I do think you might be underestimating the utility of being involved in politics.
It's common to think, say, "There are 300 million people in this country, so if I only have an amount of democratic influence equal to 1/300,000,000 of the country, then it's not worth being involved." (Speaking in terms of the US). However, the total amount of utility at stake here is huge; the government spends about 3 trillion dollars a year. If you think that, hypothetically speaking, that party A would spend that money in a way that's about 10% more efficient at creating positive utility then party B, then that's about 300 billion dollars worth of positive utility at stake here. If you have a 1/300 million influence over a decision worth 300 billion dollars of utility, then when you multiply that out your influence is worth about 1000 dollars of utility. So one would think that it would be worth a fair amount of time to try to do something useful with it.
In practice, it may be lower if you don't think that there is that much difference between the two parties, while on the other hand a person willing to spend a little time talking about politics and sending letters to their congressmen and otherwise getting involved probably has a higher degree of influence then that (especially since almost half the country doesn't vote at all). And there are also other things the government does that aren't directly related to money that can also have a significant impact.
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...
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.