Incentive-compatible surveys via posterior probabilities

© by SIAM. We consider the problem of eliciting truthful responses to a survey question when the respondents share a common prior that the survey planner is agnostic about. The planner would therefore like to have a “universal” mechanism, which would induce honest answers for all possible priors. If the planner also requires a locality condition that ensures that the mechanism payoffs are determined by the respondents’ posterior probabilities of the true state of nature, we prove that, under additional smoothness and sensitivity conditions, the payoff in the truth-telling equilibrium must be a logarithmic function of those posterior probabilities. Moreover, the respondents are necessarily ranked according to those probabilities. Finally, we discuss implementation issues.
NSF grant (DMS 1810807)
IARPA - Department of Interior National Business Center (contract number D11PC20058)
Marie Curie International Outgoing Fellowship - 7th European Community Framework Programme (grant PIOF-GA-2013-622868-BayInno)
Republic of Croatia. MZOS grant (037-0372790-2799)
Croatian Science Foundation (project 3526)