A Theory Of Rational Choice Under Complete Ignorance

This paper contributes to a theory of rational choice under uncertainty for decision-makers whose preferences are exhaustively described by partial orders representing "limited information." Specifically, we consider the limiting case of "Complete Ignorance" decision problems characterized by maximally incomplete preferences and important primarily as reduced forms of general decision problems under uncertainty. "Rationality" is conceptualized in terms of a "Principle of Preference-Basedness," according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called "Simultaneous Expected Utility Maximization" which in particular satisfies a choice-functional independence and a context-dependent choice-consistency condition; it can be interpreted as the fair agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the different possible states (respectively extermal priors in the general case).