Rationality and Zero Risk

We adopt a definition of “rationality” as robustness to analysis: a mode of behavior is rational for a decision maker if she feels comfortable with it once it has been analyzed and explained to her. With this definition in mind, is it irrational to violate continuity axioms in one’s stated preferences? Specifically, does it make sense to avoid any positive probability of a negative outcome, not matter how small? Or, if a decision maker states such a “zero risk” policy, does she mean what she says? We propose to study this question axiomatically, asking which modes of behavior correspond to such statements. The baseline model evaluates a lottery by its expected utility and an extra additive term that measures the cost of deviating from a “zero risk” choice. A generalized version allows for multiple sets of principles, where the cost of risking a set of principles is added to the expected utility of a lottery. Stronger assumptions imply that the cost of violating a set of principles is additive in the individual costs. We develop a comparative behavioral analysis that allows to make interpersonal comparisons about the relative importance of principles.