I watch a dumb reality TV show which has a certain number of contestants to start with, and every week one contestant is eliminated. Here's how the elimination process works. Every week a certain number of contestants is nominated for elimination. And then viewers get to vote online on who they want to save from elimination. (A viewer can only vote to save one person.). Whoever gets the least votes gets eliminated.
I'm interested in how to vote strategically in this process. Now if I feel strongly about wanting someone not to be eliminated, it's clear what I should do: cast a vote to save them. But my question is, what should I do if I feel strongly about wanting someone to be eliminated?
I think the answer is that I should vote to save whichever contestant I expect to receive the least votes out of the contestants other than the one I want eliminated. That way, if there's a tie between that least popular contestant and the one I want eliminated, I'll break the tie and succeed in getting them eliminated. (I think it's generally true that if voting is rational, the rational way to vote is the way you would if yours was the tie-breaking vote.) Is that right according to game theory?