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Why it's (often) rational to vote:

The upcoming election raises the important question of whether it's rational for you to vote. You might think that the answer is obviously "yes." But economists and other rational choice theorists have long argued that voting is irrational. Why? Because there is only an infinitesmally small chance that your vote will make a difference. In a U.S. presidential election, the chance that one vote will decide the outcome is less than 1 in 100 million, and it is still extremely small even in elections for the House or Senate. Thus, the 30 or 40 minutes of time that it takes to vote is probably far more valuable than whatever benefit you hope to derive from the "right" candidate winning, if the latter is divided by the ludicrously tiny chance that your vote will be decisive.

Critics of rational choice theory, of course, have had a field day arguing that rational explanations of human behavior are invalidated by the obvious fact that millions of people do vote, despite its being irrational to do so. The critics are, quite rightly, not swayed by arguments that voting is rational because people feel they have a "duty" to go to the polls. After all, why would it be rational believe you have a duty to do something that makes no difference? Duty-based explanations don't rescue rational choice theories of voting; they just add another layer of irrationality to the mix.

In fact, however, both sides are wrong. It is indeed rational for many people to vote, and therefore the existence of widespread voting is not evidence against the validity of economics or rational choice theory. For a detailed explanation, complete with equations, see my forthcoming article here.

The key insight is that the traditional rational choice theory of voting implicitly assumes that the voter cares only about their own self-interest, narrowly defined. But if you care even slightly about the potential benefits to fellow citizens of ensuring that the "right" candidate wins, then the sum total of those benefits might well outweigh the (generally low) costs of voting even after discounting for the fact that there is only a minute chance that your vote will make a difference. Real-world voters, of course, probably don't go through detailed calculations of the sort that I describe in the article. But they do likely realize that their is little chance that their vote will make a decisive difference, while also caring at least slightly about the welfare of their fellow citizens. And the combination of these two assumptions is enough, for many people, to make a rational decision to vote.

Of course, under these assumptions, it will be rational to vote only if you perceive a significant difference between the two opposing candidates or parties. And, as I note in the paper, studies do indeed show that those who perceive a big difference between the two sides are far more likely to vote than those who don't.

This theory is not entirely original to me; it was in fact proposed by philosopher Derek Parfit in his 1984 book Reasons and Persons (pp. 73-75); what I have done is explore its implications for voting theory more generally. Until now, Parfit's theory has been largely ignored by academic scholars of voting, perhaps because Parfit is not an economist or political scientist, and his book is primarily devoted to other subjects.

Not all the implications of the Parfit model are reassuring. As I show in my article, despite the fact that it is rational to vote, it is also rational for most people to be poorly informed about politics (primarily because acquiring and processing political information is much more costly and time-consuming than voting). For the minority that is well-informed, it may well be rational to analyze the information they do have in a biased and illogical way. Thus, a rational population is likely to have a large number of people who choose to vote but also tend to be ignorant and/or illogical about politics.

UPDATE: Some commenters argue that it's rational to vote because of the chance that, even if your vote isn't decisive, it can send a "message" about the degree of support for a particular candidate, policy, or party. But the same logic applies here. The chance that the "message" will be "received" is only infinitesmally greater if Candidate X gets 10 million votes than if he gets 9,999,999. The impact of any one vote on the probability of successfully sending a message is unlikely to be much greater than its impact on the probability of winning the election.

Aaron Bergman (mail):
I always thought the reason to vote was not so that your vote would count; obviously, it doesn't count for terribly much the vast majority of the time. Instead, you should vote to ensure that the vote of that idiot over there doesn't count.
11.5.2006 1:48am
Truth Seeker:
To take an extreme example, let's say one candidate said we need to start a nuclear war and the other said we need to live in peace. Presumably almost no one would vote for the first, and the second would have a near unanimous landslide. But if almost everyone thought logically that their vote wouldn't make a difference, and stayed home the illogical ones who wanted the nuclear war would vote and the warmonger would win.

This reminds me of the example the other day where the man who was told he would be executed during the next week but wouldn't know which day concluded logically that he could not be executed under these conditions, but then he was.

Together these tell me that while logic is nice and neat and mathematically sound, it is worse than wrong in real life situations, it can be dangerous, and that we should live by gut feeling and instinct and face value and ignore logic. The question is why is this? Why does pure logic result in bad decisions?
11.5.2006 2:04am
Wikstrom (mail):
quote:
"In fact, however, both sides are wrong. It is indeed rational for many people to vote.... For a detailed explanation, complete with equations, see my forthcoming article here."

________

...well, that settles it then — you have "equations".

Case closed.

????

Of course, the 'fact' is there can not possibly be objective mathematics proving your assertion. And, no doubt, the use of subjective variables will also thoroughly muddy the water.

How do you feel about the rationality of routinely buying
state Lottery tickets ?
11.5.2006 2:28am
Ron Hardin (mail) (www):
It makes no sense to vote. If everybody thought that way, of course, it would be worth voting. But they don't. So it isn't.

