The [alpha]-MEU model: A comment

In Ghirardato et al. (2004) [7], Ghirardato, Macheroni and Marinacci propose a method for distinguishing between perceived ambiguity and the decision-maker[modifier letter apostrophe]s reaction to it. They study a general class of preferences which they refer to as invariant biseparable. This class includes CEU and MEU. They axiomatize a subclass of [alpha]-MEU preferences. If attention is restricted to finite state spaces, we show that any [alpha]-MEU preference relation, satisfies GMM[modifier letter apostrophe]s axioms if and only if [alpha]=0 or 1, that is, the preferences must be either maxmin or maxmax. We show by example that these axioms may be satisfied when the state space is [0,1].