Politics is the mind-killer; our opinions are largely formed on the basis of which tribes we want to affiliate with. What's more, when we first joined a tribe, we probably didn't properly vet the effects it would have on our cognition.  
 
One illustration of this is the apparently contingent nature of actual political coalitions, and the prima facie plausibility of others. For example,

• In the real world, animal rights activists tend to be pro-choice.
• But animal rights & fetus rights seems just as plausible coalition - an expanding sphere of moral worth.

 
This suggests a de-biasing technique; inventing plausible alternative coalitions of ideas. When considering the counterfactual political argument, each side will have some red positions and some green positions, so hopefully your brain will be forced to evaluate it in a more rational manner.
 
Obviously, political issues are not all orthogonal; there is mutual information, and you don't want to ignore it. The idea isn't to decide your belief on every issue independently. If taxes on beer, cider and wine are a good idea, taxes on spirits are probably a good idea too. However, I think this is reflected in the "plausible coalitions" game; the most plausible reason I could think of for the political divide to fall between these is lobbying on behalf of distilleries, suggesting that these form a natural cluster in policy-space.
 
In case the idea can be more clearly grokked by examples, I'll post some in the comments.