A novel logit-type discrete choice model is presented whose distinctive characteristic is that it "polarizes" or forces the prediction of choice probabilities towards values of 0 or 1. In real-world empirical tests this property enabled the new formulation, which we call the polarized logit model (PLM), to outperform the predictive capacity of other classical discrete choice models. The PLM is derived from the optimality conditions of a maximum entropy optimization model with linear and quadratic constraints. These conditions yield a fixed-point logit probability function that exhibits endogeneity, which is corrected for using instrumental variables so that the model's parameters can be estimated. The PLM's marginal substitution rates are similar to those of the traditional logit models.