Should you vote?

(Assuming you’re eligible?)

An argument I came up with a while ago is that, in an election with N voters, the probability of your vote swaying the outcome could be expected to scale like 1/√N—but the utility to the world if your vote does sway the outcome could be expected to scale like N.  Under those assumptions, the expected utility of your vote for the world scales like √N (or -√N, depending which candidate you vote for).  So if you care about the world even ~1/√N as much as you care about yourself, you should probably vote, even though your vote almost certainly won’t change the outcome.  Indeed, the case is even stronger in the US (at least if you live in a swing state), both because the electoral college amplifies the probability of your vote mattering (see the Majority-Is-Stablest Theorem), and because of the US’s disproportionate influence on the world.

A version of the above argument was discovered independently by Peter Norvig, who—appropriately for an applied rather than theoretical computer scientist—plugs in some actual numbers, rather than considering the asymptotics as the number of voters goes to infinity.  Norvig finds an expected value of your vote to the United States of about $1 million (or $6 trillion divided by a 1 in 6 million chance of your vote mattering).  Another version of the argument was given by Andrew Gelman, who points out that other people’s votes are actually not well-modeled by unbiased coin flips (unless you live in Florida, I guess)—but that even under a more realistic prior, your vote still has a constant expected value to society (i.e., it doesn’t decrease with the number of voters N).

I’m aware, of course, that the above is merely a nerdy, rational argument, of a sort that’s probably never actually convinced anyone in the entire history of the world, with the possible exception of Robin Hanson.  So let me raise the stakes a little.  Let me give you an emotional argument.

Did you see WALL-E?  My favorite scene in that predictably-excellent movie—a scene I confess almost brought me to tears—actually had nothing to do with WALL-E or his robo-love-interest EVE.  It was the scene aboard the spaceship Axiom, where the leaf symbol starts flashing overhead, indicating that the earth is once again able to support life, and the fat, coddled human passengers actually have to make a decision about whether to return to earth or not.  For the first time in 700 years, the spaceship’s course is not on autopilot.  Like children away from their parents, the humans face the terrifying realization that there’s no longer any higher authority to tell them what to do.  Or rather, their robot masters are trying to tell them what to do, but the humans are not obliged to listen.

See?  Just like an election.

Your vote almost certainly won’t change the outcome; indeed, thanks to the wonders of technology, there’s probably no way to verify it’ll even be counted.  But on the one day when that leaf is flashing … to have to tell posterity you were too busy finishing a problem set?

Naturally, I also think I know which way you should vote.  But even if you’re one of the humans who thinks the spaceship carrying the last remnant of humanity should remain floating in space—since although (and here I’m embellishing the movie) the spaceship’s power will soon run out, leaving all the humans dead, it’s conceivable that the power could be extended a few years by drilling a nearby asteroid (drill, baby, drill!)—even if that’s your belief system, still I think you should vote.  Why?  Because of my newfound Zen-like equanimity, combined with the belief that your candidate’s going to lose anyway.

Then, after you’ve voted, go into the comments section and ask me a question about what’s new in computational complexity.  As a commenter on my last post helpfully opined, it’s time to start tending my garden again.

Yes We Can.  Prove We Can’t.

57 Responses to “Should you vote?”

  1. Thras Says:

    Nope. The above argument is wrong because of a mistaken argument about utility. If one candidate were planning to spend the wealth of the country on you personally and the other candidate didn’t care whether or not you existed, then the possible utility of your vote is as stated.

    Since the above is obviously wrong, so is the pseudo-mathematical argument. The utility of your vote actually goes to zero as N increases. Your vote doesn’t matter. Don’t bother.

    Further, many of the nice things that we tell ourselves about democracy tend to be false. Yes, Churchill once said that democracy was great while trying to get himself elected. For some reason I’m not actually impressed.

    When you look at the places where it’s good to live versus the places where it sucks, you find that their histories diverge a great deal. Democracy versus monarchy seems to matter a great deal less for personal freedoms than whether or not your government is run by the descendents of Northern Europeans.

