# Voting Kills

According to a recent study, on the day of a US presidential election there are, on average, an extra 24 auto-accident fatalities.  The study covered the past 32 years, not including this year.

The number of times that a single vote has affected the outcome of a US presidential election is, so far, zero.

In order for voting to be rational, the expected benefit to you from your vote having an effect on the outcome, must be greater than the expected cost of you dying in an auto accident on your way to vote.

The traffic accident study covers only 32 years; but we have over 200 years of data on individual votes not swinging an election.  Over time, it has become much less likely for one person’s vote to swing an election due to population increase.  I will approximate this effect by saying that 210 years of one vote not swinging an election is similar to 1000 years of one vote not swinging an election at current population levels.  That’s a sloppy off-the-cuff guess at how the population changes affect the probabilities.

So, the odds of your dying in a traffic accident on your way to vote would at first seem to be 24 * (1000/4) = 6000 times the odds of your vote changing the outcome of the election.  (Probably much higher. Those are the odds they would be if one person’s vote had swung the election once.)  The odds of your being disabled in a traffic accident on your way to vote would, similarly, seem to be 800*(1000/4) = 200,000 times higher than the odds of your vote swinging the election.

But they aren’t.  Another recent study by 3 people (including Andrew Gelman, one of Overcoming Bias’ readers) (pdf here), using a detailed model, estimated that the odds of one person’s vote swinging the presidential election in 2008 were, on average, one in 60 million.  So why is it that, with more than 120 million people voting this year, no one came close to having their vote swing the election?

The problem is if your vote swung the vote in your state, the vote of half the other voters in your state also swung the vote.  The number of trials here is the number of states times two (one Republican and one Democrat trial per state).  So what that figure really means is that the "average" state has a 1 in 30 million chance of swinging the vote, and you have a 50% chance of being on the winning side in that case.

(To fix my first estimate, we need to say that the figures above indicate that a given party in a given state is unlikely to have more than a 1 in (100*1000/4) = 1 in 25,000 chance of swinging the election.  This then bounds the odds of any one person swinging the election to be no more than 1 in 2,500,000 on average.)

Swinging the vote is a "black swan" event that is highly unlikely.  If it happens for a state one time in 30 million, it should happen about once every 2,400,000 years.  But when it does, millions of people can claim their vote swung the election; the "expected number" of voters who swing the vote per election is actually two.

This is a black swan:  An event that occurs so infrequently that it has an expected number of occurrences in history near zero; yet of such magnitude that its expected impact is considerable.  (And the "expected number per event" is a number that can never happen.)  Relying on history to predict the odds of such an event, as I did above, mislead you.

Back to our practical application.  The chance of your dying in a car crash on the way to vote is really only about ten times as great as the chance of your vote altering the outcome of the election.  Less, if our models of traffic indicate that most of the excess deaths were among people not on their way to vote.  But you’re not going to get that figure low enough for it to be rational for you to vote in a presidential election, unless you’re willing to die to get your candidate elected.  (Or unless, like me, your voting place is within walking distance.)

Rationally, people should be much more interested in local elections, which they have a much greater chance of affecting.

What about the opportunity cost of voting?

The 2008 presidential election cost about \$1 billion, spent contending over roughly 127 million * .2 = 24 million undecided voters.  One vote thus cost about \$40.  If you make more than \$20/hr (after taxes), you would be better off giving \$40 to the campaign, than standing in line to vote for 2 hours.

(Unless you like standing in line better than working.  It could be a good way to meet people.)

"But wait," you say.  "You’ve only considered the cost to yourself.  I’m a good patriot!  I consider value to my country as party of my utility function!"

Well, now that we’ve converted our voting decision into dollar terms, we can say that you might vote if you expect electing your candidate, vs. the other candidate, to be worth at least \$2,400,000,000 to your country.  Otherwise, you should stay home and give \$40 to the US Treasury by burning 2 \$20 bills.

