(Cross-posted from elsewhere; I thought some readers here might like it too. Please excuse the unusually informal style.)
Short answer: Actually, yes!
Slightly longer answer: Yes, if the election is close. You'll never get to know that your vote was decisive, but one vote can substantially change the odds on Election Day nonetheless. Even if the election is a foregone conclusion (or if you don't care about the major candidates), the same reasoning applies to third parties- there are thresholds that really matter to them, and if they reach those now they have a significantly better chance in the next election. And finally, local elections matter in the long run just as state or nation elections do. So, in most cases, voting is rational if you care about the outcome.
Full answer: Welcome! This is a nonpartisan analysis, written by a math PhD, of when and how a single vote matters in a large election. I've got a table of contents below; please skip to whatever section interests you most. And feel free to share this!
1. How can a single vote matter in a huge election?
2. What if I know it's not going to be close?
3. Do local elections matter?
In what follows, I'm going to be assuming an American-style voting system (first-past-the-post, for you voting-system buffs), but most of what I say carries over to other voting systems found around the world.
1. How can a single vote matter in a huge election?
To answer this, let's imagine a different voting system. In the land of Erewhon, voters cast their ballots for president just as they do here; but instead of decreeing that the candidate with the most votes is the winner, each vote is turned into a lottery ball, and one is chosen at random to determine the next president.
While this system has its drawbacks (they get fringe candidates elected every so often, and they've had to outlaw write-in campaigns to prevent every voter from simply voting themselves in), the citizens of Erewhon agree on its main advantage: every one of them knows that their vote counts, that they increase the chance of their candidate winning by just that much.
I'm going to argue that if you would bother to vote if an election were held in Erewhon, then you should also vote—for the same reason—if the same election were held the normal way, and if it looked like the outcome might be close. That is, your effect on the outcome is about equivalent if the pre-election polls fall within the margin of error (about ±3% for each candidate, or a margin of less than 6% between two candidates, for an electorate of millions). And if the polls are nearly tied, then voting in our system might have the same effect as voting hundreds or even thousands of times in Erewhon's system!
This seems counterintuitive, because we imagine that the votes of everyone else are "locked in" somehow, and that we're only deciding whether to add ours to the pile- in which case, the only way that it could matter is in the event that it makes or breaks an exact tie. And not only are those exceedingly rare (the largest such example I could find was a recent Massachusetts election for state representative, in which 13,500 ballots were cast), but if the initial count for a massive election did show a margin of one or zero, we would be headed for an interminable recount. (See, for instance, the 2008 Minnesota Senate election, which was decided by about 300 votes; the extensive recount delayed the winner's inauguration by about six months.) What this messes with, though, isn't your chance of helping decide the election, but your chance of knowing that you helped decide the election.
That is, in modern elections, there's not a perfect sharp boundary between "Candidate A wins" and "Candidate B wins", but a gigantic muddle; and if A is narrowly ahead, then every additional vote for A represents a greater chance that the recount will eventually end, or end earlier, or not be contested at all; while every vote for candidate B means a greater chance that there will be a recount, or that it will go on longer, or that it might turn out victorious for B after all. You'd never know that your vote, which changed the lead from 412 to 413, was the straw that broke the proverbial camel's back and led the other candidate to concede, but at some point that's what happens.
And even more significantly, we can't consider everyone else's votes as "locked in". If you had the ability to re-play Election Day over and over, the chaotic dynamics of everyday life would affect the vote totals. Someone makes a light about to turn red, and so she ends up at the next light behind a bumper sticker that infuriates her, and so she remembers to vote. Or someone else bumps into an old friend, and starts a conversation, and then he realizes he doesn't have enough of his lunch break left to get to the polling place anyhow. It's the butterfly effect in action, and when multiplied by millions of people it leads to fluctuations in the hundreds or thousands. (The exact mechanism for this estimate is the Central Limit Theorem.) And what that means is that the margin isn't a fixed number pending your decision to vote; it's a mix of different possibilities, and your decision changes the odds as surely as adding a lottery ball to the Erewhon election does.
