Blackwell without Priors

Abstract: This paper proposes a fully prior-free model of experimentation in which the decision maker observes the entire distribution of signals generated by a known experiment under an unknown distribution of the state of the world. One experiment is robustly more informative than another if the decision maker's maxmin expected utility after observing the output of the former is always at least her maxmin expected utility after observing the latter. We show that this ranking holds if and only if the less informative experiment is a linear transformation of the more informative experiment; equivalently, the null space of the more informative experiment is a subset of the null space of the less informative experiment. Our criterion is implied by Blackwell's order but does not imply it, and we show by example that our ranking admits strictly more comparable pairs of experiments than the classical ranking.