General Luce Model

We extend the Luce model of discrete choice theory to satisfactorily handle zero-probability choices. The Luce model (or the Logit model) is the most widely applied and used model in stochastic choice, but it struggles to explain choices that are never made. The Luce model requires that if an alternative y is never chosen when x is available, then there is no set of alternatives from which y is chosen with positive probability: y cannot be chose, if from sets of alternatives that exclude x. We relax this assumption. In our model, if an alternative y is never chosen when x is available, then we infer that y is dominated by x. While dominated by x, y may still be chosen with positive probability - even with high probability - when grouped with a comparable set of alternatives.