Does My Vote Matter?
(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!
Sections:
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.)
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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.
Explicit superrationality/Kantian reasoners are probably significantly different from other humans, e.g. probably smarter and more educated, for example. I would like to politicians of all parties notice that the electorate is more educated (and pitch their policies accordingly), to have primaries favor more sane brands of each party, and have ballot initiatives resolved in favor of global cooperation of TDTers rather than narrow rent-seeking coalitions.
You don’t need the “similar minds” to be explicit super-rationality reasoners; it suffices that they have a similar input/output mapping, so your decisions are logically coupled to someone who makes the same kind of decisions but because of “fear of hellfire”.
That’s a good point; however, there could be some elections in which the balance of opinion is different between TDT thinkers and others. (In which case, of course, they would optimize in order to have the same aggregate effect as otherwise, while allowing some TDT agents to forgo voting.)
Before the vote, how do they know, with enough accuracy for anything but a 100% turn-out to work? Polls? But by the same argument, what TDT-ers will take the time to respond to a poll?
Exactly. And in the extreme case only one person would attend the poll booth (from the team that were going to win anyway) and everyone else would stay home.
But do each of those Timeless Decision Theorists know precisely the same set of Timeless Decision Theorists as you do?
They don’t need to. I just need to expect the political biases of the TDTists the others know to be just as likely to in one direction as the other.
Um, no. Since one of the TDTists is yourself, and you already know your set of acquaintances.
The grandparent seems correct and I don’t see why “Um, no” is supposed to follow from the parent. It is possible that the amount of communication required to reach an agreement with Eugine would be too much to fit even on my rather verbose bumper sticker.
It might be easier to see if you think of the case when you know only one other TDTist and he would vote for the other guy. However, you’re not sure how many other TDTists he knows.
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...”
Or just “you should vote if”.
And as a followup, even if you’re correct about the probabilities (which I’m not sure you are), it’s not intrinsically optimal to vote, even if you care about the outcome. One must always weigh the opportunity cost of an action, and the opportunity cost depends on the person.
If a superintelligent AI is being built and an equal amount of Yudkowsky’s time will decrease the extinction probability by the same amount as voting would increase candidate X’s election probability, then it’s clearly not optimal for Yudkowsky to vote, because the neg-utility of extinction far outweighs the neg-utility of an unfortunate election.
My post was aimed at the sort of person who would vote in the Erewhon system, but not the real world; your objection applies to both. This post does a good job estimating the utility of voting in a close election; it seems to make sense for most rationalists in most elections at those stakes.
Re: rational and optimal, I’m countering a meme that calls it irrational to vote. I recognize that “optimal” is better usage here, but I wrote this for a wider audience that experiences different connotations.
Strongly disagree with this since no candidate promises to abolish democracy and high voter turn out adds legitimacy to this form of government.
Your position is consistent with your values, then, since you wouldn’t vote in Erewhon either. The irrational meme is the one that says it’s worth voting in Erewhon but not in the real world.
This isn’t totally clear to me.
Suppose we throw away the business of supporting third parties so that they’ll do better next time (which we might as well since it doesn’t appear to be part of the Erewhon scenario). I would argue that voting for one of the major parties has roughly the same expected utility both in America and Erewhon, but voting for third parties has a much lower EU in America than in Erewhon.
Suppose polls predict with their typical (pretty good) confidence that 3rd Party Person will get 4% of the votes, while the 1st Party Person and 2nd Party Person will get the remaining 96%. In Erewhon, there is a 4% chance that the 3rd party candidate gets elected. In America… still pretty much zero.
Of course that’s just aggregate effect, the voting dilemma is about marginal effect. To make it easier to picture though, let’s zoom out and talk adding not 1 more voter, but enough to give Party 3 another 1% of the populace.
