In 1989 Gilboa and Schmeidler proposed an extension of subjective expe
cted utility theory called maxmin expected utility (MMEU). We present
a new exposition of this theory and suggest an extension of MMEU which
does not allow strictly dominated alternatives to be chosen. MMEU is
related to the earlier notion of weight of evidence and an application
to welfare economics is discussed. We examine normative properties of
MMEU and argue that the theory is not vulnerable to the Dutch book ar
gument.