The $10 billion voter

Update (Nov. 8): Slate’s pundit scoreboard.


Update (Nov. 6): In crucial election news, a Florida woman wearing an MIT T-shirt was barred from voting, because the election supervisor thought her shirt was advertising Mitt Romney.


At the time of writing, Nate Silver is giving Obama an 86.3% chance.  I accept his estimate, while vividly remembering various admittedly-cruder forecasts the night of November 5, 2000, which gave Gore an 80% chance.  (Of course, those forecasts need not have been “wrong”; an event with 20% probability really does happen 20% of the time.)  For me, the main uncertainties concern turnout and the effects of various voter-suppression tactics.

In the meantime, I wanted to call the attention of any American citizens reading this blog to the wonderful Election FAQ of Peter Norvig, director of research at Google and a person well-known for being right about pretty much everything.  The following passage in particular is worth quoting.

Is it rational to vote?

Yes. Voting for president is one of the most cost-effective actions any patriotic American can take.

Let me explain what the question means. For your vote to have an effect on the outcome of the election, you would have to live in a decisive state, meaning a state that would give one candidate or the other the required 270th electoral vote. More importantly, your vote would have to break an exact tie in your state (or, more likely, shift the way that the lawyers and judges will sort out how to count and recount the votes). With 100 million voters nationwide, what are the chances of that? If the chance is so small, why bother voting at all?

Historically, most voters either didn’t worry about this problem, or figured they would vote despite the fact that they weren’t likely to change the outcome, or vote because they want to register the degree of support for their candidate (even a vote that is not decisive is a vote that helps establish whether or not the winner has a “mandate”). But then the 2000 Florida election changed all that, with its slim 537 vote (0.009%) margin.

What is the probability that there will be a decisive state with a very close vote total, where a single vote could make a difference? Statistician Andrew Gelman of Columbia University says about one in 10 million.

That’s a small chance, but what is the value of getting to break the tie? We can estimate the total monetary value by noting that President George W. Bush presided over a $3 trillion war and at least a $1 trillion economic melt-down. Senator Sheldon Whitehouse (D-RI) estimated the cost of the Bush presidency at $7.7 trillion. Let’s compromise and call it $6 trillion, and assume that the other candidate would have been revenue neutral, so the net difference of the presidential choice is $6 trillion.

The value of not voting is that you save, say, an hour of your time. If you’re an average American wage-earner, that’s about $20. In contrast, the value of voting is the probability that your vote will decide the election (1 in 10 million if you live in a swing state) times the cost difference (potentially $6 trillion). That means the expected value of your vote (in that election) was $600,000. What else have you ever done in your life with an expected value of $600,000 per hour? Not even Warren Buffett makes that much. (One caveat: you need to be certain that your contribution is positive, not negative. If you vote for a candidate who makes things worse, then you have a negative expected value. So do your homework before voting. If you haven’t already done that, then you’ll need to add maybe 100 hours to the cost of voting, and the expected value goes down to $6,000 per hour.)

I’d like to embellish Norvig’s analysis with one further thought experiment.  While I favor a higher figure, for argument’s sake let’s accept Norvig’s estimate that the cost George W. Bush inflicted on the country was something like $6 trillion.  Now, imagine that a delegation of concerned citizens from 2012 were able to go back in time to November 5, 2000, round up 538 lazy Gore supporters in Florida who otherwise would have stayed home, and bribe them to go to the polls.  Set aside the illegality of the time-travelers’ action: they’re already violating the laws of space, time, and causality, which are well-known to be considerably more reliable than Florida state election law!  Set aside all the other interventions that also would’ve swayed the 2000 election outcome, and the 20/20 nature of hindsight, and the insanity of Florida’s recount process.  Instead, let’s simply ask: how much should each of those 538 lazy Floridian Gore supporters have been paid, in order for the delegation from the future to have gotten its money’s worth?

The answer is a mind-boggling ~$10 billion per voter.  Think about that: just for peeling their backsides off the couch, heading to the local library or school gymnasium, and punching a few chads (all the way through, hopefully), each of those 538 voters would have instantly received the sort of wealth normally associated with Saudi princes or founders of Google or Facebook.  And the country and the world would have benefited from that bargain.

No, this isn’t really a decisive argument for anything (I’ll leave it to the commenters to point out the many possible objections).  All it is, is an image worth keeping in mind the next time someone knowingly explains to you why voting is a waste of time.

72 Responses to “The $10 billion voter”

  1. fred Says:

    I like the superrationality argument in favour of voting. If I do it, all the other mes do it. I’m effectively a large voting block.

  2. Colin Says:

    This works fine if I am some kind of random voter who doesn’t know which state my vote will be counted in. If I live in a ‘tipping point’ state, all the better. But surely my chance of casting the deciding vote, *given that* I live in New York state, say, is much lower than that of the average voter?

  3. Scott Says:

    Colin #2: Yes, of course it matters which state you’re in. On the other hand, a similar argument could be repeated (with smaller but still-impressive numbers, I think) for state and local elections that might be much closer.

  4. Roger Says:

    So how many trillion is Barack Obama costing us? I figure he has already cost us $1 trillion a year in deficits, and Obamacare probably has another $10 trillion in future liabilities.

