  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.
