Ranking Statistical Experiments via the Linear Convex Order and the Lorenz Zonoid: Economic Applications

TL;DR

This paper develops a new method for ranking statistical experiments based on the linear convex order and Lorenz zonoid, with applications in economic decision-making scenarios such as moral hazard and screening problems.

Contribution

It introduces the linear-Blackwell (LB) order, a novel ranking criterion for experiments, characterized by dispersion, Lorenz zonoid size, and posterior mean variability.

Findings

LB order provides a consistent ranking of experiments.

Application to economic decision problems demonstrates its practical relevance.

The approach unifies various concepts of experiment comparison.

Abstract

This paper introduces a novel ranking of statistical experiments, the linear-Blackwell (LB) order, which can equivalently be characterized by (i) the dispersion of the induced posterior and likelihood ratios in the sense of the linear convex order, (ii) the size of the Lorenz zonoid (the set of statewise expectation profiles), or (iii) the variability of the posterior mean. We apply the LB order to compare experiments in binary-action decision problems and in decision problems with quasi-concave payoffs, as analyzed by Kolotilin, Corrao, and Wolitzky (2025). We also use it to compare experiments in moral hazard problems, building on Holmstr\"om (1979) and Kim (1995), and in screening problems with ex post signals.