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From Means to Medians: Optimal Benchmark Design

2025/06/27 by Ángel Hernando-Veciana, Hernando-Veciana, Ángel
Computer Science · Decision Sciences · Business, Management and Accounting · #Blockchain Technology Applications and Security #Auction Theory and Applications #Digital Platforms and Economics

paper · pdf · doi:10.48550/arxiv.2506.22142

Abstract

Manipulation of price benchmarks has cost hundreds of millions of dollars, making manipulation-resistant design a first-order question. A puzzling empirical pattern offers a starting point: benchmarks in traditional finance are typically means, those in decentralised finance medians. I rationalise this divide with a variable cost rising in each price distortion's size and a fixed cost per manipulated price. The optimal benchmark is a mean when fixed costs are negligible and variable costs convex, a median when variable costs are negligible, and otherwise a trimmed mean, with weights reflecting cost heterogeneity.

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