I think that your vote can count even if, in retrospect, it changed nothing, so long as votes are interchangeable and anonymous.
I think that’s the crux of the issue. My take was to assign a mapping between people and votes such that your vote was in the “excess” portion and thus didn’t matter. But just because such a mapping exists doesn’t mean it is fair or valid to assign it. Instead I imagine it’s a statistics problem where all mappings are possible, which leaves you with a non-zero but tiny “contribution” to electing the winner.
And if you voted for the loser? Then I think the contribution to voter turnout mentioned in the post comes into play. Again a only very tiny amount, but non-zero.
Then finally social issues likes signaling status and desire to belong to a group probably are pretty big factors, maybe bigger than the above “real” factors.
In the end I think it’s possible to justify voting or not voting depending on your values, particularly how you value your time relative to these fuzzier benefits.
Thanks for the links. They seem to mostly be saying: the “pay off” for being the swing vote is gigantic, changing everyone’s life, so even though the chance of being that vote is infinitesimal it’s rational to go for the tiny chance of making a huge difference.
I’m sure this is valid reasoning, but it’s disappointing to me if this is the whole story. It’s like voting as lottery, that your vote essentially never matters except when it has this giant impact.
I think there is mapping problem here as well. Just as you can’t map your vote onto one of the excess votes in a normal election, you can’t map your vote onto that one winning vote in a close election. In each case it’s a game of probabilities and fractional contributions only. But I can’t sort it all out.