Effect of Choice Set Size on Choice Probabilities: An Extended Logit Model

The multinomial logit model in the context of the Luce choice axiom implies that the logarithm of the ratio of choice probabilities (the log odds ratio) of two objects depends only on the attributes of the two objects and not on the attributes of other objects in the choice set. Noting this weakness of the Luce choice axiom and the conventional logit model, [Batsell and Polking, 1985] prove the existence of a unique set of additive numbers that equate to the log odds ratio and that depend on the objects in the choice set. They observed that the Luce model spawned multiattribute extensions and applications and call for such extensions and applications of their generalization of the Luce model. We provide such an extension here and show analytically that it is possible to stay within the multinomial logit family while avoiding the IIA restriction.