Information Comparison of Order Statistics, with Applications to Auctions and Voting

Alfredo Di Tillio, Marco Ottaviani and Sørensen, Peter

No 21759, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: We compare the informativeness of order statistics in a sample of conditionally independent draws from a distribution F(x|θ) as the sample size n increases. The k-th highest of n+1 draws is more accurate than the k-th highest of n if and only if the cumulative reverse hazard − log F(x|θ) is log-supermodular. Symmetrically, the k-th lowest is more accurate if and only if the cumulative hazard − log (1−F(x|θ)) is log-supermodular. Reversals are exceptional, occurring only for experiments that are, up to increasing transformations, exponential location experiments. In large samples, middle order statistics are asymptotically fully informative, while bounded lower and upper ranks require unbounded informativeness tail conditions. When full learning fails, bounded ranks converge to location experiments, and more central ranks are Blackwell more informative. Extending the analysis from scalar order statistics to blocks of selected data, we obtain multidimensional comparisons under log-supermodularity of hazard rates. The results unify and extend information-aggregation results in auctions and provide a new order-statistic approach to strategic voting.

Keywords: Accuracy (search for similar items in EconPapers)
JEL-codes: C72 C90 D82 D83 (search for similar items in EconPapers)
Date: 2026-07
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