  2. John Sidles Says:

    Scott says: After you’ve voted, ask me a question about what’s new in computational complexity.

    Thank you, Scott! Here is my question.

    Ilya Kuprov (please, no 1960s-era jokes about The Man from U.N.C.L.E. :) ) has just published in Journal of Magnetic Resonance an article with the self-explanatory title:

    Polynomially scaling spin dynamics II: Further state-space compression using Krylov subspace techniques and zero track elimination.

    The point of Kuprov’s work is that an important class of quantum simulation problems formerly thought to be in EXP—namely, calculating magnetic resonance spectra ab initio—is actually in PSPACE/PTIME.

    My question is, what FOCS `08 articles should I read to achieve a deeper (and hopefully, more rigorous) quantum informatic understanding of Kuprov’s important (IMHO) findings?

    Please hurry, as this is what I’m reading right now! :)

  3. Stubby Says:

    there’s probably no way to verify it’ll even be counted

    I was wondering about this as I filled-out my absentee ballot. If I write in a candidate, does it get recorded anywhere? It must be recorded somewhere, at least long enough to see if there’s a groundswell of support for Peter Hook as cultural commissioner or whatever. Can I check the results? If so, if you’re in doubt about your vote being recorded, you could pick a race & cast a distinctive vote, check later that your candidate received the vote you cast, and be marginally more assured that the rest of your ballot was also recorded.

  4. Daniel Reeves Says:

    Amen to that — for swing states. But since, as you point out, other voters are not unbiased coin flips, the argument is a lot less impressive in non-swing states. There, the expected value to humanity of your vote may be non-negligible but it won’t outweigh the cost of schlepping to the polls, according to Gelman’s calculations, which strike me as reasonable.

    I propose a compromise: play the mixed-strategy Nash equilibrium where you vote with small probability. (The idea being that it’s worth your while to vote only if not too many others do.) Then you can still tell posterity that, in expectation, you participated.

    By the way, although Robin Hanson may be the only one to appreciate it, I’m being perfectly serious!

    PS to first commenter: You’re not accounting for altruism. For a self-interested agent, you’re correct.

  5. John Armstrong Says:

    What’s new in computational complexity?

  6. John Armstrong Says:

    Hm. I should probably include a link. Trying again:

    What’s new in computational complexity?

  7. Dave Bacon Says:

    Scott, could you please complete the following sentence:

    If Obama were a complexity class it would be ______
    If McCain were a complexity class it would be ______

  8. Scott Says:

    Dave:
    If Obama were a complexity class it would be BPP (natural, robust, and well-motivated, despite the murky nature of its associations with P and NP)
    If McCain were a complexity class it would be the logspace hierarchy (started out fine, but ended up collapsing to an angry NL∩coNL shell when examined closely)—or possibly BQP (because of its penchant for destructively interfering with its own success probability)

  9. Scott Says:

    Thras: You’re sorely testing my commitment to Zen-like equanimity. I was careful to write, “if you care about the world even ~1/√N as much as you care about yourself”—thus making explicit that altruism was one of the premises of the argument.

  10. Scott Says:

    The point of Kuprov’s work is that an important class of quantum simulation problems formerly thought to be in EXP—namely, calculating magnetic resonance spectra ab initio—is actually in PSPACE/PTIME.

    Well, is it PSPACE or PTIME? There’s a huge difference!

    My question is, what FOCS `08 articles should I read to achieve a deeper (and hopefully, more rigorous) quantum informatic understanding of Kuprov’s important (IMHO) findings?

    The standard proofs of BQP⊆PSPACE and BQP⊆P#P might be relevant here. As far as I know, there are no FOCS’08 papers even marginally related.

  11. jsc Says:

    We may have a permanent research position in computational complexity at my university (in Europe).
    Is there any central place to advertise such position, like http://www.iacr.org/jobs/ for cryptography ?