In Erewhon, the odds of Party 3 winning have simply increased from 4% to 5%. In America… Party 3 is still looking at pretty much zero chance of winning. The marginal effect is negligible up until at least 20%, and that’s assuming that the psychological effects mentioned in the article can be relied on to keep bumping the numbers up. So it seems that we can conclude that voting for a far-trailing 3rd party has a much greater EU in Erewhon than in America.
Please correct me if my math is wrong though, I’m only just now inventing this argument.
That argument is correct: real-world voting only has as much effect on the odds as an Erewhonian vote if the polls are within the margin of error (roughly speaking).
Voting for a party that’s well behind in the polls only has effects via future elections. These indirect effects are still significant enough, in my opinion, to make it worth voting.
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?
Corruption, or the appearance thereof. Getting everyone to agree that the process actually is random after the outcome is already decided will be nearly impossible.
Have the election determined by a function in which each candidate secretly contributes their own input.
For example:
Alice gets 30% of the vote
Bob gets 20%
Claire gets 50%
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.
Alice wins if 00 ⇐ last two digits < 30
Bob wins if 30 ⇐ last two digits < 50
Claire wins if 50 ⇐ last two digits < 100
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.
Better yet: first, an anonymized database of all ballots is made publicly available on the Internet (this can even have IDs that let people check that their vote was recorded correctly). Alice, Bob, and Claire pick integers A, B, C much larger than the number of voters (N), and commit to hashes of those integers (this step can even be done before voting). Then they reveal A, B, and C, compute A+B+C mod N, and use that voter’s ballot to determine the outcome of the election.
I like that solution, and so far I can’t see any problem with it (as long as at least person randomizes their number, there is no advantage in picking one number over another).
That’s an interesting objection, and not one that I had yet thought of. Though, I don’t share your pessimism about it being nearly impossible for observers to be certain the process is random. (Or at least as confident that the process is genuine as we are about our current, deterministic voting method.)
On the other hand, I haven’t been able to come up with a satisfying solution after thinking about it for the past few minutes. So you could be right. But maybe someone more savvy than I can come up with a better solution.
Right now, few people think that state lotteries are rigged...
There’s far less incentive for the government to care about who wins a normal lottery than about who wins an election lottery. (And I’ve read that in third world countries, the lotteries often are rigged so that cronies of officials win them.)
That’s true, so far as I know.
Ironically, there actually is corruption in state lotteries. I remember watching an Dateline NBC documentary about it. Apparently, some stores that sell lottery tickets will buy winning tickets back from their customers at a reduced price and cash in the ticket themselves. (The reason a customer would agree to this is to avoid having to pay back taxes, child support, etc.)
I don’t get this. Why would someone who stands to lose out by winning the lottery be buying lottery tickets?
Beyond the cached answer of “people are ridiculously irrational,” here are a few reasons why.
In some cases, they may not know that lottery winnings will taken before they buy the ticket. When they go to collect their winnings, an unscrupulous store clerk/manager might then inform them. Or maybe they do know beforehand, but are also aware that they can sell the ticket.
I’ve also heard of store clerks/managers misleading lottery winners about how difficult it is to collect their winnings. After a certain threshold (to pull a number out of the air, say $1000), winners have to deal with the state directly in order to collect their winnings. I imagine that this is to verify/record the winning ticket and recipient. If the store can convince you that it’s more hassle than it’s worth, then their offer to buy the ticket off you sounds more enticing.
OK, makes sense.
Good call. See MileyCyrus’s solution.
Note that the randomness doesn’t need to come into force in all cases. For instance, you could have a Condorcet system using randomness only to determine which method will be used to resolve a cycle.
There’s Eliezer’s frequent claim, that for every randomized solution, there’s a better deterministic solution that possibly requires more thought.
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.)
That’s a very 19th century view. Randomness is a fundamental feature of the world. There is no reason to believe social systems should be any different.
The core reason that non-deterministic voting systems are excluded in modern politics is that they make it harder to be a career politician and get relected. As politicians are the people who decide how voting systems look like they don’t choose non-deterministic voting systems.
