Quantile Maximization in Decision Theory

This paper introduces a model of preferences, in which, given beliefs about uncertain outcomes, an individual evaluates an action by a quantile of the induced distribution. The choice rule of Quantile Maximization unifies maxmin and maxmax as maximizing the lowest and the highest quantiles of beliefs distributions, respectively, and offers a family of less extreme preferences. Taking preferences over acts as a primitive, we axiomatize Quantile Maximization in a Savage setting. Our axiomatization also provides a novel derivation of subjective beliefs, which demonstrates that neither the monotonicity nor the continuity conditions assumed in the literature are essential for probabilistic sophistication. We characterize preferences of quantile maximizers towards downside risk. We discuss how the distinct properties of the model, robustness and ordinality, can be useful in studying choice behaviour for categorical variables and in economic policy design. We also offer applications to poll design and insurance problems. Copyright , Wiley-Blackwell.