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

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 Holmström (1979) and Kim (1995), and in screening problems with ex post signals.

💡 Research Summary

The paper introduces a new way to rank statistical experiments called the linear‑Blackwell (LB) order. While the classic Blackwell order requires one experiment to be a garbling of another—a very strong condition that is often hard to verify and too restrictive for many economic settings—the LB order relaxes these requirements and remains tractable even when the state space has multiple dimensions.

Three equivalent characterizations define the LB order:

1. Linear convex order (LCO) of posteriors and likelihood ratios – For any weight vector b, the scalar b·p_F(X) (the weighted posterior under experiment F) must be a mean‑preserving spread of b·p_G(Y) (the analogous scalar under G). This condition only involves univariate convex functions, making verification much simpler than the full multivariate convex order required by Blackwell.

2. Inclusion of Lorenz zonoids – Every Borel function h mapping signals to