George W. Bush’s presidency may have cost the US 10^3 to 10^4 times that figure.  Let’s say that having a better president is worth \$10 trillion to the US.  (For comparison, US GDP is about \$14 trillion/year.)  Let’s suppose that people who voted, did so because they were good patriots, and put the benefit to their country above the risk to their lives.  That is, the expected gain from having a better president due to their vote (\$10 trillion, divided by 60 million) outweighs the personal cost (value of own life, divided by 6 million).

This means that our rational but patriotic voters are willing to die to save their country \$1 trillion.  That’s not so irrational.

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• http://profile.typekey.com/sentience/ Eliezer Yudkowsky

One of the assumptions here would seem to be that if an election swings 100,000 to 99,998 votes, then no one is responsible for the result, but if the election result is 100,000 to 99,999, then 100,000 people are all individually completely responsible for the result.

I suspect that this is ultimately some kind of misconception about free will, as if you alone in the universe are choosing, but everyone else’s actions are fixed.

• http://blog.politicslaw.org Aaron Street

A big flaw with this argumentation is that there are a lot of other offices on the ballot than just President, all of which have a much higher (though still nowhere near 1:1) probability of being determined by a single voter.

[I live in Minnesota, and it appears plausible that one vote could determine our U.S. Senate race by the end of this week).

There have, indeed, been hundreds of local elections around the country determined by one vote over the last 200 years.

• http://hanson.gmu.edu Robin Hanson

Eliezer, that is the framework of standard game theory, which I’ll happy defend in response to a coherent critique.

• Emmett Shear

This presumes the only effect of a vote is its direct impact on the election, and that a 100,000/99,999 election has the same effect as a 199,999/1 election. Neither of those assumptions is true.

• http://doubtfulpalace.com Tim Walters

Isn’t this an iterated Prisoner’s Dilemma situation? If everyone defects (doesn’t vote), the consequences are rather dire.

In any case, I walk to my polling place (crossing no streets except my cul-de-sac, which I could walk around if necessary), and my ballot is four pages long, with many local offices, so your calculations don’t apply to me. If the country wants to save lives by designating me the sole voter, I will humbly accept.

• Aspiring Vulcan

A “rational but patriotic” person? Can a person be both? :))

• http://profile.typekey.com/GavinBrown/ GavinBrown

Morality is the practice of taking a broader view of the consequences of actions than the perspective of a single individual.

If moral actions could be justified on an individual expectations scale, then we would have no need for the concept of morality.

Another way of looking at it is that elections are mainly about holding elected officials accountable. In a game theory sense, elected officials are only actually held accountable by those who vote. By voting, you incrementally increase the size of the population to whom elected officials must cater, and also make that population more closely reflect your political views by a tiny bit. The population that votes also changes who runs, who is nominated, etc. There’s a lot more to elections than that final binary choice, and every time you vote you move the meter just a tiny bit in all of those ways.

• Benja Fallenstein

What Robin said. Or rather, the first half of what Robin said, not the second ðŸ™‚

Voting seems to me to be interesting as an example of people, at least if we take their stated motivations at face value, actually reliably acting superrationally, and justifying their actions on superrational grounds (even if they don’t call it that). Well, superrationally with regards to the people preferring the same candidate as a “reference class;” arguably, we would be even more superrational if everybody first flipped fifteen coins and only went to vote if they all landed heads. It seems obvious why the first happens while the second doesn’t: in the first case, individual deviation from superrational equilibrium (I don’t go to vote) gains little to the individual, while collective deviation from superrational equilibrium (nobody who prefers my candidate goes to vote) costs the individual a lot; in the second case, individual deviation (I go to vote even if I don’t get ten heads) gains the individual a lot, while collective adherence (everybody flips coins) gains each individual little (the reduction in probability of mortality is only a miniscule increase compared to that of driving on ordinary days).

