Experiments in the Linear Convex Order

This paper proposes two rankings of statistical experiments using the linear convex order. These rankings hold in a broader set of scenarios where intuition suggests that one experiment is more informative than another, and provide more tractable characterizations than Blackwell order, which relies on the convex order. We apply these rankings to compare statistical experiments in binary-action decision problems and in decision problems that aggregate payoffs over a collection of binary-action decision problems. Furthermore, these rankings enable comparisons of statistical experiments in moral hazard problems without requiring the validity of the first-order approach, thereby complementing the results in Holmstr\"om (1979) and Kim (1995).