However, look what happens if you vote. You vote for X, your neighbor votes against it. You cancel each other out.

If you refrain from voting, but instead convince your neighbor to vote for X, it goes 1-0 your way. You're ahead convincing even one other, as compared to voting yourself.

Imagine your voting power if you write a blog!

That depends on what is in fact true, that enough people think it's worth voting. That makes your edge argument, not voting.
11.5.2006 2:36am
James Lindgren (mail):
Ilya:

Just from your explanation above, it seems that voting would still be irrational.

You wrote:


The key insight is that the traditional rational choice theory of voting implicitly assumes that the voter cares only about their own self-interest, narrowly defined. But if you care even slightly about the potential benefits to fellow citizens of ensuring that the "right" candidate wins, then the sum total of those benefits might well outweigh the (generally low) costs of voting even after discounting for the fact that there is only a minute chance that your vote will make a difference.



Lots of people go to vote in order to vote for President when there is only a 1 in 100 million chance that their vote will benefit themselves or others. That is not a rational way to spend 45 minutes, even with altruism, if you focus, as you do, on your contribution to "ensuring that the "right" candidate wins."



The best explanation is that voting is like going to a movie or a football game. One derives pleasure from the experience. That may be because of solidarity or altruism, but it is rational to derive pleasure from voting. But it is NOT rational to believe that one is significantly adding to the "potential benefits to fellow citizens of ensuring that the "right" candidate wins," because one is not making an appreciable contribution to ensuring that anyone wins. Without more, altruism does not solve the problem you pose.
11.5.2006 2:54am
zooba:
The correct response is that any interest other than self-interest is irrational.
11.5.2006 3:30am
logicnazi (mail) (www):
Ilya,

I think the argument is that the chance of affecting the outcome may be small but the net benefit to an individual times 300 million times the probability your vote will matter outweighs the cost of voting. So the argument is reasonable but I still am not convinced.

--

More generally I think we can prove that this effect is not enough.

In particular if we assume the difference the candidate makes to any one individual is constant (i.e., independent of total population) then as the population gets large the chances of making a difference still decrease faster than the benefit to making a difference, i.e., the expectation even including other people tends to 0 as the population goes to infinity.

The chance that your vote is the one which makes a difference is the chance that the election splits exactly 50/50. Assuming that voting is a coin toss this is n!/(n/2)!*(.5)^n which I am pretty sure decreases faster than N increases, i.e., n*n!/(n/2)!^2*(.5)^n tends to zero as N goes to infinity. In fact we can 'verify' this by using the normal approximation with p=.5 this is approximately 1*N(n/2, n/4)=k*n^(-.5)*e^(-C*n) where C and k are constants. Since e^(-n)*n^.5 approaches zero this shows for a fixed per person utility the expected utility for voting tends to zero as population increases.

So at least in a population where everyone votes by coin flips a big enough population means voting has a negative expected value. Of course actual elections are not done by coin flips but my sense is that this makes it even less likely one affects the outcome. With very large populations a coin flip election would be virtually certain to be within the margin of error of any polls (standard deviation goes with (n)^.5 meaning the percent within one std. dev. goes like (n)^-.5). Thus polling statistics and other political information pretty much only give you reason to believe your vote matters even less (one canidate is winning). One can try and include more and more effects to make this more accurate but my sense is in total they won't make it more likely your vote will make a difference.
11.5.2006 4:13am
Ivan Ivanovich (mail):
Two points. First see James Surowiecki's "The Wisdom of Crowds" and second, Truth Seeker alludes to the problem with the Dove vs. Hawk example, the importance of my vote is incalculable if I want to avoid living under a Hitler or Stalin. Just today I found a book in my wife's library that sent chills down my spine. She paid 41 Kopeks for it and a note on the second page reads "Order of the Red Banner of Labour Military Publishing House USSR Ministry of Defense Moscow - 1975". In the book are censored excerpts form Maugham and Hemmingway.
11.5.2006 4:23am
logicnazi (mail) (www):
I think what is forgotten in most of these discussions of voting is that the rational thing to do is neither not voting or voting. Unfortunately the really rational solution tends to be a bit too technical for most discussions on this topic but I think it is appropriate on this blog.

If you work on the game theory on a situation like this you are going to find that the rational response will be to adopt a mixed strategy. That basically means you decide to vote with probability p and not vote with probability 1-p and use some random event to decide whether to vote or not. This seems like a perfectly acceptable resolution of the problem.

I mean the reason why this is worrying in the first place is that we can see why it would obviously be bad if no one, or only a very few fanatics, voted. But the situation where only some small percent of us end up voting each time seems perfectly fine. Since the likelihood you should vote should increase as the expected number of people voting decreases and as the likelihood of some crazy extremist winning increases this seems likely to reach a perfectly acceptable steady state.

--

Ultimately though this discussion is kinda pointless and irrelevant. The real world answer is (like the lotto) voting is not only a cost but also a psychological benefit. Many people get a kick, or social reward, for voting. I know that's why I vote and I think enough people feel this way to make it perfectly okay for anyone who doesn't enjoy voting to stay home.

