If you're trying to compute an expected utility, I don't think this is the right way to compute the probability. The probability to compute is the probability that your vote will decide the election, which I expect to be very small where I live (California) but might be large enough in swing states to make it worthwhile to vote there. Someone posted a nice paper computing this probability for several states based on Nate Silver's election data that I can't find. (A very important point here is that the amount of political leverage you have is not linear in the number of people whose votes you affect: the change in the probability of deciding the election is highly nonlinear as you get closer to the boundary where the outcome changes.)
Nevertheless, I still think that a strategy optimized for actually making a difference in politics looks very different from the strategy most people adopt.
I don't think your political influence is primarily dependent on the probability that your one, single vote will decide the election. It's a much more nebulous thing that that in reality; it's how you show up in polls, how politicians think their positions may affect your vote, how likely your demographic is to vote in the first place and how that affects politician's priorities, how well you are able to articulate your position, how many resources a political party feels they need to devote to your district instead of some other district, ect. For examp...
So you're playing the credence game, and you’re getting a pretty good sense of which level of confidence to assign to your beliefs. Later, when you’re discussing politics, you wonder how you can calibrate your political beliefs as well (beliefs of the form "policy X will result in outcome Y"). Here there's no easy way to assess whether a belief is true or false, in contrast to the trivia questions in the credence game. Moreover, it’s very easy to become mindkilled by politics. What do you do?
In the credence game, you get direct feedback that allows you to learn about your internal proxies for credence, i.e., emotional and heuristic cues about how much to trust yourself. With political beliefs, however, there is no such feedback. One workaround would be to assign high confidence only to beliefs for which you have read n academic papers on the subject. For example, only assign 90% confidence if you've read ten academic papers.
To account for mindkilling, use a second criterion: assign high confidence only to beliefs for which you are ideologically Turing-capable (i.e., able to pass an ideological Turing test). As a proxy for an actual ideological Turing test, you should be able to accurately restate your opponent’s position, or be able to state the strongest counterargument to your position.
In sum, to calibrate your political beliefs, only assign high confidence to beliefs which satisfy extremely demanding epistemic standards.