If I were to implement it, I think I'd go whole hog and make the political power score actually do something, though I'm not entirely sure what just yet.
Let nobles be able to spend these points on things, similar to how Mentors could spend their points. Everyone else would just see whatever your current maximum "score" was, but for you you'd see how many points you actually have left to spend that day/week/whatever. And they'd regenerate over time.