  12. Carl Shulman Says:

    “I’m aware, of course, that the above is merely a nerdy, rational argument, of a sort that’s probably never actually convinced anyone in the entire history of the world, with the possible exception of Robin Hanson.”

    The logic of large effects and low probabilities has always been my primary reason for voting (and influencing the votes of others, in the case of this election, which I did, informed by InTrade and Iowa).

  13. Robin Hanson Says:

    So how much do you care about other folks in the US, in terms how many dollars you’d lose to give them a dollar of benefit? And don’t also forget to discount by the probability that you will vote for the better candidate.

  14. Scott Says:

    Stubby:

    If I write in a candidate, does it get recorded anywhere?

    Not with your name attached, in any way you can look up—since otherwise, you’d presumably be able to prove to someone else which way you voted, and thereby sell your vote.

    However, there are now clever cryptographic solutions to this problem—see for example scantegrity.org. Look for this technology at a polling place near you around 2240.

  15. Scott Says:

    Carl: Alright, two exceptions! ;-)

  16. Scott Says:

    Robin: If you tried to infer how altruistic I was from my actions, I’m sure you could uncover all sorts of glaring inconsistencies with expected utility theory: you’d find me sometimes donating money or time to achieve a tiny benefit for others, other times not donating despite a huge benefit… Then again, I expect the same would be true for pretty much anyone else you examined.

    However, if by donating an hour of time (and almost zero effort, ingenuity, or money), you can achieve a million dollars expected benefit for others, then it seems to me that the case is pretty clear. Furthermore, I agree with Norvig that voting in presidential elections is probably such a case. Are there other cases?

  17. Stubby Says:

    Not with your name attached, in any way you can look up—since otherwise, you’d presumably be able to prove to someone else which way you voted, and thereby sell your vote.

    Yeah, and probably write-ins don’t get tallied unless there’s some question as to the outcome after the automated processes are complete. But if I wrote-in “Sylvester Von Neumann” for city council and one vote showed-up at the registrar’s office, I’d know that my ballot was not just disposed of.

  18. Scott Says:

    What’s new in computational complexity?

    A highly idiosyncratic and unrepresentative sample: Razborov gave a beautiful and simple proof of Bazzi’s Theorem, which some of us are now trying to extend. Aharonov, Ben-Or, and collaborators have two new preprints in quantum complexity theory which are on my to-read list. The Strong Parallel Repetition Conjecture in multi-player games and the Additivity Conjecture in quantum information theory (which is related to the complexity class QMA(2)) both turned out to be false. There’s lots more interesting stuff on unique games, parallel repetition, quantum multi-prover interactive systems with entangled provers, and the relations among all three…

  19. A True Independent Says:

    Obama is like the Monty Hall Problem. The intuitive answer feels right, looks right, and manages to fool Nobel physicists and seasoned mathematicians. It is wrong, nonetheless.

    McCain is not the opposite of his opponent; he’s simply the lesser of the two “evils.”

  20. Cynthia Says:

    I, for one, would like to see our voting system patterned after our banking system…

    First we register for an account to vote in all election, either by pointing-and-clicking on the internet or by visiting a real-life voting place. Then whenever it’s time to vote in any election, all we have to do is access our account and cast our vote.

    And since all of us voters will have our own personal and private record of how and when we all voted, it would be a lot easier to track down voter fraud.

    Look at it this way, if we fully trust are banking system to handle our money, surely we can trust a bank-like system to handle our votes!

  21. KaoriBlue Says:

    John Sidles – Very cool paper. I’ve been doing some background reading on the subject and you’ve seriously derailed my morning. :-) They demonstrate polynomial time scaling with their algorithm, but these types of simulations should also be PSPACE… am I right?

    True Independent – Obama says “X’ and really will do/wants to do/means/etc “Y”. Well, same for McCain, no? And seriously strained (thanks to Palin) supporters like myself understand this and just happen to like McCain’s “Y”. Same reason why it’s reasonable to believe that former Bush/Iraq War/etc supporters aren’t all just a bunch of gullible idiots.

