The Luce model with replicas

Abstract

We propose the notion of replicas in the context of discrete choices and introduce axioms that characterize the Luce model with replicas. This model does not fall prey to the well-known “red bus-blue bus” example originally proposed by Debreu (1960) and later made famous by McFadden. Our model satisfies regularity, strong stochastic transitivity, and is a random utility model. Due to its simplicity, this model is more parsimonious than others aimed at overcoming the “duplicates problem”.