Incentive-Compatible Surveys via Posterior Probabilities
- Creators
- Cvitanić, J.
- Prelec, D.
- Radas, S.
- Šikić, H.
Abstract
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.
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.Attached Files
Published - s0040585x97t989957.pdf
Submitted - Prelec.pdf
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Additional details
- Eprint ID
- 105718
- Resolver ID
- CaltechAUTHORS:20201001-101339197
- DMS-1810807
- NSF
- D11PC20058
- Intelligence Advanced Research Projects Activity (IARPA)
- PIOF-GA-2013-622868-BayInno
- Marie Curie Fellowship
- 037-0372790-2799
- Ministry of Science and Education (Croatia)
- 3526
- Croatian Science Foundation
- Created
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2020-10-01Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field