Theory of Probability &Its Applications, Volume 65, Issue 2, Page 292-321, January 2020.
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.

中文翻译：

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通过后验概率进行的激励兼容调查

概率论及其应用，第65卷，第2期，第292-321页，2020年1月。
当受访者在调查计划者不可知的共同点之前有共同的看法时，我们考虑引起对调查问题做出真实回答的问题。因此，计划者希望有一个``通用''机制，该机制将为所有可能的先验问题提供诚实的答案。如果计划者还要求一个局部性条件，以确保机制收益是由受访者的真实自然状态的后验概率确定的，那么我们证明，在额外的平滑度和敏感度条件下，讲真相的收益必须是这些后验概率的对数函数。此外，受访者必须根据这些概率进行排名。最后，我们讨论实施问题。