Stochastic Dominance
with Nonadditive Probabilities
Rainer Dyckerhoff and Karl Mosler
Abstract:
Choquet expected utility which uses capacities (i.e. nonadditive probability
measures) in place of 
-additive probability measures has been introduced to decision making under
uncertainty to cope with observed effects of ambiguity aversion like the
Ellsberg paradox. In this paper we present necessary and sufficient conditions
for stochastic dominance between capacities (i.e. the expected utility
with respect to one capacity exceeds that with respect to the other one
for a given class of utility functions). One wide class of conditions refers
to probability inequalities on certain families of sets. To yield another
general class of conditions we present sufficient conditions for the existence
of a probability measure P with 
for all increasing functions f when C is a given capacity.
Examples include n-th degree stochastic dominance on the reals and many
cases of so-called set dominance. Finally, applications to decision making
are given including anticipated utility with unknown distortion function.
Rainer Dyckerhoff
Fri Nov 22 14:37:47 MET 1996