  It is common to use minimax rules to make decisions for planning when there
is great uncertainty on what will happen in the future. Minimax regret 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. The use of minimax
rules avoids the need to determine probabilities for each scenario, which is an
attractive feature in many public sector settings. However, minimax rules will
have sensitivity to the choice of scenarios. In many cases using a minimax
approach will mean the requirement for what may be regarded as arbitrary
probabilities on scenarios is replaced by a similarly arbitrary choice of a
very small number of specific scenarios. We investigate this phenomenon. 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. Our analysis of these phenomena considers
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.