  5. domotor Says:

    I think it is a bit of a problem that the 10 trillion dollar is not for the voter, so I would also divide with the number of US citizens, about 300 million, which means that you probably make less than cent if you vote. Of course you might be highly affected by the outcome (e.g. if you are Barack Obama), or might want to do a nice act for your whole country. I think a much better reason for voting is that you can avoid long conversations about why you did not vote, if you want to optimize your time. And a much better system would be compulsory voting, like in Australia.

  6. 1ly1 Says:

    you should stick to doing theory cs. Not that I disagree with your moral stand.

  7. Nick Says:

    I don’t understand the obsession with being the exact person to swing the election. Voting is a collective activity. If a candidate wins an election with a million votes, no one of those million people is any more responsible for that outcome than another. Why isn’t pushing their candidate one millionth of the way closer to winning not good enough for people?

  8. Aram Says:

    Averaging the positive and negative contributions is an interesting question, given that most people are confident about their vote.

    One implication, for example, is that there are a similar number of voters that are each causing $10B of damage. If you’re one of those, you’re contributing more to society by sitting on the couch, or even doing something wildly destructive.

  9. computronium Says:

    I too want voting to matter, but this just seems like sampling error to me. Of *course* voting is worth more in critical elections, state or local. How much is it worth on average?

  10. Joshua Fox Says:

    But _I_ don’t get to keep that extra $6 trillion. It is divided over all taxpayers present and future. So the value of saving that money to me is my share plus the altruistic value I place on other people’s pocketbooks.

  11. Will Says:

    Unless I’m mistaken, the logic here seems flawed. Surely you should be dividing the “cost” of having the “wrong” president by the population of the country?

    It’s implying that we each individually lost a potential $6 trillion by voting him in. It should be $19,255.96. If there’s a one in 10 million chance to avoid losing *that* sum if you vote, it doesn’t seem quite so worthwhile!

    And that’s if your president ends up being all you expect him to be…

  12. Alex Says:

    As Bill Maher puts it, just think of all the crap you, Americans, didn’t have to put up with during the last 4 years. That alone, without its associated monetary value, is worth “peeling your backside off the couch”.

    Good luck tomorrow

  13. S.K. Says:

    Isn’t this besides the point? Isn’t voting, for either side mind you, supposed to be an important civil duty that, neglected, will lead to an erosion of the government’s respect for the people? Won’t a politician take his mandate more seriously if more people vote?

  14. Nex Says:

    This is actually an argument for not voting.

    If you assume that a president is capable of doing trillions of damage to the economy and leading to thousands of unnecessary deaths of troops and civilians then you surely don’t want to give him your mandate, better to stay at home then risk being partially responsible for such a mess.

  15. Torrence Says:

    Suppose you are in a swing state with n voters. Lets crudely model the election in your state by saying that every voter other than you is voting uniformly at random. Then your probability of casting a decisive vote scales like ~ 1/sqrt{n}.

    On the other hand, changes in policy affect everyone in the state, so the change in welfare as a result of the election scales like ~ n.

    So the expected change in welfare that you can affect scales like sqrt{n}!

    So you should care a great deal about voting, all the more so the larger your state — even though your chance of affecting the outcome is smaller in a larger state.

  16. Tyson Williams Says:

    “That means the expected value of your vote (in that election) was $600,000.”

    Shouldn’t you have to divide this number by the population of the United States since the country shares the surplus or deficit “caused” by the president?

  17. » Your vote could be worth $10 billion. Gordon's shares Says:

    […] Link. Elections have consequences. by jgordon on November 5, 2012  •  Permalink Posted in share Tagged pinboard […]

  18. Dan J. Says:

    This is analogous to the concept of pot odds in poker. I would guess that, to some degree, the voters are already aware of this, hence why I expect a higher voter turnout in states like Ohio and Florida compared to, say, California or Texas. But, of course, not many voters will consider the full implications as elucidated here.

    I do feel that your stated valuation of the Bush presidency is a little distracting and needlessly politicises what could have otherwise been a hypothetical example to serve as a demonstration of this concept in probability. On the other hand, I think it highlights the fact that there is much more to be said about the assumptions we would make in our valuation model. The expected net value of each voter will vary depending on their state of residence, the policies that influence them personally (be that socially or economically), and also the degree of true differentiation that exists between the major parties.

  19. Richard Says:

    You mention uncertainties regarding voter-suppression tactics. How concerned are you about the possibility of voting machines being hacked?

  20. blk Says:

    Isn’t this whole discussion missing out on the point of who benefits from the claimed cost of a president? It’s not like any of the mentioned presidents would just poket the trillions by himself – the money is spent in the U.S. the one or the other way (well-paying jobs in the aerospace/defence/military sector for those who work there vs. savings in health insurance cost due to higher participation). A rational voter would vote in such a way, that the GDP redistribution caused by a president maximizes his personal benefit, and depending on where you work (e.g. military vs. academia) your selfish choice may be clear but opposing.

  21. Jay Says:

    Clearly your PhD was not in statistics, Scott.

    I am still undecided. Should I vote for the guy who is about 25% of what I’d like in a President over the guy who is about 20%? Should I vote for someone who I know won’t win to make some sort of statement? Should I go to the polls and skip the Presidential race altogether? Should I skip it all and go for a run?

