A Bayesian model for multicriteria sorting problems

Decision makers are often interested in assigning alternatives to preference classes under multiple criteria instead of choosing the best alternative or ranking all the alternatives. Firms need to categorize suppliers based on performance, credit agencies need to classify customers according to their risks, and graduate programs need to decide who to admit. In this article, we develop an interactive Bayesian algorithm to aid a decision maker (DM) with a multicriteria sorting problem by learning about her preferences and using that knowledge to sort alternatives. We assume the DM has a linear value function and value thresholds for preference classes. Our method specifies an informative prior distribution on the uncertain parameters. At each stage of the process, we compare the expected cost of stopping with the expected cost of continuing to consult the DM. If it is optimal to continue, we select an alternative to present to the DM and, given the DM’s response, we update the prior distribution using Bayes’ Theorem. The goal of the algorithm is to minimize expected total cost. We develop lower bounds on the optimal cost and study the performance of a heuristic policy that presents the DM alternatives with the highest expected cost of misplacement.