Using the latest polls, the folks at Red State, Blue State, Rich State, Poor State have calculated the probability that a single vote would decide the outcome of the presidential election, i.e.:
… the probability that your vote is decisive is equal to the probability that your state is necessary for an electoral college win, times the probability the vote in your state is tied in that event.
Their result:
The states where a single vote is most likely to matter are New Mexico, Virginia, New Hampshire, and Colorado, where your vote has an approximate 1 in 10 million chance of determining the national election outcome. On average, a voter in America has a 1 in 60 million chance of being decisive in the presidential election.
If you’re lucky enough to be a New Mexico resident, your vote has an approximately 1 in 6 million chance of being the deciding vote.
The question of why we bother voting is endlessly fascinating to me. The Why Vote? article by the Freakonomics guys is great reading on that subject:
Within the economics departments at certain universities, there is a famous but probably apocryphal story about two world-class economists who run into each other at the voting booth.
“What are you doing here?” one asks.
“My wife made me come,” the other says.
The first economist gives a confirming nod. “The same.”
After a mutually sheepish moment, one of them hatches a plan: “If you promise never to tell anyone you saw me here, I’ll never tell anyone I saw you.” They shake hands, finish their polling business and scurry off.
The counterargument is always, “Well, what if everyone thought that way?” The answer to that is, of course, that not everyone thinks that way, so shut up.
But for the sake of argument, what if everyone did have this philosophy? Would it be possible to have effective elections? Maybe some folks would decide it would be worth voting if the turnout were less than 5000 people. Others maybe wouldn’t bother voting if the turnout were 500 or less. Even if that average magic number was something like 1000, that’s still a pretty solid sample size (most pre-election state polls are on the order of a few hundred participants). So in this mystical world of purely selfish people, maybe elections would still be effective.
P.S. At the end of that RSBSRSPS entry, they link to another paper they wrote in which they conclude that for people with “social preferences,” the expected utility of voting is approximately independent of the size of the electorate. I haven’t had a chance to read this yet, but it might be interesting.