A technique I often use to test a theory is to change the inputs to be the maximum and minimum possible values and see if the model still holds true. I've found it to be incredibly useful in a few specific situations.
Or more generally, look for critical points in the model and see if it still holds. Max/min values (or odd combinations of max/min for different variables) are good candidates, as are zeroes, and anything which makes part of an equation go to zero.
I've always thought this should be a very effective way to explain a point to someone, but in practice it rarely seems to work....maybe that saying applies, something about you can't use logic to change the mind of someone that didn't use logic to arrive at their conclusion.
That might be because you're trying to use it to argue politics, where it's less applicable; hard cases often make bad law, and you can easily end up with a straw man. It works better in science and engineering.