    These people aren’t stupid, their politics are just different.

  22. harrison Says:

    Of course, in models that don’t take altruism into account, you can assume that the difference between the two candidates is constant, so the expected utility of voting goes as 1/sqrt(N). So, game-theoretically, voting is a losing proposition; I do like the idea that if you’re N^-(1/2)-altruistic, it’s worthwhile.

    Hm, I should go vote so that I can get free coffee at Starbucks and ask Scott about complexity — pity Georgia failed at sending me my absentee ballot.

  23. harrison Says:

    On an altogether different note: I wonder what people in general’s reasons for voting are? I personally do it out of a silly sense of “civic duty” — I consider voting to be an essential part of the social contract in a (rough) democracy.

    I would bet this would be one of the more popular reasons among those who can give one, although I have a sinking feeling that social/”peer pressure” may well be the number one reason.

  24. Jim Graber Says:

    I voted. Here is a question, probably not in computational complexity, but hopefully somewhere close.
    I am looking for a reliable probabilistic decision procedure for any well formulated mathematical question. What’s available?
    For instance, can every question be put in a form where random k-sat applies, or is random k-sat not general enough to handle the set theory or the universal/existential quantifiers?
    If not random k-sat, what other tools are there, and which one is the most comprehensive/general?

  25. John Sidles Says:

    KaoriBlue, in rigorous context of complexity theory (according to my limited understanding of it) it is true that PTIME (more commonly called P) ⊆ PSPACE, but in the practical context of quantum simulations it is equally commonplace for calculations to be too large versus run too slowly; the methods of Kuprov and his colleagues address both concerns.

    It is lots of fun to contrast the first sentence of the article by Aharanov et al (referenced by Scott) “It is generally accepted that large quantum systems cannot be simulated efficiently by classical systems” with the concluding sentence of the (second) article in the series by Kuprov et al. “The astronomically sized matrices generated by the traditional [quantum simulation methods] are completely unnecessary.”

    We should all hope that we do not live in a (boring!) world in which only one of these two beliefs is correct, because it would be much more fun—and maybe even useful in helping humanity through this difficult twenty-first century—if both were Great Truths in Neils Bohr’s sense (“The opposite of a Great Truth is another Great Truth”).

    As for Scott’s remark that “There are no FOCS’08 papers even marginally related [to this topic]”, I have made a note to look back in time from the vantage point of the next Presidential election (in 2012), with the advantage of hindsight, to see whether (as I suspect) this is yet another Great Truth! :)

  26. Pat Cahalan Says:

    Another altruism based economy utility post:

    http://crookedtimber.org/2008/11/04/go-vote/

    @ Cynthia

    Your proposition depends upon the principle that we trust the banking system to keep track of our money. To some extent this is true, since the banking system has (more or less) an incentive to either take care of our money, or (should they fail at that) replace our money with an equitable amount of funds. That second is reinforced by government insurance.

    In other words, you can trust the banking system to take care of your money to the extent that you trust them, or some other trusted third party (the FDIC) to replace it should it go a-wandering.

    Votes are not equivalent to money, in this trust model.

    FWIW, voter fraud is fairly uncommon in the US, conspiracy theories non-withstanding… and it’s certainly outweighed by the advantage we get from the secret ballot, which would be essentially vaporized in such a model as you propose.

  27. Sumwan Says:

    Hi Scott, the link to Peter Norvig is wrong.
    And thanks for your pro-vote argument, I tried once to find such an argument but I couldn’t , beyond the obvious “If nobody voted …”.

  28. Scott Says:

    Sumwan: Thanks! Fixed.

  29. Scott Says:

    I am looking for a reliable probabilistic decision procedure for any well formulated mathematical question. What’s available?

    To a first approximation, nothing. :-)

    What does “reliable” mean in this context? Every decidable mathematical statement has probability either 0 or 1 of being true. And results of a certain A. Turing tell us we’re not going to get a mechanical procedure to decide which.

