“Maximizing expected utility (MEU)” is one assumption of (strict) Bayesian decision theory [Savage 1972]. According to the principle of MEU, in a given decision situation, the decision maker should choose one of the alternatives with maximal expected utility [For an excellent discussion of decision theory, see Jeffrey 1990]. However, MEU as the foundation of Bayesian decision theory has been under attack. One counterexample that seems to dispute MEU as a rationality principle is offered by Daniel Ellsberg[Ellsberg 1961]. While discussing what has been dubbed as the Ellsberg paradox, I will consider briefly three decision principles, each of which is different from the MEU principle.