Andrew Gelman writes, in response to my comments in this post:

Comments on comments on "Voting as a rational decision", by Andrew Gelman:After reading our article, "Voting as a rational decision," Mark Thoma asked,

If helping other people makes me happy, why would caring about other people be contrary to my own self-interest? This is essentially a question about the meaning of the term selfish. I [Mark] assume selfishness means maximizing my utility, which may or may not include the happiness of other people as an argument.

My reply:

The challenge in all such arguments is to avoid circularity. If selfishness means maximizing utility, and we always maximize utility (by definition, otherwise it isn't our utility, right?), then we're always selfish. But then that's like, if everything in the world is the color red, would we have a word for "red" at all? I'm using selfish in the more usual sense of giving instrumental benefits. For example, if I cut in front of someone in line, I'm being selfish. If I don't do it (because I get pleasure from being a nice guy and pain from being a jerk), then that's other-directed. I'm sacrificing something (my own time) in order to help others. Just because something is enjoyable it doesn't have to be selfish, I think.

To put it another way, if "selfish" means utility-maximization, which by definition is always being done (possibly to the extent of being second-order rational by rationally deciding not to spend the time to exactly optimize our utility function), then everything is selfish. Then let's define a new term, "selfish2," to represent behavior that benefits ourselves instrumentally without concern for the happiness of others. Then our point is that rationality is not the same as selfish2.

Also, some of his commenters questioned whether a single vote could be decisive, what with recounts etc. The answer is, yes, it can, because there is ultimately some threshold (even if unobservable) as to whether the recount occurs. And even if this threshold is itself probabilistic, the probabilities can be added. We demonstrate this mathematically in the Appendix to the 2004 Gelman, Katz, and Bafumi article in the British Journal of Political Science; see page 674 here.