A menu dependent Luce model with a numeraire

This paper proposes and characterizes a simple extension to the Luce rule when the value of each alternative can be enhanced or diminished by a non-negative menu dependent parameter that can be thought of as a measure of menu complexity. The characterization follows from two properties that hinge on the default option: monotone consistency and strong independent log-odds. We make no restriction on the domain of menus so that we may not see choice probabilities from every menu. For these models, we show it is possible to describe choice overload where the default option is chosen more often as menu size increases. It is also shown how this model relates to the class of perturbed utility models.