Wow, some of my favorite econobloggers have been thinking seriously about voting and why people do it. Well I'd never heard of him before, but Rajiv Sethi has an excellent analysis:
http://rajivsethi.blogspot.com/2012/11/the-rationality-of-voting.html
I'm going to add Rajiv to my blogroll, he's excellent. Basically his analysis gets to the feelings of voters. Voters feel elation not only if their side wins, but if their side wins by a big margin, and most people do indeed have an ability to contribute to the bigness of the winning margin if their side wins, as well as whether their side wins.
In contrast, the conventional economic analysis (Rajiv has many links) is that voting is pointless for everyone except the single individual that casts the deciding vote. Since most voters do not cast a deciding vote, by that criterion voting is pointless for nearly everyone because the probability of changing an electoral decision is very very small,* even people in swing-states, though it's slightly less likely to be pointless for them. I agree with Rajiv that this conventional economic analysis of voting is wrong.
(*John Quiggin, an Australian economist, has determined that the probability of casting a deciding vote may be much larger than many economists have claimed, especially for candidates other than The President.)
Rajiv says that he registered to vote within minutes of receiving his naturalization certificate. Regardless of how strictly rational of an activity voting is, many people do indeed take it very seriously, enduring long lines and other hardships. Noam Chomsky has pointed out that many people in history have fought very long and hard to get voting rights.
The very first commenter on Rajiv's post is JW Mason, who makes a somewhat different argument similar to one I have often made. Mason says that one does not really vote as an individual, but as the member of one or more groups, and voting is an activity which is part of and affirms group identity. These groups are large enough to be electorally decisive, and have interests that are broad enough to be generally affected by the election outcome.
Mason also makes another interesting observation which some people I know might not agree with:
"The whole language of choices, interests, reason, etc., doesn't refer to anything in material reality. There is no sense in which billions of neurons in a single human body "really do" constitute a moral agent but some trillions distributed across various human bodies do not."
That's an interesting view, which I think I agree with, but I can also see some counterarguments which wouldn't be easily dismissed.