The probability to compute is the probability that your vote will decide the election
I think this should be the probability of your decision procedure deciding the election. If many people are using similar decision procedures, the decision they follow commands their combined votes, and correspondingly the probability that the decision matters goes up when there are more similarly-deciding people. From this point of view, the voters in an election are not individuals, but decision procedures, each of which has a certain number of votes, and each decision procedure can decide whether it's useful to cast its many votes. A decision procedure that is followed by many people, but thinks that it only commands one vote is mistaken on this point of fact, and so will make suboptimal decisions.
Good point.
A good example of this is how certain very simplistic decision procedures, like "single issue voters", can have influence far above and beyond their numbers. If 5% of the population will always vote based on one specific issue, and that is both known and understood by politicians, then even if they are in the minority, they have a major amount of influence over that one issue, because that decision procedure is so significant. Examples: gun lobbies, labor groups, abortion, ect.
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.