Minimax decision rules for planning under uncertainty: Drawbacks and remedies

Abstract

It is common to use minimax rules to make planning decisions when there is great uncertainty about what may happen in the future. Using minimax rules avoids the need to determine probabilities for each future scenario, which is an attractive feature in many public sector settings. However there are potential problems in the application of a minimax approach. In this paper our aim is to give guidance for planners considering a minimax approach, including minimax regret which is one popular version of this. We give an analysis of the behaviour of minimax rules in the case with a finite set of possible future scenarios. Minimax rules will have sensitivity to the choice of a small number of scenarios. When regret-based rules are used there are also problems arising since the independence of irrelevant alternatives property fails, which can lead to opportunities to game the process. We analyse these phenomena considering cases where the decision variables are chosen from a convex set in Rn, as well as cases with a finite set of decision choices. We show that the drawbacks of minimax regret hold even when restrictions are placed on the problem setup, and we show how working with a structured set of scenarios can ameliorate the difficulty of having a final decision depend on the characteristics of just a handful of extreme scenarios.