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Least worst regret (and sometimes minimax) analysis are often used fordecision making whenever it is difficult, or inappropriate, to attachprobabilities to possible future scenarios. We show that, for each of these twoapproaches and subject only to the convexity of the cost functions involved, itis always the case that there exist two "extreme" scenarios whose costsdetermine the outcome of the analysis in the sense we make clear. The resultsof either analysis are therefore particularly sensitive to the cost functionsassociated with these two scenarios, while being largely unaffected by thoseassociated with the remainder. Great care is therefore required in applicationsto identify these scenarios and to consider their reasonableness.  We also consider the relationship between the outcome of a least worst regretand a Bayesian analysis, particularly in the case where the regret functionsassociated with the scenarios largely differ from each other by shifts in theirarguments, as is the case in many applications.  We study in detail the problem of determining an appropriate level ofelectricity capacity procurement in Great Britain, where decisions must be madeseveral years in advance, in spite of considerable uncertainty as to which of anumber of future scenarios may occur, and where least worst regret analysis iscurrently used as the basis of decision making.

Least worst regret analysis for decision making under uncertainty, with applications to future energy scenarios