Distributions of Posterior Quantiles via Matching

Anton Kolotilin and Alexander Wolitzky

No 2024-01, Discussion Papers from School of Economics, The University of New South Wales

Abstract: We offer a simple analysis of the problem of choosing a statistical exper- iment to optimize the induced distribution of posterior medians, or more generally q-quantiles for any q ∈ (0, 1). We show that all implementable distributions of the posterior q-quantile are implemented by a single experiment, the q-quantile matching experiment, which pools pairs of states across the q-quantile of the prior in a positively assortative manner, with weight q on the lower state in each pair. A dense subset of implementable distributions of posterior q-quantiles can be uniquely implemented by perturbing the q-quantile matching experiment. A linear functional is optimized over distributions of posterior q-quantiles by taking the optimal selection from each set of q-quantiles induced by the q-quantile matching experiment. The q-quantile matching experiment is the only experiment that simultaneously implements all implementable distributions of the posterior q-quantile.

Keywords: quantiles; statistical experiments; overconfidence; gerrymandering; persuasion (search for similar items in EconPapers)
JEL-codes: C61 D72 D82 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2024-02
New Economics Papers: this item is included in nep-exp and nep-mic
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Journal Article: Distributions of posterior quantiles via matching (2024)
Working Paper: Distributions of Posterior Quantiles via Matching (2024)
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