(Assuming you’re eligible?)
An argument I came up with a while ago is that, in an election with N voters, the probability of your vote swaying the outcome could be expected to scale like 1/√N—but the utility to the world if your vote does sway the outcome could be expected to scale like N. Under those assumptions, the expected utility of your vote for the world scales like √N (or -√N, depending which candidate you vote for). So if you care about the world even ~1/√N as much as you care about yourself, you should probably vote, even though your vote almost certainly won’t change the outcome. Indeed, the case is even stronger in the US (at least if you live in a swing state), both because the electoral college amplifies the probability of your vote mattering (see the Majority-Is-Stablest Theorem), and because of the US’s disproportionate influence on the world.
A version of the above argument was discovered independently by Peter Norvig, who—appropriately for an applied rather than theoretical computer scientist—plugs in some actual numbers, rather than considering the asymptotics as the number of voters goes to infinity. Norvig finds an expected value of your vote to the United States of about $1 million (or $6 trillion divided by a 1 in 6 million chance of your vote mattering). Another version of the argument was given by Andrew Gelman, who points out that other people’s votes are actually not well-modeled by unbiased coin flips (unless you live in Florida, I guess)—but that even under a more realistic prior, your vote still has a constant expected value to society (i.e., it doesn’t decrease with the number of voters N).
I’m aware, of course, that the above is merely a nerdy, rational argument, of a sort that’s probably never actually convinced anyone in the entire history of the world, with the possible exception of Robin Hanson. So let me raise the stakes a little. Let me give you an emotional argument.
Did you see WALL-E? My favorite scene in that predictably-excellent movie—a scene I confess almost brought me to tears—actually had nothing to do with WALL-E or his robo-love-interest EVE. It was the scene aboard the spaceship Axiom, where the leaf symbol starts flashing overhead, indicating that the earth is once again able to support life, and the fat, coddled human passengers actually have to make a decision about whether to return to earth or not. For the first time in 700 years, the spaceship’s course is not on autopilot. Like children away from their parents, the humans face the terrifying realization that there’s no longer any higher authority to tell them what to do. Or rather, their robot masters are trying to tell them what to do, but the humans are not obliged to listen.
See? Just like an election.
Your vote almost certainly won’t change the outcome; indeed, thanks to the wonders of technology, there’s probably no way to verify it’ll even be counted. But on the one day when that leaf is flashing … to have to tell posterity you were too busy finishing a problem set?
Naturally, I also think I know which way you should vote. But even if you’re one of the humans who thinks the spaceship carrying the last remnant of humanity should remain floating in space—since although (and here I’m embellishing the movie) the spaceship’s power will soon run out, leaving all the humans dead, it’s conceivable that the power could be extended a few years by drilling a nearby asteroid (drill, baby, drill!)—even if that’s your belief system, still I think you should vote. Why? Because of my newfound Zen-like equanimity, combined with the belief that your candidate’s going to lose anyway.
Then, after you’ve voted, go into the comments section and ask me a question about what’s new in computational complexity. As a commenter on my last post helpfully opined, it’s time to start tending my garden again.
Yes We Can. Prove We Can’t.