Moreover I think the focus on who wins the race is misplaced. What makes representative democracy work is not that the right person wins the race but that the structural pressure of voting forces both candidates to be relatively mainstream (in the grand scheme of things). If which of the mainstream candidates who won the election made a huge difference in the long term then irrational voting behavior like Roosevelt democrats and Lincoln republicans would have sunk our system long ago.

In other words who wins the election isn't what matters, it is what the results of the election tell future politicians who want to win. If an anti-gay marriage amendment fails by 80% the parties will make sure very different people will end up running in the future than if it loses by 45% (more cynically the same people will say different things). Thus The primary effect of your vote is not in determining who wins this election but in affecting who will run and what incumbents will do in the hopes of getting your vote next time

Understood in this fashion I think the voting paradox is even less problematic. Of course it leads to the amusing result that it is probably more important to participate in phone surveys than it is to actually vote but I suspect that is probably true.
11.5.2006 4:47am
donaldk2 (mail):
The purpose of the vote is to produce a decision that represents the will of the electorate. Voters, consciously or otherwise, understand this and act on it. Despite knowing that the individual vote will not decide the election, they act AS IF it did. This assures the correct result.

The act has a logic of its own, of a category distinct from mere selfish analysis of benefit.

(If the voter has no opinion, he should refrain.)
11.5.2006 5:01am
logicnazi (mail) (www):
Ivan,

Large and incalculable aren't the same thing at all.

Suppose you know some young boy who is charismatic, racist, intelligent and probably slightly mentally ill. Their is some (quite small) chance that he will grow up and become the next Hitler now at the helm of a nuclear armed superpower. This harm is just as 'incalculable' as the prior one.

However, it does not follow that it is morally right to kill this child to head off this low chance event. In fact it is probably still right to try to help this kid in school knowing that it will increase the chance he will become the next hitler even as it also makes it much more likely for him to become a stable, normal individual. In short a relatively small but very certain harm can rightly trump the danger of a 'incalculable' but very unlikely result. Thus just the large harms that can result from not voting don't get one anywhere since the chance that you will make a difference is so small.

As for the wisdom of crowds that doesn't argue that everyone should vote. Rather it argues that a representitive sample of people should vote. If everyone rolled a die and voted only if they got a 6 that would work just as well. In fact if you buy into this wisdom of crowds thing in elections then you should probably avoid voting if you think you are a member of an overrepresented group at the polls, i.e., if you are rich, white and conservative you shouldn't vote as these groups are significantly more likely to vote than the general population skewing the crowd wisdom.

I mean consider the classic crowd wisdom example of people guessing the weight of a bull. If people who are scared of bulls were twice as likely to submit a guess as other people you might end up with an overestimation since their fear might motivate them to see it as bigger. Thus in such a situation if you knew this and were scared of bulls then you arguably shouldn't guess (or take this into account but how many republicans are going to vote democratic because they don't turn out as much?).
11.5.2006 5:02am
logicnazi (mail) (www):
Sorry for the several comments but I keep seeing things I need to refute.

DonaldK,


The purpose of the vote is to produce a decision that represents the will of the electorate. Voters, consciously or otherwise, understand this and act on it.


I respectfully disagree with the first claim, both historically and normatively. Historically the framers went to some lengths to make sure the voter's choices were tempered by the wisdom of the elites. A point I think we would do well to remember. Normatively I think the point of elections is to produce good government. I can't imagine making someone suffer just so we can make bad deciscions at the ballot box.

Your second point is wrong for the same reasons I objected to Ivan's point above. If voters were interested in making sure the will of the majority was carried out then republicans would not regularly turn out in higher percentages than democrats. When you find me the examples of people who are choosing not to vote because they realize the other side isn't as diligent in making it to the polls I'll grant your point.
11.5.2006 5:13am
donaldk2 (mail):
logicn -

I propose a vote on whose analysis (1) is comprehensible and (2) is more plausible.
11.5.2006 5:49am
William Sjostrom (www):
When I lived in Henry Hyde's district a long time ago, I
worked with a guy who had been his Democratic opponent a couple of times. He was an exceedingly unattractive candidate, but the Democrats let him run because no serious candidate would waste his time on a campaign he was going to lose. My vote for Hyde did not affect his victory, but it did help to discourage the opposition. A narrow victory encourages the opposition, a landslide discourages them. My vote mattered because it helps force the opposition to either give up or move closer to my position. Recall Reagan's 60% plus victory in '84, followed by Bush's 54% victory in '88. They forced the Democrats to go with an apparently more conservative candidate in 1992. (Think Dukakis' comments on the death penalty, compared to Clinton's.)
11.5.2006 6:12am
Ilya Somin:
Lots of people go to vote in order to vote for President when there is only a 1 in 100 million chance that their vote will benefit themselves or others. That is not a rational way to spend 45 minutes, even with altruism, if you focus, as you do, on your contribution to "ensuring that the "right" candidate wins."

