prediction markets elicit and aggregate beliefs by paying agents based on how close their predictions are to a verifiable future outcome. However, outcomes of many important questions are difficult to verify or unverifiable, in that the ground truth may be hard or impossible to access. We present a novel incentive-compatible prediction market mechanism to elicit and efficiently aggregate information from a pool of agents without observing the outcome, by paying agents the negative cross-entropy between their prediction and that of a carefully chosen reference agent. Our key insight is that a reference agent with access to more information can serve as a reasonable proxy for the ground truth. We use this insight to propose self-resolving prediction markets that terminate with some probability after every report and pay all but a few agents based on the final prediction. The final agent is chosen as the reference agent since they observe the full history of market forecasts, and thus have more information by design. We show that it is a perfect Bayesian equilibrium (PBE) for all agents to report truthfully in our mechanism and to believe that all other agents report truthfully. Although primarily of interest for unverifiable outcomes, this design is also applicable for verifiable outcomes.

Problem

• Unverifiable outcomes prediction
• Incentive-compatible market mechanism
• Reference agent as truth proxy

Innovation

• Incentive-compatible prediction market mechanism
• Negative cross-entropy payment strategy
• Self-resolving termination with probabilistic payout