Robin, I would be willing to try and expand this into a (hopefully) coherent critique, but what it would boil down to is, if (a) people are consciously playing a superrational equilibrium, and (b) playing it costs them much less individually than everybody deviating from it would cost each of them, then who is to tell them they’re wrong to do so? Superrationality may be hard to achieve, but when you’re there and benefiting from it, why should you deviate (when you’re perfectly aware of the justification for superrationality, i.e., that others facing the same situation think similar thoughts and will make the same decisions)? I think that whether or not you agree, you probably do understand my argument already ðŸ™‚

• Benja Fallenstein

On reflection, one unstated assumption of my argument above is that voting is adversarial between people preferring different candidates, while a reasonable way to describe how people think about voting is that it is a tool for aggregating information about which candidate/party is best for the community (as the original post does). I’m too lazy to think about which of the perspectives is appropriate for answering what kinds of questions ðŸ™‚

• http://dmytry.pandromeda.com Dmytry Lavrov

Well every time a single vote swings the elections, its not just one person that’s responsible, but each person that voted.

• http://outsidethebeltway.com James Joyner

Do the data take into account weather? Are the additional deaths over and above what would be expected on that day in November? Or merely the national annual average divided by 365?

• http://profile.typekey.com/andrewgelman/ Andrew

I’ve posted a longer comment as its own blog post, but briefly in response to Benja Fallenstein: I think that voting for president is much more of an aggregation of preferences than an aggregation of information.

• JH

“In order for voting to be rational, the expected benefit to you from your vote having an effect on the outcome, must be greater than the expected cost of you dying in an auto accident on your way to vote.”

This isn’t true. You have to add in the value one receives from the act of voting. People like voting. They receive value from simply going to their polling place and voting. The proper formula is:

PB – C + V

P = Probability your vote sways an election.
B = Benefit you get from your candidate winning.
C = Cost of voting.
V = Benefit you get from the act of voting.

V is what explains why most people vote.

• http://www.ciphergoth.org/ Paul Crowley

Wow, your conclusion is actually a far stronger argument for voting than I had expected.

I’d like to hear the coherent critique and defence of the standard assumptions of game theory. I don’t think it’s exactly that unless it’s decided by one vote then your vote doesn’t count, but that is the correct calculation to plug into the utility comparison. For example, it does as it should show a greater effect when the election is close than when it is overwhelmingly on one side.

Also, talking about voting motivates those who agree with you to vote, and faking it is probably more work than voting.

• http://profile.typekey.com/aroneus/ Aron

If the going rate of dying in the country is 1 person every 10 seconds for 300M people (3.15M of 300M per year) then if 45M people were to spend an extra 30 minutes extra in a car to vote, the number of people dying in a car rather than where they would have died is 24.

Is it rational to use half-baked statistics?

• http://shagbark.livejournal.com Phil Goetz

That’s a clever point – but most people on the verge of death are not out driving cars. The majority of fatal traffic accidents are caused by people making mistakes, not by dying of cancer while at the wheel. So neither my nor your use of the statistics is fully-baked.

• Benja Fallenstein

James: Do the data take into account weather? Are the additional deaths over and above what would be expected on that day in November?

Methods. We analyzed national data from the Fatality Analysis Reporting System of fatal crashes in the United States from 1975 to 2006. We included all presidential elections since database inception (from Jimmy Carter in 1976 through George W. Bush in 2004) during the hours of polling (defined as 8:00 AM to 7:59 PM local time). For each election, we also identified the same hours on the Tuesdays immediately before and …

So, Tuesday before and after — the researchers aren’t completely stupid ðŸ™‚

Unfortunately, the currently freely available part breaks off there (there’s one paragraph before it), and Google doesn’t find an ungated PDF. The journal appears to have a six-month moving wall, meaning the article will be available for free. The downside is that, perhaps as a consequence, institutional subscriptions to the journal don’t seem to be popular with librarians. At least around here.

• freeman

Why bother trying more elaborate schemes to realize it’s a waste of time to vote in presidential elections. Worthless thankfully-incompetent probably-evil sleaze A versus Worthless thankfully-incompetent probably-evil sleaze B – what difference does it make which one wins? Does anyone really think the country would be much different if Gore had won in 2000 or Kerry in 2004? I’ll admit they were probably marginally worse than Bush, but not enough for anyone sane to bother lifting a finger to try to make a difference.

Local elections are another matter, because you might actually be able to make a significant difference there, and because most of the evil done by government is done locally.

