Peer prediction mechanisms are typically proposed and analyzed under the assumption that the report and signal spaces are identical. In practice, however, agents often observe richer information which they then map to a coarser report space. Motivated by this discrepancy between theory and practice, we initiate the study of peer prediction mechanisms with signal spaces that are richer than the report space. We begin by formalizing a model with real-valued signals and binary reports. In this setting, it is natural to study symmetric threshold strategies, where agents map their signals to binary reports according to a single real-valued threshold. For several well-known binary-report peer prediction mechanisms, we show that most equilibria under the original assumption of binary signals are no longer equilibria in our model. Furthermore, dynamic analysis proves that some of the remaining thresholds are unstable. These results extend beyond real-valued signals and binary reports to settings where the signal space is finer-grained than the report space. While the results above suggest important limitations for the deployment of existing peer prediction mechanisms in practice, we also use them to develop a new, more robust mechanism. This mechanism generates a larger number of stable threshold equilibria under our model, thus allowing the designer more flexibility in choosing how agents map their signals to reports.

翻译：同伴预测机制通常在假设报告空间与信号空间相同的前提下提出和分析。然而在实践中，智能体常常观察到更丰富的信息，并将其映射到更粗粒度的报告空间。受理论与实践的脱节启发，我们首次研究信号空间比报告空间更丰富的同伴预测机制。我们首先构建一个包含实值信号与二元报告的理论模型。在此设定下，研究对称阈值策略是自然的选择——智能体根据单一实值阈值将信号映射为二元报告。针对几种经典的二元报告同伴预测机制，我们证明在原始二元信号假设下的多数均衡不再适用于我们的模型。进一步，动态分析表明部分剩余阈值具有不稳定性。这些结论不仅适用于实值信号与二元报告的设定，更能推广至信号空间粒度细于报告空间的更广泛场景。虽然上述结果揭示了现有同伴预测机制在实际部署中的重要局限，但我们同时基于这些发现开发出更稳健的新型机制。该机制在我们模型下能产生更多稳定的阈值均衡，从而赋予设计者更大的灵活性来选择智能体映射信号至报告的方式。