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 $R^n$, 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.

当未来可能发生的事情存在很大不确定性时，通常使用极小极大规则来制定计划决策。使用极小极大规则可以避免确定每个未来场景的概率，这在许多公共部门环境中是一个有吸引力的功能。然而，极小极大方法的应用存在潜在的问题。在本文中，我们的目的是为考虑极小极大方法的规划者提供指导，包括极小极大遗憾，这是该方法的一种流行版本。我们分析了在有限的一组可能的未来场景的情况下极小极大规则的行为。极小极大规则将对少数场景的选择具有敏感性。当使用基于遗憾的规则时，也会出现问题，因为不相关的替代属性的独立性失败，这可能会带来对流程进行博弈的机会。我们分析这些现象时考虑到决策变量是从凸集中选择的情况${右}^n$，以及具有有限决策选择集的情况。我们表明，即使对问题设置施加限制，最小最大遗憾的缺点仍然存在，并且我们展示了如何使用一组结构化场景来改善仅依赖于少数极端场景的特征做出最终决策的难度。