Some commonly used inter-domain-routing policies?e.g., those using BGP's MED attribute for cold-potato routing?are beyond the scope of routing theory developed to date. This is because these policies cannot be expressed as a linear preference ranking of available routes at each node. Existing characterizations of well-behaved path-vector routing, however, critically depend on this linear ranking and do not naturally extend to more complex policies. In this paper, we present a framework that is able to model these more general policies. We use it to give the broadest-known sufficient condition for robust convergence of path-vector protocols, even when complex policies are used. In doing so, we present a new, unified notion of order on policies; this reduces to earlier results in the case of restricted policies, but it allows us to analyze the practically useful but inconsistent policies that could not be directly modeled before. As an application, we rigorously analyze (and improve) various robust protocol-design proposals.