Decision Making Under Interval Uncertainty: Towards (Somewhat) More Convincing Justifications for Hurwicz Optimism-Pessimism Approach

Authors

Warattaya Chinnakum, Chiang Mai UniversityFollow
Laura Berrout Ramos, The University of Texas at El PasoFollow
Olugbenga Iyiola, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

3-2020

Comments

Technical Report: UTEP-CS-20-23

Abstract

In the ideal world, we know the exact consequences of each action. In this case, it is relatively straightforward to compare different possible actions and, as a result of this comparison, to select the best action. In real life, we only know the consequences with some uncertainty. A typical example is interval uncertainty, when we only know the lower and upper bounds on the expected gain. How can we compare such interval-valued alternatives? A usual way to compare such alternatives is to use the optimism-pessimism criterion developed by Nobelist Leo Hurwicz. In this approach, we maximize a weighted combination of the worst-case and the best-case gains, with the weights reflecting the decision maker's degree of optimism. There exist several justifications for this criterion; however, some of the assumptions behind these justifications are not 100\% convincing. In this paper, we propose new, hopefully more convincing justifications for Hurwicz's approach.