• MZ

the odds of your dying in a traffic accident on your way to vote would at first seem to be 24 * (1000/4) = 6000 times the odds of your vote changing the outcome of the election

Stated this way, it sounds like there’s far more risk than benefit to voting. Of course, the benefit is so low (ostensibly at least, but more on that in a minute) that the risk is extremely low too. Let’s go back to the original statistic. 24 extra automobile fatalities on election day. I assume that’s in the entire United States. What’s the baseline? There are about 44,000 fatalities per year, or about 120 per day. That’s an increase of 20%. Sounds bad… until you consider that fatalities are not distributed evenly. You probably have a two fold higher chance of dying on a Friday or Saturday night than on a Tuesday. And you’re probably not doing anything near as important as voting at that time. So if it’s irrational to go vote, then I expect you never to leave your house on the weekend.

But that’s the point. You do leave your house on the weekend because the probability of being in a fatal accident is so low.

Your argument, really, is that the benefit of voting is so much lower. This is only true if you accept the single reason that you gave for voting — influencing the outcome of the election. People vote for other reasons, the most important of which is probably the psychological satisfaction of knowing that they contributed to something bigger than them.

No matter how much of a rationalist or utilitarian you are, I assume you do things in life other than eat, drink, sleep and work. You accept costs and risks to engage in avocations — things that bring you joy or comfort. How many movies in the last decade have you seen in the theater that turned out to suck? Multiply that by an \$8 ticket and time wasted, and factor in what the actual benefit of seeing a movie in the theater is, and it seems that movie-going is much less rational than voting. But you do it anyway, because there are psychological benefits that are difficult to quantify, and because, all things considered, losing \$8 on a movie here and there is a cost you can endure.

Well, the probability of getting in a fatal car accident on election day is definitely a cost you can endure, given the benefits.

• http://shagbark.livejournal.com Phil Goetz

“If the going rate of dying in the country is 1 person every 10 seconds for 300M people (3.15M of 300M per year) then if 45M people were to spend an extra 30 minutes extra in a car to vote, the number of people dying in a car rather than where they would have died is 24.”

Your analysis suggests that riding in a car is no more dangerous than anything else Americans do. And that’s ridiculous, so you should know right away that your analysis is wrong.

People who die in this country are usually sick, and not about to drive off to vote. Heart disease and cancer are not the leading causes of auto accidents.

• http://profile.typekey.com/aroneus/ Aron

“so you should know right away that your analysis is wrong.”

It’s nice when we know it right away. :p

Likewise, if you further dis-aggregate the statistics you will find that the risk is increased more for some people over others. Perhaps the 24 extra deaths can be entirely explained by people with extremely poor eyesight who rarely drive except on voting day. If so, then it would hardly be relevant to consider the stat for the rest of us.

• http://shagbark.livejournal.com Phil Goetz

Aron: Yes, the figure 24 can be attacked in a variety of ways. Still, even if all you do is consider your chances of being killed per minute spent in a car, you’ll probably find that voting is more likely to kill you than to change the outcome.

• http://profile.typekey.com/andrewgelman/ Andrew

Freeman,

Some people feel as you ,but many Americans have strong preferences for one candidate or the other. The evidence from party platforms and votes in Congress is that the Democrats and Republicans differ quite a bit, more so than left and right groupings do in most other developed countries.

• Jason Brennan

In a forthcoming article of mine on voting (Polluting the Polls: When Citizens Should Not Vote), I put in a footnote something about how the expected harm one does by driving five minutes to a polling station is many thousands of orders of magnitude greater than the expected utility of one’s vote. I used Brennan and Lomasky’s formulae for the expected utility of voting (I consider their work superior to the formulae Gelman et al used). I found data on the average expected externality per driver per year for each state from some published economics piece and made some reasonable extrapolations.

However, though I think it is true that one does more expected harm from driving to the voting station than one does expected good by voting well when one gets there, I don’t yet see why this proves voting is irrational. You assert “In order for voting to be rational, the expected benefit to you from your vote having an effect on the outcome, must be greater than the expected cost of you dying in an auto accident on your way to vote.” This probably seems obvious to you–of course, to be rational, benefits must exceed costs! (I assume by “benefits to you” you just mean that it benefits things that you care about–you aren’t assuming that only egoism and non-tuism are rational, since it’s no longer rational to think that in light of the past 40 years of philosophy.)