    (Actual) question for Scott: Do you think voting is so important that you would give people who wanted to vote for the other candidate (i.e. not the one you’re voting for) a ride to the polls? A bus full? In a swing state?

  22. asdf Says:

    The analysis is unrealistic (“nonphysical” as a physicist would put it, I guess). If there is an ultra-close election, there is a recount that is won by whichever side litigates harder and manipulates the press more. It no longer matters which side got the most actual votes, as long as it’s close enough. This happened in Florida in 2000 and in Ohio in 2004. It also understates the hassles of voting: 1) lines in OH and FL this year are up to 10 hours long in some districts with a certain demographic mix; 2) registering to vote subjects you to numerous potential privacy problems. We need some pretty serious reforms.

  23. Scott Says:

    domotor #5:

      I think it is a bit of a problem that the 10 trillion dollar is not for the voter, so I would also divide with the number of US citizens, about 300 million, which means that you probably make less than cent if you vote

    LOL! ($10 trillion) / (300 million citizens) ~ $33,333 per voter.

    Though actually, I specified a $6 trillion payout, and there are ~200 million eligible voters, so

    ($6 trillion) / (200 million eligible voter) = $30,000 per voter.

    This is another startling figure: if you’re an American voter, then George W. Bush cost you personally, on average, something on the order of $30,000.

    So in particular, if each of those 538 Floridian voters knew (with the benefit of hindsight) that they would have a ~1/500 chance of swaying the election outcome, the expected value to them personally of voting would still be $60, which is not bad for an hour’s work.

    It’s funny: many commenters have pointed out that, to make the case for voting being rational, you need to say something about patriotism or altruism, since even if the expected value of your vote to the country is ~$600,000, the expected value to yourself is tiny. And in general, of course, they’re completely right. And Norvig makes exactly the same point in his FAQ. In the special case of Florida 2000, though, even the expected value to yourself would’ve been a cool $60.

  24. JG Says:

    I have problems with a lot of this analysis.

    1. I don’t think you should assume the other candidate would have been revenue neutral.

    2. You have to assume that we got literally nothing for our $6 trillion. This is possible, but the specific argument Whitehouse is making is complete nonsense. The amount of deficit is not the meaningful quantity. That is just a question of whether we are financing our spending by tax or by borrowing. The relevant question is whether we are getting for our spending worth cost.

    3. Whitehouse (and Scott) interpret the quantity deficit / population as the cost to each citizen. This seems wrong. Could we make ourselves richer by raising taxes so that we have no deficit? The relevant variables are spending and what we got for it. You can argue that Bush’s spending was a bad deal, but the above calculation is incorrect.

    4. I would entertain the argument that your vote is going to be decisive in exactly the situations where the outcome is the least important. If the electorate is so undecided between two candidates that your vote makes the difference, then there can’t be a huge difference in quality between the two.

  25. Scott Says:

    JG #24:

      If the electorate is so undecided between two candidates that your vote makes the difference, then there can’t be a huge difference in quality between the two.

    ROTFL!! The 2000 election was the ultimate counterexample to that thesis, a thesis that I don’t think had anything going for it even a priori.

  26. Scott Says:

    Jay #21:

      Clearly your PhD was not in statistics, Scott.

    Was yours?

      Do you think voting is so important that you would give people who wanted to vote for the other candidate (i.e. not the one you’re voting for) a ride to the polls? A bus full? In a swing state?

    No, I absolutely wouldn’t bus Republicans to the polls, certainly not in a swing state. On the other hand, I would at least extend Republicans the courtesy of not actively interfering with their right to vote, which is more than they extend to Democrats these days.

  27. John Says:

    asdf: “If there is an ultra-close election, there is a recount that is won by whichever side litigates harder and manipulates the press more. It no longer matters which side got the most actual votes, as long as it’s close enough.”

    I believe that this makes your vote MORE likely to make a difference, not less likely. As Scott said, there doesn’t have to be an exact tie for your vote to be deciding. The tallies just have to be close enough that your vote triggers a recount. Whether a recount is triggered and the outcome of the recount are random variables that depend on the vote tallies.

  28. JG Says:

    “ROTFL!! The 2000 election was the ultimate counterexample to that thesis, a thesis that I don’t think had anything going for it even a priori.”

    Eh, I disagree. We don’t know the counterfactual and more importantly we (I?) didn’t know at the time how different things would be. Anyways I am much more interested to hear your response to my other points.

  29. Bringham Young Says:

    The idea of a value function is foolish at the extremes: if it were valid then we should live our lives according to extreme Christian principles since doing so might be the only way to get to heaven (a thing of infinite value) as opposed to winding up in hell (a thing of infinite negative value). The chance of these values being correct is exceptionally close to zero….but the value of heaven is infinite! So now I have to believe….I’m sorry, but there is no logical reason for an individual to vote!!!!!

  30. Bringham Young Says:

    One more thing, Scott: even if we accept the argument for why it is worth voting we should balance it against the chance of getting in a terrible accident on the way to the poling station….surely the chance of such an accident happening is greater than 1 in 10 million! And the cost of this accident to me could be huge…it could be my life…again, apart from any emotional benefit there is no logical reason for an individual to vote!!!!!

