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. Examples include questions about causal effects where it is infeasible or unethical to run randomized trials; crowdsourcing and content moderation tasks where it is prohibitively expensive to verify ground truth; and questions asked over long time horizons, where the delay until the realization of the outcome skews agents' incentives to report their true beliefs. We present a novel and unintuitive result showing that it is possible to run an $\varepsilon-$incentive compatible prediction market 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. We show that it is an $\varepsilon-$Perfect Bayesian Equilibrium 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.

翻译：预测市场通过根据代理人预测与可验证未来结果的接近程度支付报酬，来激发和聚合信念。然而，许多重要问题的结果难以验证或不可验证——其真实答案可能难以或无法获取。这类问题包括：因不可行或不道德而无法开展随机试验的因果效应问题；因验证真实答案成本过高而受限的众包与内容审核任务；以及时间跨度较长的问题（结果实现的延迟会扭曲代理人报告真实信念的动机）。我们提出一个新颖且反直觉的结论：通过向代理人支付其预测与精心选择的参考代理人预测之间的负交叉熵作为报酬，可以在不观察结果的情况下运行一个ε-激励兼容的预测市场，从而从代理人群体中激发并高效聚合信息。我们的核心洞见是：拥有更多信息渠道的参考代理人可作为真实答案的合理代理。基于这一洞见，我们提出了自我解析预测市场——该市场在每轮报告后以一定概率终止，并根据最终预测向除少数代理人外的所有参与者支付报酬。我们证明，在该机制中，所有代理人真实报告且相信其他代理人同样真实报告构成一个ε-完美贝叶斯均衡。该设计虽主要针对不可验证结果，但对可验证结果同样适用。