Jim,

Whether or not it is rational depends on how much of a benefit there is to those other people (the 300 million citizens of the US and possibly even some foreigners) and how much the voter cares about them. For the technical analysis, see the discussion in my article, where I show that it is still rational to vote under plausible assumptions about how large the difference between the two candidates is and how low the chance of decisiveness is.
11.5.2006 6:16am
Ilya Somin:
In particular if we assume the difference the candidate makes to any one individual is constant (i.e., independent of total population) then as the population gets large the chances of making a difference still decrease faster than the benefit to making a difference, i.e., the expectation even including other people tends to 0 as the population goes to infinity.

The benefit may indeed approach zero as the population approaches infinity. However, the real world population of the US (both voting population and the larger population of potential beneficiaries of the "right" candidate winning) is a lot less than infinity. Given that fact, it is still possible for voting to be rational given 1) the chance that your vote will be decisive, and 2) the difference in quality between the two candidates. My analysis (and Parfit's) shows that voting can indeed be rational under plausible estimates of these two variables for US presidential elections. I admit that it would be irrational to vote if the population was infinity, but that scenario is nowhere near what exists in the real world.
11.5.2006 6:19am
Ilya Somin:
I always thought the reason to vote was not so that your vote would count; obviously, it doesn't count for terribly much the vast majority of the time. Instead, you should vote to ensure that the vote of that idiot over there doesn't count.

The idiot's vote already doesn't "count," in the sense that it has only an infinitesmal chance of deciding the outcome of the election, just like yours. Of course, if there is a large number of idiots voting, then their votes will be likely to determine the outcome collectively. In that case, however, your 1 non-idiotic vote won't be enough to change the outcome.
11.5.2006 6:22am
Ilya Somin:
My vote mattered because it helps force the opposition to either give up or move closer to my position. Recall Reagan's 60% plus victory in '84, followed by Bush's 54% victory in '88. They forced the Democrats to go with an apparently more conservative candidate in 1992. (Think Dukakis' comments on the death penalty, compared to Clinton's.)

An interesting point. But it's highly unlikely that your one vote was decisive in that process. Had you stayed at home, the Democrats would probably still have been forced to nominate someone like Clinton in '92. At most, you increased the chance that they would have to do so by an infinitesmally small amount.
11.5.2006 6:25am
MikeD:
I think the key really is the effect the voting results have on the major party platforms, candidate selection, etc. Considered from this perspective, even individual votes can be meaningful as they are counted as part of the overall result no matter who actually wins. I've used this reasoning in the past when voting for Libertarian candidates. Of course, Libertarians never win anything, but if they start consistently picking up a few percentage points, and the main party candidates continue to have very close elections where a few percentage points are meaningful, then just maybe one of the major parties will start to tack in a few Lib party planks as a gesture towards that few percent.

Like for example, the Republicans tend to have a certain attraction to Libertarian types because of their party's broadly consistent "correct" gun control stance; maybe some Democrat will see an opportunity to steal some of these votes by advocating better drug policies? Ya never know.
11.5.2006 7:08am
Bill Woolsey (mail):
If the point of the analysis is to explain what people in fact do, the "irrationality of voting" uses the benefit that the voter perceives from having the election come out the way he or she prefers. Whether this is solely a matter of personal self-interest or else includes the benefit to others doesn't matter. What would the voter be willing to pay to get that result, using his or her actual budget contraint? Perhaps the well being of others is important. Maybe it is instead a matter of who the voter will see on TV for the next several years, and he prefers the more entertaining public official. Or perhaps there is some actual calculation of the impact of the policies on one's personal wealth. None of that matters.

Further, the "moral duty" response is perfectly sensible as long as the moral scheme is not one of act utilitarianism. I suppose one could argue that if one is an act utilitarian, then one cannot have a moral duty to vote. But just about every other moral scheme could include a duty to vote.

Some of those making comments need to think about this just a bit more. The low probability that one's vote impacts the result is an assumption of this argument. If very few people vote, or else you have reason to believe that the the margin will be close (rather than just assuming that all possible result combinations are equally likely,) then this will of course impact the expected benefit of a vote.

And, of course, if the point is to explain what people do, then the issue isn't whether or not the person's view of morality is correct or even rational. The issue is what people believe they should do, not whether or not a moral philosopher finds their view legitimate.

Personally, I believe in a rule-consequentialist morality, similar to rule-utilitarianism. I think I do have a duty to cast an informed vote. I don't beleive that the consequences of my individual vote are particularly important, and so, have often voted for candidates with very low probabilties of success. The irrationality of voting argument does impact my behavior, even though I vote all the time. I think I should vote for the best candidate, and not worry too much about strategic considerations based about very low probability events. You see, I am not an act utilitarian.
11.5.2006 7:09am
pedro (mail):
Shorter Ilya: a hyperfinite sum of infinitesimals may be appreciable.
11.5.2006 7:31am
Hanah Volokh (mail) (www):
I vote because it makes me feel like a good person. Calculate that, economist-man!
11.5.2006 8:35am
Huh:
Isn't the calculation affected by the fact that you're almost always voting in multiple elections, most of them local (where presumably your vote has MORE impact)? This lowers the cost of voting in those same-ballot choices where your vote has little or no effect.