Please explain to me why your assertion is true. In particular, please explain why the rationality of behavior must be always be evaluated in terms of individual utility as opposed to being evaluated as being part of a collectively rational activity.

• Hyphen

I get to vote by mail (thanks oregon) so the worst that could happen to me because of voting is a papercut. I’m willing to take that chance.

• http://profile.typekey.com/hopefullyanonymous/ Hopefully Anonymous

“Worthless thankfully-incompetent probably-evil sleaze A versus Worthless thankfully-incompetent probably-evil sleaze B – what difference does it make which one wins? Does anyone really think the country would be much different if Gore had won in 2000 or Kerry in 2004).

It’s interesting how robust this meme is, given that it has survived (at least in some people) until the final and least popular days of the Bush administration.

• Paul

Hyphen: You could be hit by the extra postal truck dispatched to pick up all the mail-in votes.

• Abigail

Is JH arguing past the question of rationality?

JH said, You have to add in the value one receives from the act of voting. People like voting. They receive value from simply going to their polling place and voting. The proper formula is:

PB – C + V

P = Probability your vote sways an election.
B = Benefit you get from your candidate winning.
C = Cost of voting.
V = Benefit you get from the act of voting.

V is what explains why most people vote.

A: I agree that I get a value from voting, a good feeling, whatever that might be. I could tell myself that my feeling is “irrational”, and therefore I would be better off not voting for the reasons above. Or I could just vote, because of the good feeling I get from it.

What is the cost to me of voting? The time it takes, (I too walk to the polling station), and the risks of going there, which are different from the risks of being where I would otherwise be. Voting gives me an emotional reward.

The good feeling outweighs the costs for me.

This could be an argument against working hard to ensure all ones behaviour was rational. What advances my interests best? Why does anyone assume that it is rationality? If living in a “fool’s paradise” makes me happier, and does not bring me up against Reality in too painful a way, so that I become rational where necessary, whenever I do find that I bump against reality, why spend effort “overcoming bias” at all? Because it is “fun”, and gives an emotional reward?

• billswift

Isn’t it interesting how some people use the word meme as a derogatory? They only use it for things they don’t agree with instead of actually considering the point.

There isn’t really much difference between the parties, except to a small degree in their lies and rhetoric.

Here’s John Derbyshire’s take on the election:

Name of Party Votes Won Percent of Total

Tax And Spend Party 68,440,793 52.8

Borrow And Spend Party
(Also known as “Tax your
Kids and Spend Party”) 59,390,576 45.8

Stop Reckless Spending Parties 723,293 0.6

All hail democracy!!!

• http://shagbark.livejournal.com Phil Goetz

JB wrote:

Please explain to me why your assertion is true. In particular, please explain why the rationality of behavior must be always be evaluated in terms of individual utility as opposed to being evaluated as being part of a collectively rational activity.

I was being lazy. The last part of the post considers collective utility.

I think it’s interesting that you can take the money values involved in behaviors with public benefits, and calculate the ratio of self / community interest that people use in their decisions. (I didn’t do that, because I think it would be better to use a less ideology-laden behavior to come up with that figure.)

• http://shagbark.livejournal.com Phil Goetz

Abigail wrote:

This could be an argument against working hard to ensure all ones behaviour was rational. What advances my interests best? Why does anyone assume that it is rationality? If living in a “fool’s paradise” makes me happier, and does not bring me up against Reality in too painful a way, so that I become rational where necessary, whenever I do find that I bump against reality, why spend effort “overcoming bias” at all? Because it is “fun”, and gives an emotional reward?

Good question. To some extent, rationality is a public good. Your being rational may benefit others more than yourself. (Although in the case of voting, the original post suggests it may harm others.)

So, to a self-interested agent, is rationality irrational?

• Oolon_Colluphid_Dem

“The number of times that a single vote has affected the outcome of a US presidential election is, so far, zero.”

