Dov Samet (Tel Aviv University): "Desirability relations in Savage's model of decision making"
The subjective probability of a decision maker is a numerical representation of a qualitative probability which is a binary relation on events that satisfies certain axioms. We show that a similar relation between numerical measures and qualitative relations on events exists also in Savage’s model. A decision maker in this model is equipped with a unique pair of probability on the state space and cardinal utility on consequences, which represents her preferences on acts. We show that the numerical probability-utility pair is a representation of a family of desirability relations on events that satisfy certain axioms. We first present axioms on a desirability relation defined in the interim stage, that is, after an act has been chosen. These axioms guarantee that the desirability relation is represented by a probability-utility pair by taking for each event conditional expected utility. We characterize the set of representing pairs by measuring the optimism of probabilities on consequences and the content of utility functions. We next present axioms on the way desirability relations are associated ex ante with various acts. These axioms determine the unique probability-utility pair in Savage’s model.