Also, it seems a bit ironic to me that the election for which we have the most information (Presidential), is the one where we have the least individual power.

Finally, what does the research say about controversial initiatives that share the ballot with otherwise "irrational" at-large races? What if people are voting about say, gay marriage or, more locally, an annexation proposal. In those instances people have more information and are more polarized. In this situation voting in a presidential election / senate race would have almost no cost at all, since it takes only a few seconds to register your choice, and you're already there to vote on the more important local initiative. I would think that the increased voter turnout in such situations actually points toward voter rationality, but I could be wrong.
11.5.2006 8:38am
JTB:
Nobody votes anymore because it's too crowded at the polls.
11.5.2006 9:43am
byomtov (mail):
I think James Lindgren's point about deriving pleasure from voting is a good one, ignored in any analysis that considers the potential effect on the election outcome as the only benefit of voting.

We derive pleasure, after all, from expressing our opinions - consider blog comments. There is also peer pressure to vote. It may be interesting to build rational choice models, but explanations that ignore psychological motivations are unconvincing to me.
11.5.2006 10:19am
Dan Simon (mail) (www):
Thus, a rational population is likely to have a large number of people who choose to vote but also tend to be ignorant and/or illogical about politics.

You keep harping on this point, Ilya—but doesn't it also apply equally to people purchasing goods and services in a free market? And why doesn't the solution that works in the free market—"rationally ignorant" consumers tapping into the wisdom of experts through formal and informal information networks—work equally well in the political sphere?
11.5.2006 10:24am
Brett Bellmore:

And why doesn't the solution that works in the free market—"rationally ignorant" consumers tapping into the wisdom of experts through formal and informal information networks—work equally well in the political sphere?


Because,

1. You don't have the choice of not making the purchase,

and,

2. The two major firms have coluded to create insurmountable barriers to entering the market,

So it's not even remotely a free market.
11.5.2006 10:47am
Sasha Volokh (mail) (www):
Ilya -- I would recommend that you structure Equation 2 differently. Suppose D is high enough so you get positive utility from informing yourself. That doesn't mean you'll inform yourself: You may get still higher utility from not informing yourself, because you save $90 and the greater information may not change your vote.

Because your model doesn't say whether the greater information changes your vote, we can't answer whether you'll choose to inform yourself. In fact, your model assumes there are benefits of electing your "preferred candidate," so it's as if the preferred candidate is given. If so, why inform yourself at all?

Whereas if you tweaked the model so the information would give you some probability of changing your view of who was the better candidate (call that the probability that information is important), then you'd have not only a threshold D but also a threshold probability of information being important.

Admittedly, your goal is more modest: You show that the utility of being informed is downright negative, so perhaps you don't need to go through all this discussion of what happens if it's positive. Still, I think it would be useful, because maybe D is high enough sometimes in your model, and even then it's not rational to inform yourself because information might not be meaningful.

As for the altruism: You might consider directly citing Edlin's equation 2 for your Equation 1, since it's mathematically very similar.

Edlin says the probability of being pivotal is proportional to 1/n -- I don't have time to check the math, but somehow it seems wrong to me, and logicnazi's point above that, what with combinators, it decreases much faster than 1/n, might be reasonable. If that's the case, then turnout should be much lower in elections with a higher voter base (federal vs. state, big countries vs. small countries), so if that doesn't happen, it's a strike against the altruism hypothesis. Of course, under Edlin's 1/n view, the 1/n cancels with the multiplicative n of altruism (and, moreover, he explains in section 3.3 that the stakes are higher in bigger elections), so this idea of mine only works if Edlin is wrong.

Finally, I think it may be worthwhile to note what's come up in a couple of comments so far, and is mentioned in Edlin: That as turnout falls, it becomes worthwhile for some marginal people to vote, so under any view there isn't zero voting. This could involve discussing mixed strategies or section 2.2 of Edlin.
11.5.2006 10:59am
abb3w:
I think logicnazi's position is close, but not quite dead on.

Ilya's argument seems to assume that the primary effect of your vote is to sway an election one way or another. This neglects the impact of the larger second order effect: by voting, you send a message by your visible example, showing that you consider the democratic method the Right Way to try and run a government. You are not merely acting to support your candidates, but the electoral process.

With the secret ballot, your vote is only seen as part of a tally (electronic voting reliability issues aside)... but your voting is seen by everyone standing in line, by the poll volunteers, by your family, and perhaps by your co-workers if you take time off from work to go vote. Don't underestimate the importance of the "monkey see, monkey do" effect.