Of course, if one candidate is polling 10 points ahead of the other, then those fluctuations will be irrelevant. If the margin is closer, then it just might have an effect; remember that polls have several sources of error in them, so you can't be exactly sure of the margin before voting actually happens. And in those cases where the actual vote turns out to be extremely close, like Minnesota in 2008, your choice to vote swings those odds just as if you'd poured in thousands of Erewhonian lottery balls with your candidate's name on them. (That is, it changes those odds by a fraction of a percent, but the ability to nudge the odds by that much in an electorate of millions is pretty impressive!)
2. What if I know it's not going to be close?
If the difference between the top candidates is outside the combined margin of error (7 points or more in a big election), then it's true that your vote won't affect the outcome of the current election, but it can matter greatly for the next one. This especially holds when there's a third party you prefer to the current major parties, but there are other relevant reasons to vote even if that's not the case.
First, about third parties: the conventional wisdom that they can't win is an outright falsehood. We tend to forget that Ross Perot nearly became President: he held a six-point lead in June 1992 over both Bush and Clinton, and despite his candidacy crashing and burning later on (for reasons more personal than systemic), he still won nearly 20% of the popular vote in the end. In addition, there are two current Senators who were elected as independents.
For a third party that's not polling well enough yet, votes now matter for future elections, and there are several significant thresholds. If they get rounded up to 1% on Election Day, then they get mentioned in election coverage. (Next, getting rounded up to 2% sounds much more impressive than getting rounded down to 1%.) If they get to 5%, then they can qualify for FEC matching funds, and double their ability to reach voters next time. And 10% is a significant number for media exposure (as well as invitations to the main debates). Higher than 20%, and we're talking about a viable candidate; there's a runaway dynamic in three-candidate races where as soon as the third party looks viable, any voters from the other parties who prefer the third party will suddenly switch (now that they're no longer worried about supporting an obvious loser), and suddenly the third party becomes the front-runner. (This kind of behavior is common in game theory in what's known as a coordination problem.)
Even if there's not a third party you prefer to the main ones, the margin of victory now helps determine what sort of candidates the parties select next time. If one party wins an election by more than 10% (this round number has a psychological hold on people, so it's what usually counts as a "landslide victory"), then next time that party is more likely to nominate a less moderate candidate, while the defeated party is likely to nominate a more moderate candidate. (Also, it goes without saying that you should be voting in primaries as well!)
All of these thresholds can hinge just as easily on a few hundred votes, and so your vote can matter greatly. You just need to care about what happens two, or four, or six years from now.
3. Do local elections matter?
Most certainly. First, your vote affects the odds more strongly in a local election. (And, of course, there can be margins of zero or one votes, without recounts, in local elections!) Secondly, there are a number of important issues decided at the local level, both directly (tax and bond issues) and through representatives (especially local school boards). And finally, many big names in politics start out in local elections: the current President began as an Illinois state senator, and the current Vice President began as a city councilman.
It's more difficult to do research at the local level. Project VoteSmart may have data on some of the candidates (including the voting record of incumbents, public statements, and response to a questionnaire about their positions). Otherwise, your local newspaper may be the best bet (short of going to campaign events yourself). But a little bit of research can go a long way here.
(Addendum: If I'd been composing this for the Less Wrong crowd, I'd have also noted that the decisions of people similar to you should be correlated, which adds another multiplier to the effectiveness of voting. I might like I bumper sticker that says "I'm a timeless decision theorist, therefore I vote!")
(Second addendum: I'm mindful of the dangers of posting this within a few days of a major election. I've done my very best to keep from mindkilling language; I hope you do the same in the comments.)
I want one that says "I know as many Timeless Decision Theorists who would vote for the other guy as for my guy, therefore none of us vote even though voting would cause our preferences to be maximised!"
ie. "Timeless" considerations go both ways here (and elsewhere), not just towards the option that we incidentally associate with 'virtue'.
That would be a surprising discovery to make, since people algorithmically similar to you will tend to be similar in their who-to-vote-for decisions.
I was planning on writing my own defense of voting post as well[*]. My favorite example is how the current Governor of (my brief home) state of Washington got elected. She won by ~100 votes at the time; that's fewer votes than a single election day shuttle volunteer swings.
