Econometric Models of Probabilistic Choice: Beyond McFadden’s Formulas

Abstract

Traditional decision theory assumes that for every two alternatives, people always make the same (deterministic) choice. In practice, people’s choices are often probabilistic, especially for similar alternatives: the same decision maker can sometimes select one of them and sometimes the other one. In many practical situations, an adequate description of this probabilistic choice can be provided by a logit model proposed by 2001 Nobelist D. McFadden. In this model, the probability of selecting an alternative a is proportional to $\exp (\beta \cdot u(a))$, where u(a) is the alternative’s utility. Recently, however, empirical evidence appeared that shows that in some situations, we need to go beyond McFadden’s formulas. In this paper, we use natural symmetries to come up with an appropriate generalization of McFadden’s formulas.