Decision Making with Barely Any Information: The Role of Mixed Strategies

Abstract

At the 6th annual Maximum Entropy Workshop Carlos Rodrigues presented an amusing problem in decision theory. In this problem the normal application of expected utility theory leads to an unacceptable conclusion. We restate the problem, and the “paradox.” We then give an “almost but not quite exactly unlike” formulation in which the paradox is resolved. We then pursue the new formulation to show how adopting a mixed strategy makes it possible to “certainly” gain while playing the game. We next show that in a suitable limit the “expected gain” goes to zero. Finally, we speculate on the possible application of these ideas to situations with “great uncertainty.”