There's no need to invoke any kind of fancy "superrationality." There's just a conflict between individual rationality and group rationality.

As a leader or activist, it's in my interest to believe and say things like "Yay voting!" because that helps me lead mobs of people and achieve the election results I prefer.

As an individual private citizen, it's in my interest to stay home and donate to charity, because my vote has much less than a 1/100,000,000 chance of swinging an election: history shows that national voting preferences are drawn from a curve that is much more like a normal distribution than a uniform distribution, and the peak of the normal curve in any given election is going to be off by 1-5% of registered voters based on economic data, approval ratings, etc. In other words, a standard analytical rationalist should be able to predict that less than 1/100,000,000th of the curve of possible election turnouts fit under the exact 50-50 tie that you would need for your vote to matter in any straightforward instrumental sense. If you would take 5:4 odds in favor of either candidate, you shouldn't be betting that the race will end in a tie even at odds of 100,000,000 to 1, and if you can't figure out who to take 5:4 odds for by Election Day, then you haven't read Green & Gerber's paper.

More importantly, even if there were a statistical tie, it would be settled by recounts, fraud, and the appeals process. See, e.g., 2000, 1960, and 1876. Elections that are within a few thousand votes come down to a contest of political will, sly manipulation, and spin waged among professional political operatives and election monitors/officials. If you really want to invest a few hours of your time to swing an election, you shouldn't bother voting: you should volunteer to monitor a polling station.

I have no idea how to even begin analyzing standard vs. Hofstaderian decision theory, but it doesn't matter for the example of national elections. A truly rational electoral activist would not vote, find a way to convincingly lie and claim that she voted, and use the extra 2 hours to make more phone calls urging others to vote. Possibly in some bizarre cyberpunk future that we may all yet live to see, Omega-like beings will create fanciful situations in which voting causes others to vote, but in the meantime mucking about with timeless decision theory to explain voting behavior is like applying relativistic mechanics to a high school track meet.