Marzena J. Rostek PROJECT TITLE: ”Fatalistic Choice Rules” MOTIVATION AND MODELING

MOTIVATION AND MODELING Maxmin (choosing an alternative with the highest minimal outcome) and maxmax (choosing an alternative with the highest maximal outcome) have played an important role as tools and concepts in the choice literature. They have been used as assumptions and derived as solutions to optimization problems in a wide range of applications: individual decision making under risk and uncertainty, social choice, analysis of political elections, games, to mention the most prominent. Curiously, there does not exist a concept that captures less extreme choice behavior. The closest existing approaches are α-maxmin (Arrow and Hurwicz, 1972), combination of expected utility and maxmin (Gilboa (1988), Jaffray (1988)) and neo-additive capacities (Chateauneuf, Eichberger and Grant, 2002). The first one is a weighted average of minimal and maximal outcome and therefore the preferences that it induces do not depend on any intermediate values. The other concepts rely on expected utility optimization and thus, require much stronger restrictions on preferences and beliefs than the original maxmin and maxmax. The goal of this project is to develop a formal way of modeling choice of decision makers who anticipate an intermediate level between maxmin and maxmax. We call the reasoning underlying such choice behavior fatalistic. Specifically, consider a decision maker choosing among uncertain alternatives. We say that she chooses fatalistically if, given her beliefs about outcomes, she evaluates an alternative by a quantile (τ ∈ [0, 1]) of the corresponding beliefs distribution (for example, a median). She is a τ -quantile maximizer if she is choosing an alternative with the highest τ th quantile payoff. Thus, the concept unifies the existing approaches and generalizes them in a smooth way. The decision rule we define has a number of appealing features. (a) In contrast to reasoning based on expectation, the optimal choices are determined by the interaction of cardinal properties of beliefs and only ordinal properties of outcomes. (b) By introducing a new primitive, it allows to weaken the role of beliefs in modeling and making predictions. (c) The model delineates the relative role of the structure of payoffs and beliefs on the optimal choices. It generates and formalizes heterogeneity in reasoning across individuals with different anticipation levels (τ).