  31. Dhruv B. Says:

    Apologies upfront for making a tangential point, but it was bothering me in this otherwise great post.

    “Of course, those forecasts need not have been “wrong”; an event with 20% probability really does happen 20% of the time.”

    This is true only in the frequentist view of probability. In the Bayesian view, those experts are merely expressing their beliefs and the world doesn’t have to do a damn thing to respect it.

    An event with 20% “probability” might never happen.

  32. Scott Says:

    Dhruv #31: Obviously—OBVIOUSLY!—when I wrote that “an event with 20% probability really does happen 20% of the time,” I meant, as I said, an event that actually had 20% probability, not one that was incorrectly claimed to have 20% probability. If the forecast is wrong, then it’s wrong, which is a possibility that I implicitly acknowledged by saying that the forecast “need not have been ‘wrong'” (not that it wasn’t wrong).

  33. Scott Says:

    Bringham Young #29:

      The idea of a value function is foolish at the extremes: if it were valid then we should live our lives according to extreme Christian principles since doing so might be the only way to get to heaven (a thing of infinite value) as opposed to winding up in hell (a thing of infinite negative value). The chance of these values being correct is exceptionally close to zero….but the value of heaven is infinite!

    Absolutely not. The fallacy with Pascal’s Wager—as countless people have pointed out before me—is that it illegitimately focuses on only one absurdly-unlikely possibility to the exclusion of all others. What if there’s a demon god who will send me to hell if I pray, and to heaven if I don’t pray? A priori, that’s every bit as likely as the more traditional kind of god, thereby negating Pascal’s conclusion.

    But no similar objection applies to voting. Yes, the probability that your vote in 2000 would have tipped the outcome to Gore over Bush might have been tiny (though not nearly as tiny as in Pascal’s-wager scenarios!). But I claim we can know for damn sure (or rather, about as well as we know anything in life) that if it did tip the outcome, then the utility for the world would have been hugely positive. So your analogy fails completely.

  34. Bringham Young Says:

    Yes, I know the refutation of Pascal’s Wager…but you’ve still been trumped by my argument re the probability of getting in a fatal accident on the way to the poling station! Don’t vote people, it’s not worth it!

  35. Silas Barta Says:

    May I suggest, again, that you bet against Obama? With the markets putting his chance at ~80%, you could get a massive return on your money from him losing.

    So, either he wins, or you ~quadruple your money. Now *that’s* outcome-smoothing!

  36. Asif Says:

    Wouldn’t you be considering all the Ex-presidents presidencies? Assuming the loosing candidates would’ve been revenue neutral(i’m not sure if it’s a valid term) like you did here, if you calculate all other president’s times, then the $figure of the title might lose a few digits i think.

  37. Luke Parrish Says:

    The main objection I have to this is the assumption of the benefit of hindsight… Obviously none of those 500 voters knew that Bush would cost the country trillions (or that Gore wouldn’t). So it’s not fair to price a vote that high, even if you do live in a swing state.

  38. Scott Says:

    Luke Parrish #37: Well, I thought at the time that Bush would be a near-cataclysmic disaster, and I turned out to be correct. (Obviously, I didn’t know that the failure mode would involve a botched occupation of Iraq, unchecked housing bubble, etc. I simply saw the lack of intellectual curiosity oozing out of Bush’s every pore and knew it was trouble.) It can be a terrible burden to be right so consistently, especially about such depressing things.

  39. Scott Says:

    Bringham Young #34:

      you’ve still been trumped by my argument re the probability of getting in a fatal accident on the way to the poling station! Don’t vote people, it’s not worth it!

    What makes this argument funny to me is that I did once get into a car accident on the way to vote, in 2004—the only car accident in my life. I was driving a Prius, and was rear-ended by a woman driving an SUV, so I thought maybe she was trying to prevent me from voting. :-)

    In any case, this consideration is no longer really relevant to me, since my polling place this year is right on the MIT campus, in easy walking distance to my home.

    Yes, it’s possible that I’ll get hit by a car while walking to vote (though I’ll be walking to campus anyway, to go to work). But it’s also possible that my apartment building will burn down, and that having left home early to vote will have saved my life. Or that, while standing in line to vote, I’ll get into a conversation with someone that will lead to a major new research result. What kills your argument is that, with this sort of thing, we really are back in Pascal’s-wager territory, where it’s pretty much impossible to say which of countless unlikely scenarios predominate. A contest between a Democrat and a Republican for the White House is one of the rare cases where one can say with great clarity which one will be better for the foreseeable future (at least for the country and world, if not for you individually).

  40. Ely Says:

    Robin Hanson on how to vote in a recent OB post called “How to Vote”

  41. Scott Says:

    Roger #4:

      So how many trillion is Barack Obama costing us? I figure he has already cost us $1 trillion a year in deficits, and Obamacare probably has another $10 trillion in future liabilities.

    blk #20:

      Isn’t this whole discussion missing out on the point of who benefits from the claimed cost of a president?

    Your comments raise a good point: there really are two separate issues here, the destruction of wealth and the transfer of wealth from those who need it to those who don’t. If I conflated these two issues, it’s because I think the Republican records on both are equally terrible, and the implications for how one should vote are the same.

