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 example, even if it didn't change any elections at all, I think that we would be funding college in a very different way if a higher percentage of college students voted.
Nevertheless, I still think that a strategy optimized for actually making a difference in politics looks very different from the strategy most people adopt.
Probably true. The strategy most people adopt looks more to me like "let me try to spend the minimal amount of time necessary in order to get enough information to let me feel confident in deciding who to vote for". Much less payoff then a deliberate strategy to maximize making a difference, but much less cost involved as well. There's also a general attitude among a lot of people that, at a rule, doing at least that is your responsibility as a citizen, and I think that is probably correct.
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.