    Or are you just hoping for a procedure to decide “most” statements? But then under what probability measure?

    You mentioned random k-SAT. There are indeed extremely impressive algorithms for deciding random k-SAT instances (such as the survey propagation method), but even those might not work efficiently exactly at the threshold (as far as I know that’s still open—anyone care to clarify?).

  30. Cynthia Says:

    Pat Cahalan,

    Since we are finding more and more reasons not to trust electronic voting machines, many voter-rights advocates are calling for a return to the paper ballot. So in order to avoid this, a voting system which operates like a bank seems like a better alternative. And since I’d rather not be bombed back to the paper age of voting, I’m willing to sacrifice a little secrecy in voting in order to keep ballot tampering held to a minimum!

    http://www.democracynow.org/2008/11/3/on_eve_of_election_day_is

  31. Job Says:

    Probably the biggest reason to vote is to avoid being dismissed as “not having a say” because “you didn’t vote” and thus “can’t be taken seriously”. (you can try to argue with this, but in the end you know you’ll lose)

  32. Dave Bacon Says:

    “…possibly BQP (because of its penchant for destructively interfering with its own success probability)”

    I wonder f there is there way to make BQP only contain “destructive” interference (or only contain “constructive” interference.) (Work in a fixed basis, define transition amplitudes to be real, then the probability is a sum over amplitudes but you this sum must contain an amplitude of differing sign…)

  33. Cynthia Says:

    Pat,

    Let me also add that I really don’t see why it’s so important to keep voting a secret affair. Since no one is afraid to show their support for a candidate by putting campaign signs in their yards, by wearing campaign garb, or by going to campaign rallies, then no one should be afraid of others knowing who they are voting for…

  34. John Sidles Says:

    Cynthia Says: I really don’t see why it’s so important to keep voting a secret affair.

    Here’s why.

    Bill Cosby? Hey-hey-hey! I’m on the “Enemies List”! :)

  35. David Wagner Says:

    I believe that all votes (including writeins) do get tabulated, even if there is no chance it will change who wins. At least that’s my understanding of how it works in every county I’ve studied carefully. Many Americans think that county officials just don’t bother to count absentee ballots, or write-in votes, if the contest isn’t close — and this is just plain wrong.

    In some states write-in votes only count if they are for a “qualified” write-in candidate. In other words, in those states, candidates are only eligible if they file a form with the election officials and are officially qualified; write-ins for anyone else are noted by the election officials but not tabulated by name. In other states, there’s no requirement for “qualification”; all write-ins count. It depends upon the state.

    Most counties don’t report the names of write-in candidates and how many votes they got on their basic election report (e.g., the report on their web site), because otherwise you’d be overwhelmed with data. Also it takes days after the election to count the write-ins, so vote tallies for write-in candidates are usually not available on election night. This may be the source of the misconception that election officials don’t bother to count write-ins (a myth that is, to my knowledge, false). If you care, call up your county election office after the election is over and certified (anywhere from 10-30 days after the election) and let them know that you’d like to see a results report that shows how many votes were received for each write-in candidate. If you ask specifically for that, they may provide you a copy upon request (depending upon the county’s policies).

  36. Pat Cahalan Says:

    @ Cynthia

    > we are finding more and more reasons not to
    > trust electronic voting machines

    I’ll flip this last statement on its head, to “we’ve never had a reason to trust electronic voting machines, and all tests of these machines have given us no reason to grant trust”. Otherwise, I agree.

    > Since I’d rather not be bombed back to the paper
    > age of voting

    How is this a “bombing”? What, in your opinion, is/are the advantage(s) of a voting machine vs. a paper ballot? My district in CA still uses the ink and scantron style optical scanning ballot, which took me all of about 30 seconds to fill out, is cheaper than most EVS systems, is machine-readable for speed of returns (if same-day gratification on election day is important to you), and has a verifiable paper trail for audit.

