Robust rationality and decisions under severe uncertainty

Abstract

This paper develops a prescriptive approach to decision-making with severely uncertain information, and explores risk-taking behavior, based on non-probabilistic set-models of information-gap uncertainty. Info-gap models are well suited for representing uncertainty arising from severe lack of information, and lead naturally to a decision strategy which maximizes the decision-maker's immunity to uncertainty, while also achieving no less than a specified minimum reward. We prove a “gambler's theorem” which quantifies the trade-off between reward and immunity to uncertainty. This trade-off forces the decision-maker to gamble, but without employing a probabilistic framework. We present a complementary theorem expressing the trade-off between immunity and windfall reward, and a further result characterizing the antagonism between robustness to failure and opportunity for success. Next, we develop a measure of risk-sensitivity based on the idea of immunity to uncertainty, without any probabilistic underpinning and without the assumptions of von Neumann–Morgenstern utility theory. We prove a theorem which establishes the relation between a decision-maker's aversion to uncertainty and the information which is available to him. Our final theorem establishes conditions in which the magnitude of the decision-maker's commitment of resources will increase with his fondness for risk.