LUCE RULE WITH ASSOCIATION

Abstract

We develop an extension of Luce’s random choice model that incorporates a role for the association of alternatives. Each alternative is characterized by a salience value, a Luce value, and its associated alternatives. The salience value captures the alternative’s desirability to attract the decision maker’s attention, the Luce value measures the alternative’s desirability, and the association relation forms subjective partition for the alternative set. The decision maker is first attracted by some alternative according to a salience-based Luce-type formula, and then chooses among its associated alternatives according to another desirability-based Luce-type formula. We come up with two primitive conditions on the choice rule to fully characterize the desired representation. While retaining the simplicity of the Luce rule, the theory accommodates some well-known behavioural phenomena about individual choices, such as the attraction effect (violations of regularity) and violations of stochastic transitivity.