In standard discourse one says that political talent can got lost. Good politicians who have no trouble getting relected in the current system suddenly face a real chance of losing their jobs.
For presidential elections, getting a candidate elected president that’s hated by 99% of the population seems a bad outcome. A candidate shouldn’t only appeal to a small niche of people.
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?
The entire second section (What if I know it’s not going to be close?) focuses on several reasons to vote that apply to non-swing state residents.
No, it offers one such reason that only applies to non-swing state residents who wish to promote a third party. The other reason it discusses, influencing the margin of victory, is irrelevant, because in a non-swing state the margin is guaranteed to be large and the victory is going to be by a landslide. Since hardly anyone wants to vote for a third party in the first place, this one reason matters only for a small minority of voters in non-swing states.
More importantly, the entire first section is misleading. It introduces a hypothetical presidential election “in the land of Erewhon”, and claims that if the real election is close, the analogy shows you should vote. The fact that this reasoning doesn’t apply to the vast majority of voters in the real presidential election in the US is never mentioned.
Do you disagree with any point in my summary (the “Slightly Longer Answer” bit), or just with my style of presentation?
I don’t know that I can put my disagreement more clearly than in the second paragraph of the comment you replied to, but to answer your question nonetheless: I think your summary suffers from lying by omission. You are not saying anything that is false, but an uninformed reader is likely to be misled by your text into falsely thinking that their vote matters more than it really does.
I deeply value honesty, and I wouldn’t offer an argument if I thought it would be misunderstood by the relevant readers. But I can’t really imagine there are many people that will read my article (especially given that I’m sharing it here and among my personal friends), find it a persuasive reason to vote (compared to more emotional appeals), and yet not understand how the Electoral College works.
The same logic applies to other offices, local races, and ballot initiatives, with higher probability but lower impact.
What tim said; also, everything here applies to Senate and House races as well.
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.
If you actually want to vote Romney you will roll the fair die and have a 2⁄3 chance of voting Romney. If you don’t want to vote Romney you don’t roll the fair die in the first place and therefore it doesn’t come up greater than 2.
Strictly speaking, if you wanted to vote for Romney, you could roll as many fair dice as you like until one comes up greater than 2, leaving a ~1 chance of voting for whoever you intended in the first place.
It depends a bit on how you parse the sentence. If you roll 5 times you didn’t role a dice but five dice.
Coincidence?
Yes!
More like a common cause :)
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.
Good someone pointed this out! I think this is correct and an important point. Voting is to a large extent about expressing loyalty to king and land (or system and government for those of you who do not live in constitutional monarchies). It is one of the processes that build trust in the society and thus in efficient coordination. Looking just at who will win the election is too a narrow perspective to properly understand the effect of voting.
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:
Nobody votes, you lose the election.
Everyone votes, you win the election.
The benefit of your desired party winning the election is greater than the cost to go and vote. But if your vote adds only 0.01% chance of winning, which is not enough to outweigh the time spent for voting, why is it better for everyone who knows the secret if all of them voted?
The answer is that by voting, you don’t only increase that chance by 0.01% for you, you also increase it for everyone else. So if there was two of you, you can both vote and each of you will gain a double increase for the same cost. But if you’re altruistic, then the most logical thing would be to vote.
Sorry if my idea is repeated in the article or in some of the comments, I didn’t read everything.
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 where the result affects more people in a larger way, or
(b) After voting in a local county election where their vote has a larger effect on the outcome, but where the result of the election affects fewer people in a smaller way, or
(c) According to some reliable function relating scale and impact of election
I’d also be interested to see how this compares to, say, how empowered people feel after their favorite football team wins or loses a game.
If the confidence fairy has been shown not to exist. (The confidence fairy is the theory that the reason banks are not lending right now is due to a lack of confidence in the market.) Then why should we believe that feelings of hopelessness or empowerment will effect the economy? (productivity is an economic feature) What seems to me more likely to affect productivity is whether or not one got a good night’s sleep the night before and ate a decent breakfast.
