Incentives for Answering Hypothetical Questions

Prediction markets and other reward mechanisms based on proper scoring rules can elicit accurate predictions about future events with public utcomes. However, many questions of public interest do not always have a clear answer. For example, facts such as the eects of raising or lower-ing interest rates can never be publicly veried, since only one option will be implemented. In this paper we address re-porting incentives for opinion polls and uestionnaires about hypothetical questions, where the honesty of one answer can only be assessed in the context of the other answers elicited through the poll. We extend our previous work on this problem by four main results. First, we prove that no reward mechanism can be strictly incentive compatible when the mechanism designer does not know the prior nformation of the participants. Second, we formalize the notion of help- ful reporting which prescribes that rational agents move the public result of the poll towards what they believe to be the true distribution (even when that involves reporting an answer that is not the agent's rst preference). Third, we show that helpful reporting converges the nal result of the poll to the true distribution of opinions. Finally, we present a reward scheme that makes helpful reporting an equilibrium for polls with an arbitrary number of answers. Our mechanism is simple, and does not require information about the prior beliefs of the agents.