Evan, I think the best strategy for having a fruitful discussion with one of your professors is to know her positions well enough to ask her provocative questions. If she struggles with an answer, then point her to the relevant literature. With a political science professor, listen to what she says about economics and economists. In private conversations, ask her what literature she has read on economic topics or by economists. Bring up some arguments by economists who write about politics, like Mancur Olson.
http://en.wikipedia.org/wiki/Mancur_Olson
