The Focal Luce Model

Abstract

We develop a random choice model in which a decision maker divides the alternatives she faces into two groups, where one group is focal and thus she is more likely to choose alternatives in that group relative to alternatives in the non-focal group: The Focal Luce Model (FLM). The FLM generalizes Luce’s model and naturally captures bounded rationality models while behaviorally distinguishing between what is focal and the magnitude of the bias due to focality. We show how to identify utilities, focal sets, and bias terms from choice frequencies and behaviorally found the FLM with two weakenings of independence from irrelevant alternatives (IIA) which account for the decision maker’s revealed focus. We introduce a new condition on focal sets, Conditionally Decreasing, which captures an increasing difficulty of focusing on multiple alternative and encompasses several models of limited consideration. We apply our model to experimental data, illustrate the importance of accounting for focus in demand estimation, and propose a simple method to identify focal sets.

Keywords: Random Choice; Focal Luce Model; IIA; Consideration Set; Conditionally Decreasing

JEL Classification: D01; D81; D9