If folk psychology (hope, despair) is epiphenominal then there is no reason to believe they have causal effects in the world.
To clarify (I didn’t do a good job above), I meant to ask “do certain perceived psychological effects (which probably do correlate with neurophysiological mechanisms) correlate with voting events AND significant positive and negative effects on the populace in terms of perceived well-being and productivity?
I did not know that about banking, although I did not expressly believe the alternative either. I will definitely look at that a little more. Intuitively I also agree with the sentiment that many other seemingly mundane things probably have a greater overall impact on societal production than relatively uncommon events.
Ok, I do wonder how one would distinguish between perceived effects vs real effects. The real effects of say civil rights legislation was greater freedom and opportunity for minorities. We are a better more productive society when we, at least in theory, give everyone an equal chance to succeed. That’s the real material result of the 60′s civil rights movement.
The psychological effect of those who benefited was maybe “I am a valued member of society.” I’m not sure how one teases that apart from the positive effect of simply being able to get a job or a loan without being discriminated against. I am just wondering out loud. I really wonder how much of a difference perception or attitude makes over and above real material changes.
I suspect that my perceptions positive or negative of the results on an election are determined by whether or not I experience real benefit or harm. I also suspect that we sort of backtrack and revise our memories to convince ourselves that we are masters of our domain when the opposite may be true.
But I don’t know. I could be all wrong.
I find that primary elections, other than for President, are rarely contested by serious candidates...
That’s often true in Congressional elections, where an incumbent or a strong candidate will “clear the field”, but it’s definitely not the case in local elections. Also, there are often very competitive primaries in places where the general election is a foregone conclusion.
In my district, every Democratic candidate ran unopposed in the primary election, including for state and county offices. So I didn’t bother to vote in it.
Fair enough.
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 1:sqrt{N} 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.
How did you calculate those odds? Shouldn’t it be the binomial distribution where n=number of voters, k=n/2, and p=.5, meaning the probability of you being the deciding vote is (.5^n)*(n choose n/2). Still better than Erewhon, though.
I’m not particularly confident that I’m right about this though, so please explain if I’m wrong.
Yes, and Sqrt(n) (times a small constant) is a good approximation to the above for large n. See Stirling’s formula.
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.
I imagine most people feel relieved when one candidate wins rather than another because they think there is going to be a difference in practice between what one & the other would do. Convincing people that you’re going to do X, Y, & Z is the purpose of a political campaign. In reality, the elected official has no obligation to actually do X, Y, & Z.
No obligation, sure, but in practice most officials do things that are basically predictable from their campaign predictions (once you apply an appropriate filter of cynicism). If one candidate promises to do X, and the other promises not to, you can reasonably conclude that the chance of X actually being done is substantially higher if the first candidate is elected.
(One reason for this is that even politicians find it difficult to lie convincingly and directly. They much prefer to be evasive or subtle on questions where their beliefs are inconvenient. Thus a bold promise is usually reasonably informative.)
According to this site Obama has not kept more than 50% of the promises he made during his campaign. To me that is evidence that what a politician promises to do is not a reliable indicator of what a politician will do.
I said that one should apply a filter of cynicism first.
Obama’s actions on several fronts have certainly dismayed his supporters, but that’s a far cry from them being indistinguishable from the policies that McCain or Romney would have enacted. (In particular, if you really think that stimulus and health care expansion were likely to have happened in the same way under McCain, I have to question your grip on reality.) In order to make voting worthwhile, you don’t have to take politicians’ statements at face value, you just have to be able to estimate some significant differences in their likely actions.
Stimulus possibly, but health care probably not.
I suppose a big chunk depends on what it is exactly you want or expect a politician to do. If the only things that matter to you are that power is decentralized, freedom increased, & less violence is done at the decree of government officials, then it really does not matter who you vote for. The differences between politicians are largely in what way power be further centralized, freedom decreased, & more violence be done. Those differences are not significant to me so long as one politician is not much more likely than another to launch a nuclear bomb or declare martial law.