We study a model of interdomain routing in which autonomous systems' (ASes') routing policies are based on {\em subjective} cost assessments of alternative routes. The routes are constrained by the requirement that all routes to a given destination must be confluent. We show that it is NP-hard to determine whether there is a set of stable routes. We also show that it is NP-hard to find a set of confluent routes that minimizes the total subjective cost; it is hard even to approximate minimum cost closely. These hardness results hold even for very restricted classes of subjective costs. We then consider a model in which the subjective costs are based on the relative importance ASes place on a small number of objective cost measures. We show that a small number of confluent routing trees is sufficient for each AS to have a route that nearly minimizes its subjective cost; these routing trees can be computed easily with a distributed algorithm. Furthermore, we prove that this bound is almost tight.