View article

This paper studies a feedback form framework for preference learning, which we call ranked choices. In this setting, participants rank their top k (k≥ 1) choices from an individualized display set. As such, this setting generalizes many commonly studied feedback structures, such as discrete choices. We introduce a distance-based (Mallows-type) ranking model using a new distance function termed reverse major index (RMJ), which can be used to learn participant preferences from their ranked choices. Despite the requirement to sum over all permutations, the ranking model yields simple expressions of ranked choice probabilities, enabling effective inference of model parameters from data with theoretically proven consistency. Through comprehensive numerical studies on several data sets, we showcase the model's efficiency for parameter estimation and favorable generalization power, especially under limited information.