I think pwno is proposing that we do it precisely because it doesn't align with our convictions. (He might advise Trump supporters to vote for Clinton.)

I'm sure I remember reading, but can't now find, an anecdote from Eliezer back in the OB days: he was with a group of people at the Western Wall in Jerusalem, where there's this tradition of writing prayers on pieces of paper and sticking them in cracks in the wall, so as a test of the sincerity of his unbelief he wrote "I pray for my parents to die" and stuck that in the wall. Same principle.

(Personally I think it's a silly principle. Human brains aren't very good at detaching themselves from their actions, and I would only cast a vote if I were happy for my preferences to get shifted a little bit towards the candidate I was voting for.)