  Prediction markets elicit and aggregate beliefs by paying agents based on how
close their predictions are to a verifiable future outcome. However, outcomes
of many important questions are difficult to verify or unverifiable, in that
the ground truth may be hard or impossible to access. Examples include
questions about causal effects where it is infeasible or unethical to run
randomized trials; crowdsourcing and content moderation tasks where it is
prohibitively expensive to verify ground truth; and questions asked over long
time horizons, where the delay until the realization of the outcome skews
agents' incentives to report their true beliefs. We present a novel and
unintuitive result showing that it is possible to run an
$\varepsilon-$incentive compatible prediction market to elicit and efficiently
aggregate information from a pool of agents without observing the outcome by
paying agents the negative cross-entropy between their prediction and that of a
carefully chosen reference agent. Our key insight is that a reference agent
with access to more information can serve as a reasonable proxy for the ground
truth. We use this insight to propose self-resolving prediction markets that
terminate with some probability after every report and pay all but a few agents
based on the final prediction. We show that it is an $\varepsilon-$Perfect
Bayesian Equilibrium for all agents to report truthfully in our mechanism and
to believe that all other agents report truthfully. Although primarily of
interest for unverifiable outcomes, this design is also applicable for
verifiable outcomes.
