Peer Prediction with More Signals than Reports
This addresses a practical limitation in deploying peer prediction mechanisms for eliciting truthful information from agents in real-world settings, though it is incremental in refining existing theory.
The paper tackles the mismatch between peer prediction theory, which assumes identical signal and report spaces, and practice, where agents have richer signals but coarser reports, by analyzing mechanisms with real-valued signals and binary reports. It finds that most equilibria from binary-signal models break down, with some thresholds unstable, but develops a new mechanism that yields more stable threshold equilibria for better designer flexibility.
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.