    > I’m willing to sacrifice a little secrecy in voting in
    > order to keep ballot tampering held to a minimum!

    Without a secret ballot, you have a great number of additional vectors for ballot tampering. You cannot escape this, it’s inherent in a non-secret ballot. You may not mind this, but given that I can’t see *any* practical reason whatsoever to use any sort of electronic machine, I don’t see any reason to submit to a non-secret ballot for no gain.

  37. Cynthia Says:

    John,

    As near as I can tell, being blacklisted by Richard Nixon or (god forbid) by Joe McCarthy has more to do with what you say and do than how you vote.

  38. Cynthia Says:

    Fair enough, Pat. But I don’t think anyone can deny that we need a better voting system in terms of convenience and accuracy.

  39. KaoriBlue Says:

    Kuprov et. al. (referenced by John) – “The astronomically sized matrices generated by the traditional [quantum simulation methods] are completely unnecessary.”

    Out of curiosity, are there particular examples of quantum systems in, say, chemistry where SSR and all other known pruning algorithms perform very poorly?

  40. John Sidles Says:

    KaoriBlue Says: Are there particular examples of quantum systems in, say, chemistry where SSR and all other known pruning algorithms perform very poorly?

    KaoriBlue, among the greatest mysteries of quantum chemistry (and condensed matter physics too) is not “Why is system X hard to simulate?”, but rather “Why does density functional theory work so well?” (see the Wikipedia pages on the Kohn-Sham equations and the Hohenberg-Kohn theorems for details).

    By the way, the original 1965 article by Kohn and Sham is (if memory serves) among the most-cited articles in the physical sciences. So it is pretty darn amazing that after forty-three years, the mathematical foundations of this formalism remain poorly understood.

    Perhaps it’s because the full power of modern quantum information science has not yet been brought to bear? :)

  41. Cynthia Says:

    P.W. Atkins springs to mind when I think of quantum chemistry. Believe it or not, he’s a pretty good writer of pop science. One of my favorite of his is entitled “The 2nd Law: Energy, Chaos, and Form.” But then, I, like many others, have a deep fascination with the second law, especially as it relates to the origins of the universe.

  42. John Sidles Says:

    :) :) :) Best wishes for zen-like equanimity to all! :) :) :)

  43. Jim Graber Says:

    Scott,
    Thanks for the answer.
    Yes, I don’t expect 100% accuracy, or even 100% providing an answer, but 100% coverage is more what i’m looking for. Any reasonable measure will do, although now I’m wondering what I’m missing here. I’m still not clear whether random k-sat attacks “all” or most questions or only a specialized subset. I am concerned about whether all questions can be put in the necessary prenex form or whatever

  44. Ping-Che Chen Says:

    Cynthia,

    The prime reason behind secret ballot is to prevent vote buying. It’s probably not a serious problem in the US, but it’s still a serious problem in Taiwan. Although it’s very difficult to attest the real effect of vote buying, the fact that people are willing to pay real money to buy votes seem to indicate that at least they think it’s worth the money.

    It’s also important that in some less civilized countries, people are harassed for supporting a candidate. If voting is not secret, many people will be too afraid to vote and it won’t be real democracy.

    Of course, these seems to be very alien ideas in the US, but secret ballot still makes sure that a voter’s decision will not be influenced by other pressures (for example, a young adult wants to vote for a candidate whom his entire family opposed).

  45. Cynthia Says:

    Ping-Che Chen,

    Since it don’t take an Einstein to figure out how individuals are most likely to vote, I don’t see how it really matters whether ballots are secret or not, as they relate to buying votes.

  46. Pat Cahalan Says:

    re: vote buying

    There’s two types of vote buying, buying on promise and buying a receipt. Buying on promise means I give you $100 and you tell me you’re voting for John Ya Ya. Buying a receipt means I give you $100 and you vote for John Ya Ya and I can confirm that indeed you did what I paid you to do.

