But it's not an even race. Based on the polls, it looks like R or D have a 99% Chance (C) of winning. If Fr = -10, Fd = 5, and Fg = 10, but Cr = .48, Cd = .48 and Cg =.01, maybe I ought to consider that, since I don't want R to win more than I don't want D to win. That would be something like voting for max(Fr*Cr,Fd*Cd,Fg*Cg). So I don't vote for the guy I like the most, I vote for the guy I like who's most likely to win. Let's call this the "Most likely winner" strategy.
But there are a lot of other guys voting out there. My vote will be a very small percentage of the total votes cast. My vote will be 1 out of all the Votes (V) each candidate gets. Vr or Vd will be related to Cr or Cd pretty close to Vr/V ~ Cr and Vd/V ~ Cd. My vote will actually be the largest percentage of the total for a candidate if it is for the candidate who gets the least votes. Or in a close election where I vote for the winner, my votes power could be seen as 1 over the difference between winner and 2nd place. Here's where I start getting confused. I think that if the previous part is true, then it should be true if I vote for second place: my_vote_power = 1/(V_first - V_second). So it looks like I've come up with 2 ways to measure the power of my vote, 1 relative to the difference between my candidate and the highest other vote receiving candidate, and 1 relative to the total vote count of my candidate.
I'm having a hard time putting this into equation format, but I think this adds up to a strategy where I want to vote to maximize the power (with either measure) of my vote for candidates that I prefer. So to determine which power measure to use for each candidate it would be something like power_canidate = max( 1/(C_candidate*100), 1/(abs(C_candidate*100-max(C without current candidate)))). Then I get confused how to combine that mathematically with how much I Favor each candidate, but I think it should turn out so that I vote for my favorite candidate unless the candidate I favor most likely to win has a higher vote power.
What do you think is the most rational way to pick your candidate? Does it ever make sense to vote for candidates who are unlikely to win? How would you mathematically describe a "Vote against the worst candidate" strategy?
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