#### Publication Date

2-2007

#### Abstract

According to decision making theory, if we know the user's utility Ui=U(si) of all possible alternatives si, then we can uniquely predict the user's preferences. In practice, we often only know approximate values Vi~Ui of the user's utilities. Based on these approximate values, we can only make probabilistic predictions of the user's preferences. It is empirically known that in many real-life situations, the corresponding probabilities are described by a logit model, in which the probability pi of selecting the alternative si is equal to pi=exp(b*Vi)/(exp(b*V1)+...+exp(b*Vn)). There exist many theoretical explanations of this empirical formula, some of these explanations led to a 2001 Nobel prize. However, it is known that the logit formula is empirically valid even when the assumptions behind the existing justifications do not hold. To cover such empirical situations, it is therefore desirable to provide a new distribution-free justification of the logit formula. Such a justification is provided in this paper.

## Comments

Technical Report UTEP-CS-07-08