Assuming you think democracy is the best approach you can come up with, voting is the rational thing to do. If you prefer Anarchy to Democracy, you'd be much better off lobbing grenades around at politicians and election workers on election day — which may or may not say something about the differences between the United States and Iraq.
11.5.2006 11:10am
Luke:
Maybe rational choice theory does not accurately describe the way that people make decisions. Isn't this a possibility?
11.5.2006 11:33am
reneviht (mail) (www):
Why are we treating the value of votes as infinitesimals? For informal planning purposes, the value of one vote is small enough that this approximation makes sense. But since the value seems to be taken as 1/(total number of votes), or some other real number, the value of a vote is infinitely larger than infinitesimal for strictly analytic purposes. Going from pure logical models to the informal approximation seems like a good way to get confused.
Re Ilya Somin:
Had you stayed at home, the Democrats would probably still have been forced to nominate someone like Clinton in '92.
Well, yes, and possibly not. I doubt a sentence that uses an unspecified probability is meaningful from a strictly rational standpoint. It's emotionally discouraging, but that's about it.
11.5.2006 11:37am
Brian Kennedy (mail):
Mr. Sjostrom beat me to a point. It is not just casting the vote that is decisive in who "wins" a particular election that might have some effect. The number of votes cast a particular way may have an effect either on the choices offered the next election or on the policy the winner pursues.

Consider, to use another example, a voter who was relatively indifferent as between Bush and Clinton in 1992, and thought that a vote for Perot would be construed as a message that Bush or Clinton -- one of whom the voter realized would win -- should get deficit spending under control. The expected "D" (benefit per person of the NET difference between Clinton and Bush winning) would be close to zero for that voter. The "D" for an actual Perot win, even for that voter, might be very NEGATIVE. Why, though, could not that voter reason that the chance of Perot winning was nil (thus discounting that negative D) and the chance was positive that EACH vote for Perot would add to the likelihood that the next president would pursue deficit reduction policies? If so, would it not be rational to view a vote for Perot as conferring a benefit on the voter and (appropriately discounted) on his fellow citizens? Granted, I have a hard time figuring out how to get that value above the cost of voting. In Mr. Sjostram's example, where the vote is for a major party candidate who might win, the percentage-of-vote utility might in some instances, however, be an important utility to be added to the decisive-vote utililty in your equation.
11.5.2006 11:47am
Syd Henderson (mail):
There have been many times in the country's history where a major party has coopted a position held by a third party. Voting for a third party can make a difference, especially if they start getting 4-5% of the vote.

I also agree with abb3w's comments.
11.5.2006 12:08pm
Jody (mail):
Giving (denying) your candidate (opponent) a mandate is also a reason to vote even if the actual outcome is a foregone conclusion. By increasing (decreasing) the winning difference you enhance (limit) the effectiveness of your candidate (opponent) even if your vote isn't the deciding vote.

Sure it's another epsilon in the calculation, but it's an epsilon that occurs with certainty.
11.5.2006 12:39pm
Ivan Ivanovich (mail):
I'm very satisfied with all the good discussion and that someone besides me has read Surowiecki. I'm going to vote on Tuesday because I'm still pissed off that my 21st birthday fell 2 weeks after Barry Goldwater was defeated and I made a vow that it would never happen again on my account. Rationality be damned. :>)
11.5.2006 12:58pm
vinc (mail):
Interesting. I'm not sure how well this logic works. I think you need to deal with the fact that the vote splits.

In a close election (the only one where your vote matters) all the other voters, who are just as rational as you in this model, voting for the same reasons, and have equal access to information, have split evenly between the two candidates (say A and B).

Say I prefer candidate A. What do I know that the people who prefer B don't know? Nothing. So either I am interpreting the facts incorrectly or they are.

If we assume I am exactly as good a decision-maker as the average voter and that the "quality" of voters is the same for both candidates, then I should believe that the probability of my preference for A being correct is actually just 1/2, and B is just as likely to be the better candidate, and the EV of my vote is therefore 0.

So I should only vote if I think I am "better" than the average voter--or, if I think the quality of voters for candidate A is higher than for candidate B. (Quite a lot better, using Ilya's numbers.) Here, "better" is well-defined, meaning "better at determining which candidate will increase other people's utility."

At least half the voters have to be wrong here and are therefore voting for irrational reasons.

Anything wrong with this?
11.5.2006 1:01pm
nyejm (mail) (www):
Greg Mankiw has a piece on the rationality of not voting today:
11.5.2006 1:03pm
nyejm (mail) (www):
11.5.2006 1:06pm
Sasha Volokh (mail) (www):
vinc: There's a Feddersen and Pesendorfer paper on exactly that: "The Swing Voter's Curse," 86 Am. Econ. Rev. 408 (1996). Edlin has a discussion of why he thinks this sort of Bayesian updating doesn't happen (I forgot why exactly, perhaps because people are super-confident of their own views?).

More generally, you can do the following: "Yes, I realize that I'll only be pivotal if the vote splits 50-50. So, when thinking how to vote, I should assume that the vote has split 50-50. Does that change my vote? No, because I vote because of my values, and the fact that the vote has split 50-50 means that others are split 50-50 on values grounds. That other people hold different values doesn't tell me anything about the rightness of my own values. Therefore, I continue to vote without caring how others vote."