    Setting aside the profits of Halliburton, etc., the botched occupation of Iraq could be seen mostly as just a negative-sum destruction of some of the world’s wealth, as if some major cities had been set on fire and left to burn to the ground for no reason.

    The Bush tax cuts, by contrast, were a massive transfer of wealth from everyone else to the super-rich. Some people (especially if they’re rich :-) ) might count that as a net gain. I count it as a net loss, since wealth that could’ve been used for the betterment of humankind was instead spent on yachts and lavish parties. And no, I’m not some communist; I’m a liberal capitalist. I think individuals should be allowed to amass vast private fortunes, but not as a matter of “divine right”—simply because it’s an excellent incentive for them to create value. So the question is, do they have more incentive to create value if they pay Bush-era taxes than if they pay Clinton-era taxes? I’ll let Peter Norvig answer that question. From his election FAQ:

      Although I know a dozen billionaires and over a hundred millionaires, I never once heard one express the idea “I was going to start a business, but with the marginal tax rate at 39% instead of 35%, I guess I won’t.” Rather, every entrepreneur I know is interested in whether their venture will have a 1000% return or a 10,000% return — the tax rate is irrelevant. I think Obama’s policies fit the world as I see it: we need small businesses and consumers to grow together. Obama is concentrated on helping them; Romney seems to concentrate on making the rich richer.

    As for Obamacare, I think that cuts across the two issues of total pie size and pie allocation. According to most economists, treating previously-uninsured people before they need to go to the emergency room will simply represent a net savings (or equivalently, creation) of wealth for the country. Meanwhile, requiring insurance companies to cover people with preexisting conditions, and requiring healthy people to subsidize that by buying insurance, will represent a transfer of wealth from people who can afford it to people who can’t. I support both aspects.

  42. Scott Says:

    Richard #19:

      How concerned are you about the possibility of voting machines being hacked?

    I’m pretty concerned—especially because, if it happens and there’s no paper trail, it might be impossible ever to prove that it happened. Relatively speaking, though, I’m more concerned about the purging of minorities from the rolls, the underfunding of elections in Democratic areas and consequent enormous lines, voter ID laws (whose intent of reducing Democratic turnout is freely admitted, in private, by the Republicans who pushed these laws through), phone-jamming of Democratic GOTV operations, and countless similar shenanigans. Why? Because none of these threats are hypothetical: they’re things we know for a fact the Republicans are doing and have done.

    I predict that electronic voting-machine security will become a serious issue in American public consciousness (as opposed to just nerd consciousness), when and only when it’s shown that voting-machine hacking was actually carried out successfully on a significant scale in a US election. The trouble is that, as I said before, it might be almost impossible to prove, even if it is carried out—especially if it’s carried out successfully. :-)

  43. Dan J. Says:

    A robust explanation of why voting is in fact perfectly rational is provided by the application of game theory. Let the player set consist of [Voter A, Voter B] and the move set consist of [Vote, Don’t Vote]. The payoff matrix of each player deciding to vote consists of “Limited Democracy” on the main diagonal with the other values represented by “Autocracy” and “Full Democracy”. Assuming that both players are perfectly rational utility maximisers, both Voter A and Voter B will always select the move “Vote”. The game is directly extendible to an n-player set.

    The same conclusion may be arrived at in normative ethics by application of the Kantian Categorical Imperative. Namely, one should act only according to the maxim whereby you can, at the same time, will that it should become a universal law.

  44. Michael Brazier Says:

    A word on Nate Silver’s prediction. Silver is taking as his raw data a set of state polls which predict (or assume) that the electorate of 2012 will, with respect to party affiliation, closely resemble the electorate of 2008. If that prediction of party turnout is correct, Obama will indeed be re-elected … but that prediction is completely crazy, impossible to make seriously. If you correct the polls to historic partisan splits Romney is a few points ahead of Obama, and wins easily in the electoral college.

  45. Mark Lewko Says:

    Tonight I watched several republican politicians and pundits profess their overwhelming belief that Mitt Romney is going to win the election. While I understand the political/PR motivation for their claims, I find it remarkable that they are willing to make these claims when the statistics/markets put the odds much, much lower. I thought the host of the show should interrupt them and say `well the prediction markets put Romney’s chances at about 32%, so if you really overwhelmingly believe Romney is going to win this is a great bargain! How many contracts are you willing to buy right now?’.

    Instead of trying to refute your assumptions and analysis point-by-point, let me take a more capitalistic approach. Your analysis puts the value of a vote around $33,000 (or $6 Billion as initially claimed). It would be illegal for me to offer to sell you my vote for less. However, I (honestly) find myself in interesting situation. I planned poorly and I am away from my home state, New Hampshire, where I am eligible to vote (which being a swing state likely also raises the value of my vote under your analysis). If I was in New Hampshire, I would vote for Obama, which I believe coincides with your view. So if you agree to cover my travel expenses (transportation to the polls certainly appears to be permissible gift under election laws), which I estimate to be in the $1,000 to $2,000 range, a great bargain compared with the $33,000 value you place on my vote, I will book a ticket and fly to New Hampshire and cast my vote. Otherwise I will not. Let me know as soon as possible, so I can book that ticket!

