The constrained multinomial logit: A semi-compensatory choice model

The traditional formulation of logit models applied to transport demand assumes a compensatory (indirect) utility function in which the consumers’ strategy assumes a tradeoff between attributes. Several authors have criticized this approach because it fails to recognize attribute thresholds in consumer behavior, or a more generic domain where such a compensatory strategy is contained. In this paper, a mixed strategy is proposed, which combines the compensatory strategy valid in the interior of the choice domain with cutoff factors that restrain choices to the domain edge. The proposed model combines the multinomial logit model with a binomial logit factor that represents soft cutoffs. This approach extends previous contributions in several ways and allows multiple dimensions for cutoff factors. In addition to considering individual behavior, it introduces system constraints such as capacity and inter-agent interactions (choice externalities). This extension yields a non-linear problem, which is solved by analyzing the fixed point problem. Additionally, a set of evaluation tools, a social utility of the constrained problem, and a measure of the shadow price of each constraint, are proposed