    There’s a pretty big difference between the two. You should read Ed Felten’s blog (http://www.freedom-to-tinker.com/) and Caltech/MIT Voting Technology Project for the Election Assistance Commission’s reports.

    Accuracy is a problem mostly because we use more than a dozen methods of voting in this country (sometimes multiple systems in the same state by district), many of which are designed, quite frankly, by people who know nothing about user interfaces :)

    I don’t believe that convenience should be much more than a desirable add-on, while many people regard it as a necessary feature. Some election experts push for Internet voting (because they stress convenience and turnout), whereas I’ve been studying infosec security for long enough to know that you don’t want to put the elections on the IT, to paraphrase Dubya.

    In person, paper audited, secret ballots are the only way to go to ensure long term stable and reliable election returns. Standing in line for two hours once a year is hardly a major time commitment (I’ll grant you, moving polling dates to a non-working day would probably be a damn fine idea).

  47. Wei Dai Says:

    If you tried to infer how altruistic I was from my actions, I’m sure you could uncover all sorts of glaring inconsistencies with expected utility theory

    … and this post seems to be a prime example. Scott, you live in Massachusetts, not Florida, right? If so, your chance of casting a marginal vote is much smaller than 1 in 6 million. The only consistent choices are to stay home and not vote (if you’re selfish), or to move to Florida ahead of the election and vote there (if you’re altruistic). Voting in Massachusetts can’t be squared with expected utility theory, I think.

  48. Paul Beame Says:

    Washington is not usually considered a swing state but the governor’s race in 2004 was close enough to disabuse one of the notion that their votes don’t matter. This initial count gave the Republican a 271 vote lead out of roughly 2.75 million votes. The first automatic recount gave him a 42 vote margin. Candidates can request a manual recount beyond that if they put up the money (which will be refunded if the result flips). Meanwhile, a few hundred uncounted ballots were found after an official noticed that he was not on the voter rolls despite having voted. In the final hand recount the Democrat won by around 130 votes. Multiple lawsuits were filed and the Republican only conceded more than 6 months later. (P.S.: in a nasty rematch of this contest this year, the incumbent Democrat won by 7% despite polls suggesting that the race was a toss up.)

    I guess that there are two conclusions one might draw: Each vote really counts – or the noise in counting ballots outweighs the likely influence of your vote. (Ryan O’Donnell liked to use this example in his talks that majority is stablest.) The bottom line seems to be that there are races that are a lot CLOSER than the Theta(sqrt(n)) one would expect from random voting by everyone else. This certainly increases the utility.

    On the other voting topic: A key tenet of voting is that nobody should be able to coerce your vote. Whatever system of voting we have there is nothing wrong with being able to prove that you voted but not to prove HOW you voted (which opens it up to coercion). A transparent election would be one in which the proof of the vote would allow you to prove to yourself that your vote is correctly recorded but you can only prove to someone else that you voted. There are electronic systems (with paper trail) that achieve these properties computationally. Unfortunately, with a mostly mail-in ballot, we’ve moved to a mode that is much more open to coercion: You could show someone your ballot, put it in the envelope in their presence, sign it across the seal and hand it to them to mail in. Maybe this seems far-fetched to you? One could imagine the peer pressure of a group of people agreeing to get together to have a voting party. Nothing requires that you keep your ballot secret in this context. For example the only secrecy provision in Washington State Law is the following: “No paper ballot or ballot card may be marked in any way that would permit the identification of the person who voted that ballot.”

  49. John Sidles Says:

    Wen Dei: Voting in Massachusetts can’t be squared with expected utility theory, I think.

    Yes … which means … so much the worse for expected utility theory!

    The recent NYT article In Modeling Risk, the Human Factor Was Left Out is a fine discussion of the unresolved tension between axiom sets that (1) define good theorem-proving environments, versus (2) describe real-world system dynamics … the point being, very often we must choose between beauty and utility.