Here you are just flat wrong. Every single vote “affects” the outcome of the election. That is a self-evident fact. You should have said that no single vote has ever determined the outcome of an election.

• Oolon_Colluphid_Dem

I would really love to meet these mythical people who only vote in presidential elections because they believe their one vote will determine the outcome. I’ve never met one, nor have I seen one online, or talked to anyone who has met one. I doubt believe they exist and if they do I highly doubt they are anywhere close to the majority.

These people seem to be the focus of a great deal of those who believe voting to be a waste-at-best or even a vice. Yet I don’t see that much data on exit polling or nationally conducted surveys that show these one-vote-deciders even exist outside of the imagination of third party voters and anarchists.

So some information on these one-vote-deciders would be appreciated.

• JH

Oolon_Colluphid_Dem, those people do exist. Haven’t you ever heard someone say, “I live in California, so my vote doesn’t even count; Obama is going to win easily. If I lived in Virginia, then my vote would mean something.”

• Abigail

Phil Goetz- is rationality irrational to a self-interested agent?

“If ignorance is bliss, tis folly to be wise”. But ignorance is not necessarily bliss.

It is necessary for parts of society to behave rationally, when doing their job. Surgeons, engineers, etc. However, outside of doing a job, people are often irrational, and it is not certain that being rational would be good for each, or for Society. Example, one consoling another who is bereaved. I feel consoled by the other, though I do not believe in an afterlife, have genuinely lost the deceased; but a hug makes me feel better. I do need to dwell on rational considerations, but also need to mourn, to heal, which is not a rational process.

I read this blog because I wish to improve my ability to think rationally, but I am not convinced that being rational is appropriate in all circumstances, for the individual or the tribe.

• YesAnonymous

No one is a perfectly rational selfish utility maximizer. That’s why classical economics doesn’t work.

Rationality in all walks of life make one an uncaring, unfeeling, unsympathetic, and often immoral robot.

• Indy Ray

The statistics are all off. let’s for a moment go over the statistics

We know the the increased probability of dying due to an auto accident on election day is about:
24/(3 x 10^9)

The probability of one vote changing the election is up to:
1/201

or assuming the flawed 1000 year probability suggested by the poster:
1/1001

but likely less. Now lets get those in perspective

Death probability:
3/(3.75 x 10^8) with a pretty small deviation

probability of influencing the election:
0/1 to 374625/(3.75 x 10^8)
187312/(3.75 x 10^8) with a deviation of the same

so they have the same denominators so (187312/3) or about 62437 times more likely to have a single vote influence the election then to die on the way to the elections.

Keep in mind that the values are approximate and the sampling data is poor, but the statistics are sound.

• Indy Ray

And that’s not taking into account the influence you have on changing the vote even if not directlly changing it, which in 2004 in florida has shown to have been as good as about 1/500 which increases the value of voting.

Or the count of people a post about the likelyhood of death while going to the election may influence, which has much higher potential, thus increasing the value of ignoring said post and voting anyways.

As it turns out, statistics are just a way to play around with numbers to make people believe you. Atleast use good statistics now.

• Tim Fowler

re: “So what that figure really means is that the “average” state has a 1 in 30 million chance of swinging the vote”

The average state has a lot more than a 1 in 30 million change of swinging the vote. Even states with only 3 electoral votes have a much higher than 1 in 30 million change of swinging the election.

• Philip Goetz

1 in 30 million chance of the victor winning by 1 vote, and of that swinging the election.

• http://shagbark.livejournal.com Phil Goetz

” The average state has a lot more than a 1 in 30 million change of swinging the vote. Even states with only 3 electoral votes have a much higher than 1 in 30 million change of swinging the election.”

I meant, “The average state has a 1 in 30 million chance of /it’s/ electoral vote being decided by one vote.”

There may be a higher probability that your vote will swing the national vote due to electors challenging the constitutionality of being forced to vote according to the popular-vote win. Stuff like that, black swans inside our election system itself, could account for most of the probability of your vote swinging the outcome.

• Doug Winter