    (Note: It’s too late to get an absentee ballot. You can certainly criticize my poor planning, but I can’t see how this would effect your economic calculation).

  46. domotor Says:

    In reply to your reply to my comment:

    Now you forgot to divide with the probability that you change the outcome. I meant that you have to divide that with the number of voters. So the correct formula imo is

    1/10 million times ($6 trillion) / (200 million eligible voter) = $.003 per voter. This is your personal expected gain from going to vote, if we only consider how much money you make.

  47. domotor Says:

    And sorry, here we should not divide by 200 million voters but rather by 200 million tax payers.

  48. Scott Says:

    Mark Lewko #45: Very interesting proposal; thanks for offering! :-) But I’m afraid you got the calculation wrong. $30,000 is a reasonable ballpark estimate of the value to the country of each individual vote for Obama, if you simply divide the likely value of preventing Romney’s election by the number of voters. Indeed, because we know that the election will be close (within a few percentage points), and because you live in the potential of swing state of New Hampshire, the value of your vote is actually a good deal higher: let’s take Norvig’s estimate of $600,000, for the marginal value of each additional Gore vote in the 2000 election, and let’s be generous and up the value to a cool $6,000,000 because of your New Hampshire residence.

    Even then, to get the value of your vote to me individually, you still need to divide by the something like the population of the country, which yields a grand total of … 2 cents.

    Now, in considering whether I should pay for your flight, why is it necessary to consider the value to me individually, rather than the value to the country? Well, if I were willing to donate $X for something that had a value of $X to the country, then I could simply get it over with by donating everything I own to the Treasury department!

    Now, it’s true that election season gives me an opportunity to donate $X for something whose value to the country is much greater than $X — e.g., for just a few hundred dollars, I might be able to get a whole busload of Democrats to the polls. But the money that I’m willing/able to spend for that altruistic purpose, I already have spent, donating it to Obama/Biden and various Democratic House and Senate campaigns—which, frankly, is a hell of a lot more cost-effective than subsidizing one person’s travel (by plane, I assume) back to New Hampshire, a person who I can’t even be sure is going to vote for Obama at all and isn’t playing some practical joke on me.

    Even so, as a goodwill gesture, and because I like the chutzpah of your proposal, I hereby declare myself willing to donate up to $20 toward your travel back to New Hampshire today (provided you do travel there and vote)—which is a thousand times more than your vote is worth to me individually. Email me to arrange payment details if you actually do it. Other readers of Shtetl-Optimized are welcome to pitch in as well; we can take up a collection for you.

  49. Rob Renaud Says:

    If you really believe your analysis, how can you justify not assassinating a poorly elected president?

    $7.7 trillion dollars is approximately 35 Googles (the company). I’d be happy if my lifetime contribution to the economy is 1/10,000 Googles.

    There is basically no way I could even come remotely close to doing 1/1000 (7.7 billion dollars) as good as the simple act of killing a poorly elected president.

  50. Michael McGraw-Herdeg Says:

    A slightly less refined but more general version of Gelman’s claim (“1 in 10 million”) is that a good estimate your probability of being the pivotal voter in an arbitrary election is 1/N. Some discussion in http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1024976.

  51. Scott Says:

    Rob #49:

      If you really believe your analysis, how can you justify not assassinating a poorly elected president?

    It’s hard for me to believe that you can’t answer this question yourself. Just sticking to obvious facts, without even getting into the hard moral questions:

    1. If (say) Bush had been assassinated in office, then Cheney would have become the president, and he would have had the country’s overwhelming support to do whatever he wanted. Good work!

    2. Not being perfectly altruistic, I value my own life and freedom almost as much as I value the fate of the world.

    3. If you weren’t aware, assassinating a president is actually nontrivial. The most likely outcome is probably the destruction of the would-be assassin’s own life, with the president staying alive and even gaining additional support.

    On the broader moral question: yes, it’s true that if someone had assassinated Hitler in 1934, throwing away their own life in the process, that person would have performed an incalculable service to humankind. On the other hand, while I do think George W. Bush was probably the worst president in American history (yes, worse than Harding, Nixon, and Reagan), I’m not so delusional as to think he was even remotely comparable to Hitler. Bush “merely” cost the world $6 trillion and somewhere between 10,000 and a million lives (exactly how many to lay at his feet is debatable); he didn’t perpetrate a genocide.

  52. Kenneth W. Regan Says:

    I didn’t realize before reading this post that the name “FiveThirtyEight” can also refer to the number of extra votes Gore needed in Florida. The Wikipedia page with that title does not mention Florida at all.

  53. Roy G. Biv Says:

    Since nobody seems to be pointing out the enormous elephant in the room, I will do it. It doesn’t matter who you intend to vote for:

    The countless amount of articles I have been seeing with regards to unethical and unjust voting practices is mind-boggling. It seems that America is corrupt beyond corrupt, but what’s new? The election outcome will probably be fixed.

    For example, not only are some voters being told to vote on Wednesday, apparently it is next to impossible to select Obama on some rigged voting machines. It automatically selects Romney. See this video:

    http://ca.news.yahoo.com/blogs/ticket/watch-glitch-voting-machine-pennsylvania-171806481–election.html

    If you can stomach it, search the net/reddit for more instances.