    This axiomatic tension has moved to center stage in modern economics and financial engineering … so it is interesting to inquire: to what extent are similar tensions moving to center stage in modern quantum information science?

    There is a recent preprint by Hui Khoon Ng and John Preskill that I admired as an effort to resolve these axiomatic tensions.

    Scott, a “tending-the-garden” post on sustaining an appropriate balance between mathematical beauty and engineering realism in quantum information theory would be very welcome!

  50. Gil Kalai Says:

    Dear all,

    One mental experiment I am fond of asking people is this:

    Suppose that just a minute before the votes are counted you can change the outcome of the election (say, the identity of the winner, or even the entire distribution of ballots) according to your own preferences. Let’s assume that this act will be comlpetely secret. Nobody else will ever know it.

    Will you do it?

    (This is somewhat related to the (problematic) analysis in the post based on the utility of voting as reflecting the possibility of one’s vote being decisive. )

  51. Job Says:

    Gil, that’s a question that’s tough to answer. I’d like to say that i wouldn’t but i don’t know that for sure. If i weren’t convinced of either candidate or had a feeling of inadequacy (which i sometimes do) in making such a decision, then i wouldn’t.

    But if i were absolutely convinced that one was clearly the best option… There certainly are scenarios where you have to override the majority (when you can), however undemocratic that may be. If people in a bar elected to beat up a pregnant lady, i wouldn’t let it happen just because the majority decided.

    If the choice was that obvious then i would it, and to be honest i don’t know if the choice for this election wasn’t that obvious, so personally i don’t know that i wouldn’t do it.

  52. KaoriBlue Says:

    Gil,

    It would have to depend on the legality of the issue at hand… obviously I would intervene in Job’s “assault on pregnant lady” scenario, but something like California’s proposition 8 (recent state-wide ban on gay marriage) is trickier. I think a good rule of thumb is to be as democratic as you possibly can be within, say, a moderately strict constructionist interpretation of the Constitution.

  53. Paul Beame Says:

    Gil,

    If I read your question properly it would imply that, if I acted, I (along with everyone else) would be ignorant of the true totals; this better models the “would I really want to be decisive?” question. I am not sure what my answer would be but I think that some of the reason for/value in voting is not just that I want to decide but a conditional “if people are divided on the issue then I will be happy to tip the balance”. Making this statement, even secretly, has value to me even if its premise isn’t satisfied.

    The odd thing is that I might be more inclined to exercise the full power if I could also magically learn the true totals first and then make the decision on whether to override. Post facto it often seems clear when voters have screwed up and I should substitute my judgement for theirs. I’d trust myself better in this context.

  54. Evan Says:

    Cynthia,

    I suspect that if you knew who people voted for you would be surprised more than you expect. Lots of people try to “fit in” when political discussion comes up and hide their true intentions. The real example why the secrecy of ballots is so important is simple: Your boss announces that anyone who votes for the councilman who supports unions or environmental regulations will be fired. There are plenty of other examples, but the pattern is the same. People with power will try to coerce others to vote a certain way. Currently it is not much of a problem in the US (though there are still attempts to disenfranchise by precinct, counting on the averages to work out in your favor). If ballots were not secret you can bet it would be a problem, and fast.

  55. Cynthia Says:

    I totally agree with you, Evan. Keeping ballots secret is the best way to prevent voters from being coerced into voting a certain way. But I still think a voting system can be designed so that it’s not only secret, but also secure and accurate. Such a system would enable voters to go online to cast their ballots as well as access their own personal voting records.

  56. Gil Kalai, Says:

    Dear Paul,

    I think in my question the “real results” will never be known. But I do not mind the variation where you can look first at the results. (So you can ask yourself this questions on the 2000, 2004, and 2008 US-elections where you already know the outcomes.)

    I have a poll on this question on my blog:

    http://gilkalai.wordpress.com/

  57. Democracy, but not Democracest Says:

    If nobody votes, then nobody gets the government they want.
    If everybody votes, then nobody gets the government they want.