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