On the other hand, if the election is purely about the factual question of who will be better for the country, where everyone would agree if only they knew all the facts but in fact people disagree because they all have partial facts -- then your view, and the Feddersen-Pesendorfer view, is correct. Reality is probably somewhere intermediate between those two poles.
11.5.2006 2:07pm
Sasha Volokh (mail) (www):
I can't find the Feddersen and Pesendorfer paper online, if you don't have JSTOR or something similar. Another similar paper of theirs is here.

The Edlin paper is available through here -- just search for "Voting as a Rational Choice."
11.5.2006 2:15pm
Kovarsky (mail):
(1) I don't think i've seen in any of the links (i haven't read them all) any good explanation for why it is "strictly economically rational" (a term whose significance i will define momentarily) to vote in districts that tilt heavily one way or another. defining the "power of one's vote" as (1/n)*BENEFIT strikes me as somewhat crude. i think, generally speaking, the "power" of a vote is the likelihood that you cast the decisive vote in the election, which IS infinitesmally small districts with strong supermajorities.

(2) but people still vote even though it's not "strictly economically rational." that's because the penalty/benefit analysis isn't "strictly economic." but it's not "altruism," it's the social sanction (call it a coercive norm, whatever) associated with NOT voting that, I think, accounts for the cosmetically irrational behavior.

i don't think there's anything particularly unique about the phenomena; its just an example of coercive social norms correcting market imperfections.
11.5.2006 2:44pm
Kovarsky (mail):
correction - above should say "large districts with strong supermajorities."
11.5.2006 2:45pm
frankcross (mail):
I haven't dug into the research, but it seems that the rational voter model could be easily tested by relating turnout to the expected closeness of an election. My intuition tells me that there is probably an association here, but not a powerful one. If so, that suggests that voting is driven primarily by the personal utility of voting (as suggested by Jim, Hannah and others).
11.5.2006 3:29pm
Nathan_M (mail):
I'm astonished a law professor would not run a theory like this by someone in the statistics or econometrics department before publishing a paper. The estimate that a voter has a 1 in 100,000,000 chance of deciding the outcomes of an election (which is the number Dr. Somin uses) is demonstrably wrong, albeit only demonstrable by someone who has forgotten less statistics than I have.

Since I can't prove the assumption is wrong, I'll show why it's implausible. 122 million people voted in the 2004 Presidential election. If each one had a 1 in 100,000,000 chance of determining the outcome of the election, then there is only a 30% chance no single vote would have be decisive (the formula to calculate that is (99,999,999/100,000,000)^122,000,000). Assuming 80,000,000 people, on average, have voted in each of the past 10 presidential elections, the probability of no one casting a decisive vote is 0.0003.

There are some serious problems with the argument I have made, but I hope it can still demonstrate how ridiculous Dr. Somin's figure is. Hopefully someone more literate in statistics will weigh in to correct us all.
11.5.2006 3:39pm
Speaking the Obvious:
Ilya: "I show that it is still rational to vote under plausible assumptions about how large the difference between the two candidates is and how low the chance of decisiveness is."

Can you explain, from a libertarian perspective, how any difference between electable Republican and Democratic candidates can be reasonably described as "large"? Perhaps that fantasy was supportable 12 years ago, but we've seen since then how committed Republicans are to re-election vs. principles of limited government.

BTW, in addition to the "economic" argument against voting, there is the "moral" argument. When one has a reasonable expectation that someone you're considering choosing to act as your agent will, if given that position, act immorally--say, by engaging in actions that predictibly lead to the deaths of hundreds of thousands, or by imprisoning large numbers of people for non-violent activities--one has a moral obligation to not choose that person. If it so happens that all such people available for that position can be reasonably expected to so act, one has a moral reason to not make a selection, rather than a moral reason to "choose the least worst of the bunch". This is because you carry a moral responsibility for putting X into office by voting for X, but you don't carry a moral responsibility for X's obtaining office by not voing for Y.

In addition to the economic and moral arguments, there is the epistemological argument, created in 2000. Odds are high your vote won't count, but in the unusual circumstance where you vote did count, no one will believe your vote counted. Races so close are never believed (by a significant fraction of the country), despite recounts, court decisions, etc.
11.5.2006 5:08pm
Ross Levatter (mail):
I recall back in 1992, when I was part of a 21 man physician group, a colleague confronted me wishing to know whether I was going to vote for Bush or Clinton.

It seems that he, a very conservative Mormon who had never met a Republican he wouldn't support or a Democrat he would support, was SHOCKED when, on polling all my other partners, found Clinton leading 11-9. Given his view of the deleterious consequences for medical care, and the medical profession, of Clinton's "health care" plans (and I agreed with my colleague on this), he was shocked it was so close and wanted to know my vote.

First I told him I wasn't going to vote.

Second, I told him that if the group polled as he indicated the best thing to do would be to send two partners out to vote for Clinton and let the rest of us work uninterrupted.

