Are the highest sample realizations selected from a larger presample more or less informative than the same amount of random data? Developing multivariate accuracy for interval dominance ordered preferences, we show that sample selection always benefits (or always harms) a decision maker if the reverse hazard rate of the data distribution is log‐supermodular (or log‐submodular), as in location experiments with normal noise. We find nonpathological conditions under which the information contained in the winning bids of a symmetric auction decreases in the number of bidders. Exploiting extreme value theory, we quantify the limit amount of information revealed when the presample size (number of bidders) goes to infinity. In a model of equilibrium persuasion with costly information, we derive implications for the optimal design of selected experiments when selection is made by an examinee, a biased researcher, or contending sides with the peremptory challenge right to eliminate a number of jurors.

Previous research has established that the predictions of game theory are quite sensitive to the assumptions made about the players’ beliefs. We evaluate the severity of this robustness problem by characterizing conditions on the primitives of the model—the players’ beliefs and higher-order beliefs about the payoff-relevant parameters—for the behaviour of a given Harsanyi type to be approximated by the behaviour of (a sequence of) perturbed types. This amounts to providing belief-based characterizations of the strategic topologies of Dekel et al. (2006). We apply our characterizations to a variety of questions concerning robustness to perturbations of higher-order beliefs, including genericity of types that are consistent with a common prior, and we investigate the connections between our notions of robustness and the notion of common p-belief of Monderer and Samet (1989).