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.