  Least worst regret (and sometimes minimax) analysis are often used for
decision making whenever it is difficult, or inappropriate, to attach
probabilities to possible future scenarios. We show that, for each of these two
approaches and subject only to the convexity of the cost functions involved, it
is always the case that there exist two "extreme" scenarios whose costs
determine the outcome of the analysis in the sense we make clear. The results
of either analysis are therefore particularly sensitive to the cost functions
associated with these two scenarios, while being largely unaffected by those
associated with the remainder. Great care is therefore required in applications
to identify these scenarios and to consider their reasonableness.
  We also consider the relationship between the outcome of a least worst regret
and a Bayesian analysis, particularly in the case where the regret functions
associated with the scenarios largely differ from each other by shifts in their
arguments, as is the case in many applications.
  We study in detail the problem of determining an appropriate level of
electricity capacity procurement in Great Britain, where decisions must be made
several years in advance, in spite of considerable uncertainty as to which of a
number of future scenarios may occur, and where least worst regret analysis is
currently used as the basis of decision making.
