Robust rationality and decisions under severe uncertainty

✍ Scribed by Yakov Ben-Haim

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 250 KB
• Volume: 337
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(00)00016-8

✦ Synopsis

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 speci"ed minimum reward. We prove a `gambler's theorema which quanti"es the trade-o! between reward and immunity to uncertainty. This trade-o! forces the decision-maker to gamble, but without employing a probabilistic framework. We present a complementary theorem expressing the trade-o! 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 "nal theorem establishes conditions in which the magnitude of the decision-maker's commitment of resources will increase with his fondness for risk.