Every choice function is pro-con rationalizable

We 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. We show that every nuance of the rich human choice behavior can be captured via this structured model. Our technique requires a generalization of the Ford-Fulkerson theorem, which may be of independent interest. As an application of our results, we show that every choice rule is plurality-rationalizable.