Informed Truthfulness in Multi-Task Peer Prediction

The problem of peer prediction is to elicit information from agents in settings without any objective ground truth against which to score reports. Peer prediction mechanisms seek to exploit correlations between signals to align incentives with truthful reports. A long-standing concern has been the possibility of uninformative equilibria. For binary signals, a multi-task mechanism [Dasgupta-Ghosh '13] achieves strong truthfulness, so that the truthful equilibrium strictly maximizes payoff. We characterize conditions on the signal distribution for which this mechanism remains strongly-truthful with non-binary signals, also providing a greatly simplified proof. We introduce the Correlated Agreement (CA) mechanism, which handles multiple signals and provides informed truthfulness: no strategy profile provides more payoff in equilibrium than truthful reporting, and the truthful equilibrium is strictly better than any uninformed strategy (where an agent avoids the effort of obtaining a signal). The CA mechanism is maximally strongly truthful, in that no mechanism in a broad class of mechanisms is strongly truthful on a larger family of signal distributions. We also give a detail-free version of the mechanism that removes any knowledge requirements on the part of the designer, using reports on many tasks to learn statistics while retaining epsilon-informed truthfulness.