Source and rank-dependent utility

Abstract

Foundations are provided for rank-dependent preferences within the popular two-stage framework of Anscombe–Aumann, in which risk and ambiguity feature as distinct sources of uncertainty. We advance the study of attitudes towards ambiguity without imposing expected utility for risk. As a result, in our general model, ambiguity attitude can be captured by non-additive subjective probabilities as under Choquet expected utility or by a specific utility for ambiguity as in recursive expected utility or, if required, by both. The key property for preferences builds on (discrete) rates of substitution which are standardly applied in economics. By demanding consistency for these rates of substitution across events and within or across sources of uncertainty, we obtain a model that nests popular theories for risk and ambiguity. This way, new possibilities for theoretical and empirical analyses of these theories emerge.

Uncertainty and compound lotteries: calibration

“…This is in contrast to the standard approach in the literature which focuses only on the DM's preferences over acts to derive representations of ambiguity averse behavior. 2 In order to model and gain insight into the empirical link between ROCL and ambiguity aversion, we extend the domain of the DM's preferences to include the union of compound lotteries and Savage-acts. This extended domain is just sufficient for our purposes, since if we fix a set of probability measures over the state space, and consider a probability distribution over the measures in this set, each act induces a compound lottery.…”