  54. AW Says:

    You haven’t responded to several people who have pointed out the ridiculousness of this casual assumption:
    assume that the other candidate would have been revenue neutral
    “LOL” is overused on the internet, but that assumption–and the casual way it’s simply tossed in–literally made me laugh out loud. Neither you nor Norvig offer any evidence for this (and, given how often professional economists disagree about the outcomes of policies, any such evidence would hardly be conclusive–as others have pointed out, we simply don’t have a counterfactual).

    Take the increase in the debt over the past four years. If you like, add to it the projected increase due to Obamacare. Now, I’m going to blithely assert without evidence that McCain would have been revenue-neutral. See how much Obama cost!

    Also, I take issue with your statement from #39:
    A contest between a Democrat and a Republican for the White House is one of the rare cases where one can say with great clarity which one will be better for the foreseeable future (at least for the country and world, if not for you individually).
    Yes, with great clarity–so much clarity that, no matter your opinion on the subject, a sizeable fraction of the electorate disagrees with you.

    It’s fine to disagree strongly with others, and to have strong opinions. But statements like the above–that the “better” choice is both unique (which implies that everyone has the same value definition for “better”) and astoundingly obvious–imply that the large number of people who /don’t/ vote for that “better” choice are either ignorant, malicious, or both. If you can’t think of a real, honest, legitimate reason why someone would vote for a major candidate you oppose, that says more about the bubble you live in than it does about your ideological opponents.

    (And, though one might have a knee-jerk reaction to think so based on my comments above, I’m not a Romney supporter.)

  55. Vijay Krishnan Says:

    If Nate Silvers actually believes his 86.3% estimate, he should go long on Obama on intrade which gives Obama odds of about 68%. He is looking at an excellent statistical arbitrage and gets to bet anywhere from a few ten grand to a few hundred grand at these odds.
    http://www.intrade.com/v4/misc/scoreboard/

  56. Raoul Ohio Says:

    Scott,

    I am certainly no fan of G. W. Bush, but he is hardly the worst president in US history.

    For example, check out some Andrew Jackson factoids:

    1. His drunken pals set the White House on fire at the inauguration.

    2. The pesky congressman Davy Crockett kept defending Indian treaties on which his own signature X was on, rendering it more difficult for Jackson and cronies to steal their land. Jackson orchestrated a campaign of lies that would have done Karl Rove proud to get Crockett out of congress.

    3. The account in the meticulously documented “Frontiersman” by Allan Eckert, of the fight between Jackson and Simon Kenton, proves that Jackson was at least ten years older than his official age, which means he was born in England, and thus not eligible to be President anyway.

    4. Etc.

  57. Nikola Says:

    This stuff got me thinking about a model of when it makes sense to vote in general.

    P(N,n) = B(N,n)*p^n*(1-p)^(N-n) is the binomial distribution where B(a,b) is binomial coefficient and p is apriori probability of one candidate wining.
    Let n = N/2 (one vote decides) and p = 1/2+s where s indicates how much more likely it is for one candidate to win:
    P(N) = B(N,N/2)*0.5^N*(1-s^2)^(N/2)

    for large N this behaves like:
    P(N)=(1/N)^(1/2)*(1-s^2)^(N/2)

    Now notice how if the candidates are equal the chance of you swinging the vote falls with the square root of the population but if either one if more likely to win it falls exponentially.

    Now the benefit of voting is
    B(N)=Bself+A*N*Bsoc
    Where Bself is what we gain by voting, Bsoc is the average benefit per person and A is our altruism constant.
    We calculate Bself with either
    Bself = 0.01$ = 0 or Bself = O(1) = 0
    And plug it in:

    P*B = A*Bsoc*sqrt(N*(1-s^2)^N)

    So it would make sense to vote only if the race was a dead draw (that would be the swing states in the US i guess) and even then the utility only grows with the square root of the population.

  58. The Election Outcome « Gödel’s Lost Letter and P=NP Says:

    […] EV. At FiveThirtyEight, 10:10am ET is still the latest update. In Scott Aaronson’s election item, I commented that “538″ is also the number of voters Al Gore needed in Florida. InTrade […]

  59. John Says:

    Raoul, are you really comparing setting a fire at a party to lying to start a multi-trillion dollar war that resulted in tens to hundreds of thousands of deaths? And that’s just one incident. Bush easily beats Jackson.

  60. Kenneth W. Regan Says:

    Looks like Silver went 51-for-51. He may miss a couple Senate races in the way upper Midwest, perhaps there wasn’t much polling. A good day for numbers.

  61. S Says:

    AW at comment 54: you said

    “It’s fine to disagree strongly with others, and to have strong opinions. But statements like the above–that the “better” choice is both unique (which implies that everyone has the same value definition for “better”) and astoundingly obvious–imply that the large number of people who /don’t/ vote for that “better” choice are either ignorant, malicious, or both. If you can’t think of a real, honest, legitimate reason why someone would vote for a major candidate you oppose, that says more about the bubble you live in than it does about your ideological opponents.”

