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Incentive-Compatible Surveys via Posterior Probabilities

Cvitanić, J. and Prelec, D. and Radas, S. and Šikić, H. (2020) Incentive-Compatible Surveys via Posterior Probabilities. Theory of Probability & Its Applications, 65 (2). pp. 292-321. ISSN 0040-585X. doi:10.1137/s0040585x97t989957.

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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.

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Additional Information:© 2020 Society for Industrial and Applied Mathematics. Received by the editors October 7, 2018. This paper was presented at the conference “Innovative Research in Mathematical Finance” (September 3-7, 2018, Marseille, France). A previous version of this article circulated under the title “Mechanism design for an agnostic planner: Universal mechanisms, logarithmic equilibrium payoffs and implementation.” The first author was supported in part by NSF grant DMS 1810807. The second author was supported by Intelligence Advanced Research Projects Activity (IARPA) via the Department of Interior National Business Center (contract number D11PC20058). The third author was supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme (grant PIOF-GA-2013-622868-BayInno). The fourth author was supported in part by the MZOS grant 037-0372790-2799 of the Republic of Croatia and in part by Croatian Science Foundation under the project 3526. Originally published in the Russian journal Teoriya Veroyatnostei i ee Primeneniya, 65 (2020), pp. 368–408. We are grateful to George Georgiadis, Matthew Elliott, Katrina Ligett, and Patrick Ray, the conference audiences at the Southwest Economic Theory Conference 2014, 13th Conference on Research on Economic Theory and Econometrics, and the 2017 Bayesian Crowd Conference, and to the anonymous referees for useful comments and suggestions. The views and conclusions expressed herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DoI/NBC, or the U.S. Government.
Funding AgencyGrant Number
Intelligence Advanced Research Projects Activity (IARPA)D11PC20058
Marie Curie FellowshipPIOF-GA-2013-622868-BayInno
Ministry of Science and Education (Croatia)037-0372790-2799
Croatian Science Foundation3526
Subject Keywords:proper scoring rules, robust/universal mechanisms, Bayesian truth serum, mechanism implementation, ranking experts
Issue or Number:2
Record Number:CaltechAUTHORS:20201001-101339197
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Official Citation:Incentive-Compatible Surveys via Posterior Probabilities J. Cvitanić, D. Prelec, S. Radas, and H. Šikić Theory of Probability & Its Applications 2020 65:2, 292-321; doi: 10.1137/s0040585x97t989957
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105718
Deposited By: Tony Diaz
Deposited On:01 Oct 2020 18:55
Last Modified:16 Nov 2021 18:45

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