Binary-Report Peer Prediction for Real-Valued Signal Spaces

Theoretical guarantees about peer prediction mechanisms typically rely on the discreteness of the signal and report space. However, we posit that a discrete signal model is not realistic: in practice, agents observe richer information and map their signals to a discrete report. In this paper, we formalize a model with real-valued signals and binary reports. We study a natural class of symmetric strategies where agents map their information to a binary value according to a single real-valued threshold. We characterize equilibria for several well-known peer prediction mechanisms which are known to be truthful under the binary report model. In general, even when every threshold would correspond to a truthful equilibrium in the binary signal model, only certain thresholds remain equilibria in our model. Furthermore, by studying the dynamics of this threshold, we find that some of these equilibria are unstable. These results suggest important limitations for the deployment of existing peer prediction mechanisms in practice.