Literally 1 dude volunteering/being hired for that day would have won the other side the governor seat. Yet I have a friend who still lives in Washington and makes fun of me for voting and volunteering.
[*] I'm not sure if I will now, given two excellent posts regarding voting recently. Mine is far more fluffy and involves less math so I'm thinking I may just scrap it.
Relevant paper: Gelman, Silver and Edlin estimated that the average American voter has a 1 in 60 million chance of deciding the election.
This is a minor objection, but voting can't be rational and it can't be irrational. Voting isn't a system of thinking. You may want to rephrase your argument as "voting is optimal if you..."
Strongly disagree with this since no candidate promises to abolish democracy and high voter turn out adds legitimacy to this form of government.
I'm writing a research paper on electoral reform and - while contemplating Arrow's impossibility theorem - I had the same idea. What's so bad about non-deterministic voting systems that they have to be excluded from the start, especially if (assuming I understand the theorem correctly) they are the only ones that can simultaneously satisfy all of Arrow's other four criteria?
Have the election determined by a function in which each candidate secretly contributes their own input.
Each candidate secretly writes down an integer. When everyone is done, they reveal what they wrote. The election is determined by the final two digits of the sum.
As long as even one person is able to keep their input secret, it would be impossible for any candidate to rig the system. Anyone concerned about the election being rigged can unilaterally make harder to rig by working harder to keep their integer a secret.
This doesn't necessarily apply. The usual caveat with the anti-randomization advocation is "except when defeating more intelligent or more privileged enemies". These are the same sort of considerations that the voting systems have to handle. (That is, tactical input from motivated individuals in contrived extreme worst case scenarios.)
I don't understand; how can you talk about close vs. non-close presidential elections and not mention the electoral college? Virtually all the reasons you're giving only work for people voting in swing states, so how can you offer them as valid reasons for everyone?
Please vote for Mitt Romney if and only if you throw a fair die and it comes up greater than 2.
Was that a partisan appeal or not? Be consequentalist about policy analysis, I dare you.
This is the wrong way to think about it. One's vote matters not because in rare circumstances it might be decisive in selecting a winner. One's vote matters because by voting you reaffirm the collective intentionality that voting is how we settle our differences. All states exist only through the consent of it's people. By voting you are asserting your consent to the process and it's results. Democracy is strengthened through the participation of the members of society. If people fail to participate society itself suffers.
I have thought about this, to destroy my past erroneous belief that a single vote doesn't make a difference. Imagine that you know a secret that few people know, which tells you that the right candidate to vote is definitely candidate X. All the people who know the secret also might think in the same way as you - that a single vote doesn't matter. But the difference between all of those people voting and no one of them voting is winning the election. So there's the two situations:
I wonder if the psychological effects of voting on individuals (feelings of empowerment, possibly of hopelessness or hope) have a significant positive or negative effect on the populace in terms of productivity or well-being soon before and/or shortly after an election.
And if so, how the magnitude of such an effect might correlate with the scale, expected outcome, or actual outcome of a given election (or issue). i.e. might people feel more empowered
(a) After voting in a Presidential election where their votes have a smaller effect on the outcome, but wh... (read more)
I find that primary elections, other than for President, are rarely contested by serious candidates...
Furthermore, even if you think of everybody else's vote as locked in the odds of you being the deciding vote (assuming everybody else votes randomly and you don't know how) is which is a lot better than your odds in Erewhon. Furthermore, in a close election with partisan voters and undecideds your odds are even better.
Voting is rational if you care about the outcome, will politician X or politician Y get elected. This raises the question, at least for me, why should I care whether politician X or Y gets elected? It has been my experience that NO politician will bring about the outcomes I actually desire. Voting is the means, but what end are you expecting it to achieve?
Even if none of the candidates are close to optimal, there can still be relevant differences between them that are large enough to matter. (If you imagine yourself feeling a bit relieved should one candidate win rather than the other, then there's a difference.)
There's a stupid meme that says you need to endorse everything a candidate stands for in order to vote for them. But for a utilitarian, that's a ridiculous threshold.