A contrast between two decision rules for use with (convex) sets of probabilities:
-Maximin versus E-admissibilty.
This paper offers a comparison between two decision rules for use when uncertainty is
depicted by a non-trivial, convex2
set of probability functions . This setting for uncertainty
is different from the canonical Bayesian decision theory of expected utility, which uses a
singleton set, just one probability function to represent a decision maker's uncertainty.
Justifications for using a non-trivial set of probabilities to depict uncertainty date back at
least a half century (Good, 1952) and a foreshadowing of that idea can be found even in
Keynes' (1921), where he allows that not all hypotheses may be comparable by qualitative
probability in accord with, e.g., the situation where the respective intervals of probabilities
for two events merely overlap with no further (joint) constraints, so that neither of the two
events is more, or less, or equally probable compared with the other.
Here, I will avail myself of the following simplifying assumption: Throughout, I will avoid
the complexities that ensue when the decision maker's values for outcomes also are
indeterminate and, in parallel with her or his uncertainty, are then depicted by a set of