    Note that most people “can’t think of a real, honest, legitimate reason why someone would vote for a major candidate [they] oppose”, so by your argument, most people live in a bubble. Given that most people live in a bubble, it becomes reasonable to believe “that the large number of people who /don’t/ vote for [a candidate] are … ignorant …” =P

    I would like to believe your assertion that a divided electorate suggests a difficult decision, but the evidence suggests otherwise; I don’t think your worldview is consistent with observed real-world facts. For example, how do you explain the large number of intelligent, highly-educated people who think the decision is easy? How do you explain Republicans’ rejection of scientific facts? How do you explain the impossibility of Romney’s fiscal plans?

    While it may be surprising that half the country supports an obviously worse candidate, this is what the evidence suggests.

  62. asdf Says:

    Ken #60 (and John #27), 538 more votes wouldn’t have helped Gore in Florida. The Florida outcome was determined by dozens of separate lawsuits in the individual counties, with the Bush campaign winning almost all of them even though they were arguing XYZ in one place and the exact opposite of XYZ in another. The outcomes were not random variables. The Republicans outlitigated Gore at every turn. If Gore had 538 more votes (and it would have had to be in some specific counties) the GOP legal team would have just had to crank a little harder. 10,000 more votes might have made a difference. Jeffrey Toobin’s book “Too Close to Call” has a detailed history.

  63. darfferrara Says:

    I don’t disagree with the cost estimate you provide, but you do assume away the problem of knowing who the ‘costly’ candidate is a priori. It reminds me of a quote attibuted to William F Buckley, “They told me if I voted for Goldwater, he would get us into a war in Vietnam. Well, I voted for Goldwater and that’s exactly what happened.”

    I believe that Peter Shor is working on a quantum algorithm that will solve this problem though. Unfortunately, it requires quantum hardware that supports ten qubits, so it will be a long time before it is practical :)

  64. lylebot Says:

    I hope Michael Brazier will return to explain why he thought the party affiliation numbers reported by polls, and the turnout predicted by polls, were “completely crazy”. And also to tell us whether he’s changed his mind now.

  65. Kenneth W. Regan Says:

    Ad “asdf”: Arguably right, but the number is still highly symbolic. The real number that would have headed off the ability to keep any partial count showing Gore ahead off the board would have been about 800 extra in the initial automatically mandated machine recount.

    Incidentally, I was active in 538.com threads during the 2008-09 MN Franken-Coleman recount. The Star-Tribune kept a running tally, but did not include ballots challenged by the other side, which made an incentive to challenge more to prevent its ever showing the other guy ahead. From initial results and some geography I worked out the respective rates at which each side was making challenges that were unlikely to be successful, and thus projected a “true” total. I publicly projected Franken ahead in January and was within 50 of the final margin. Blovious lawyering shamefully delayed the resolution to June, but at least I have that experience of it not altering the numbers (on optical ballots, mind you).

    Most topical “Nate Silver Fact” here by Jacobo Tarrio: “Nate Silver knows the position AND the speed.” (Read “momentum” for “speed”:-)

  66. John Sidles Says:

    A concise and well-reviewed summary of lessons-learned regarding health-care, that has acquired increasing relevance in light of the election result, is Herzlinger and Parsa-Parsi Consumer-driven health care: lessons from Switzerland (2007).

    Conclusion  At least some paths-forward for the evolution of Romney/Obamacare may be acceptable to conservatives and progressives alike.

  67. Wanda Tinasky Says:

    Great, so you’re arguing that voting is rational if you have the ABILITY TO PERFECTLY PREDICT THE FUTURE. In which case I would argue that your opportunity cost for driving to the voting both goes up drastically since what you should really be doing is forming an optimal stock-trading strategy based on prescience.

    The true justification for not voting is:

    1) I have no idea what a candidate would really do once elected. Campaign promises are always vague and politicians are all professional liars anyway.

    2) Even if I _did_ know what a candidate would do I have little-to-no ability to predict the long-term consequences of those actions. (Is raising taxes the answer? Is cutting spending the answer? Not even trained economists agree). You may view this as a corollary to Rice’s Theorem.

    The purpose of voting is to inject randomness into the system and to keep the obvious wackos out.

  68. Sudip Says:

    Concerning the expected profit calculation, I think that the $600,000 should be divided by 300 million to come to a per capita figure. Then it gets totally beaten by the $20 that I can save by not voting.

  69. Jay Says:

    Scott, now the party is over, could you explain the PCP theorem and its consequences? More specifically, I do not understand why it has not been used to verify mathematical proofs as the four-color theorem, and why it is so useful for studying approximation problems?

  70. Jay Says:

    ain´t over till it´s over :-)

    http://news.nationalpost.com/2012/11/13/woman-runs-down-husband-because-he-failed-to-vote-and-let-obama-to-win/

  71. asdf Says:

    Florida strikes again — we’re seeing something like Bush v. Gore 2000 playing out in the Allen West vs. Patrick Murphy congressional election in Florida’s 18th district. Anyone interested can websearch for details so I’ll skip them.

  72. Best Computer Science Blogs of 2012 Says:

    […] to Begin: Check out The $10 Billion Voter for an extended technical argument in favor of the concept that it is rational for citizens to vote […]

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