Every Choice Function Is Pro-Con Rationalizable

Abstract

Dogan and Yildiz introduce and analyze the pro-con model that is inspired by Franklin’s prudential algebra. Consider an agent who is endowed with two sets of orderings: pro- and con-orderings. For each choice set, if an alternative is the top-ranked by a pro-ordering (con-ordering), then this is a pro (con) for choosing that alternative. The alternative with more pros than cons is chosen from each choice set. Each ordering may have a weight reflecting its salience. In this case, the probability that an alternative is chosen equals the difference between the total weights of its pros and cons. Although, this is an additive model similar to the random utility model with structurally invariant primitives, authors show that every (random) choice function is (random) pro-con rational. Their technique requires a generalization of Ford-Fulkerson theorem. The connection between the random model and its deterministic counterpart demonstrates a fruitful use of classical integer programming techniques in choice theory.