He thought I was joking...
11.5.2006 5:20pm
Respondent (mail):
I believe that, for the most part, the culture that indoctrinates people on how important it is to vote, leading to all those stupid civic service announcements, "no matter whom you support, remember to get out and vote", or Orwellian patriotic slogans such as "Freedom Day", is imposed on us by elected leaders to try to give the public a false sense of control, and hide them from the true picture: the country cannot even remotely be called a republic. On the federal level, over 90 percent of laws passed every year are passed by unelected agencies. It is the wolf coming as a sheep, for the agencies perform quintessentialy legislative functions. They have the power to create crimes, raise certain taxes (the telephone tax comes to mind), decide on punishments for crimes, and are responsible for the vast majority of laws binding everyone from the blue collar worker, the company that doesn't prefer to discriminate to acheive a racial balance ( EEOC reports about "progress" in hiring female construction workers in a company I'm familiar with must constantly be filed), the person who enjoys playing with aircraft smoke detectors (not that it should be legal, but the legislative power is vested in Congress), and even the person who prefers a 6-gallon flush toilet,. Elected officials don't want to take responsibility for most decisions, so they pass them on to virtually unaccountable regulators, and then double the chutzpah by pretending that we the people have a real say in the government of our country.
All the foregoing just adds to the irrationality of voting.
11.5.2006 6:26pm
Kovarsky (mail):
In addition to the economic and moral arguments, there is the epistemological argument, created in 2000. Odds are high your vote won't count, but in the unusual circumstance where you vote did count, no one will believe your vote counted. Races so close are never believed (by a significant fraction of the country), despite recounts, court decisions, etc.

what is epistemic(ological) about that argument? am i missing something.
11.5.2006 7:09pm
Ilya Somin:
I haven't dug into the research, but it seems that the rational voter model could be easily tested by relating turnout to the expected closeness of an election. My intuition tells me that there is probably an association here, but not a powerful one. If so, that suggests that voting is driven primarily by the personal utility of voting (as suggested by Jim, Hannah and others).

THe research does indeed show that closer elections have higher turnout. But the second point doesn't necessarily follow. Even in a non-close election, there is a tiny chance (ex ante) that the polls are wrong and your vote will be decisive.
11.5.2006 7:50pm
Ilya Somin:
You keep harping on this point, Ilya—but doesn't it also apply equally to people purchasing goods and services in a free market? And why doesn't the solution that works in the free market—"rationally ignorant" consumers tapping into the wisdom of experts through formal and informal information networks—work equally well in the political sphere?

In a market, the situation is completely different, because the individual consumer's decision to buy a product or refuse to do so is almost always decisive. Thus, there is a much stronger incentive to be informed. There is also a much stronger incentive to find good experts to rely on.

I discuss the issue of using experts in more detail in many of my academic writings, some of them available on my website here (linked on the VC blogroll).
11.5.2006 8:01pm
Hoya:
What is strange about the assumption about rationality in both the strictly self-interested and in the limited altruism models. Why think that rationality is to be understood in terms of expected benefit of one's own act?

Many actions are justified by their being one's fair share of a common burden, even if failing to do one's share on some occasion will make no difference to the overall success of the scheme. Maintaining car pool lanes can be like this: it doesn't make a bit of difference in the traffic flow if I use a car pool lane even when I am driving solo, and the chances of being caught are really, really low. Why refrain? Well, because it is unfair. So: why is 'fairness requires it' not a perfectly good reason to act in some way, if 'self-interest requires it' or 'the overall good requires it' are perfectly good reasons?

If fairness is itself a good reason for acting, then voting can be justified in that way. It is the one's share of the common burden of selecting good candidates for office.
11.5.2006 8:06pm
k parker (mail):
infinitesimal
"You keep using this word. I do not think it means what you think it means."

(And Nathan_M, your objection may have more statistical insight, but mine is more literary--err, or at least cinema-ary.)
11.6.2006 12:50am
logicnazi (mail) (www):
Ilya,

Fair enough. Dealing with actual numbers and not just assuming they are infinite...ughh how disgusting :-)

I guess I should have taken a look at the paper before I jumped in to comment. Bad habit and all.
11.6.2006 5:39pm
Patri Friedman (mail):
I don't know where this 1 in 100,000,000 number comes from, but it is totally bogus without unreasonable assumptions. You can work out the probabilities using the dbinom function in R. Specifically, the chance of being a swing vote in an election with N people is dbinom(N/2, N, p) where p = the probability voters are voting with. For p = 0.5, the chance of being a swing vote is surprisingly high, for example if there are 100M voters:

> dbinom(50000000, 100000000, 0.5)
[1] 7.978846e-05

But if p is even slightly different from 0.5, the probability becomes vanishingly small, as the law of large numbers takes over:

> dbinom(50000000, 100000000, 0.501)
[1] 1.103748e-91

To be 1 in 100,000,000, p needs to be about 0.5002 / 0.4998. Unless the election is that close, your whole argument goes out the window.
11.7.2006 3:06pm