What Price Kilo-Votes?

Imagine that at every U.S. presidential election, the system randomly picked one random U.S. voter and asked them to pay a fee to become a “kilo-voter.” Come election day, if there is a kilo-voter then the election system officially tosses sixteen fair coins. If all sixteen coins come up heads, the kilo-voter’s vote decides the election. If not, or if there is no kilo-voter, the election is decided as usual via ordinary votes. The kilo-voter only gets to pick between Democrat and Republican nominees, and no one ever learns that they were the kilo-voter that year.

“Kilo voters” are so named because they have about a thousand times a chance of deciding the election as an ordinary voter does. In the 2008 U.S. presidential election the average voter had a one in sixty million chance of deciding who won the election. The chance that sixteen fair coins all come up heads is roughly a thousand times larger than this.

Consider: 1) How much is the typical voter willing to pay to become a kilo-voter? and 2) How much does it cost the typical voter, in time and trouble, to actually vote in a U.S. presidential election? As long as these numbers are both small compared to a voter’s wealth, then for a voter motived primarily by the chance to change the election outcome, these numbers should differ by at least a factor of one thousand.

For example, if it takes you at least a half hour to get to the voting booth and back, and to think beforehand about your vote, and if you make the average U.S. hourly wage of $20, then voting costs you at least $10. In this case you should be willing to pay at least $10,000 to become a super-voter, if you are offered the option. Me, I very much doubt that typical voters would pay $10,000 to become secret kilo-voters.

Yes, the 2008 election influenced the lives of 305 million U.S. residents, and someone who cared enough might pay a lot for a higher chance of deciding such an election. But typical voters would not pay a lot. Which suggests that the chance to decide the election is just not the main reason that they vote. The chance of being decisive actually doesn’t seem to matter remotely as much to typical voting behavior as it should to someone focused on changing outcomes. For example, states where voters have much higher chances of being decisive about the president don’t have much higher voter turnout rates, and turnout is actually lower in local and state elections where the chances of being decisive is higher.

My conclusion: we don’t mainly vote to change the outcome.

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  • Saw you asking this on twitter. I thought the question (in 140 chars) was hard to understand. So I think as asked the question may have been too abstract to get an interesting answer. I suspect framing the question in partisan fashion might result in different or at least more interesting answers.

    If you ask a Republican if paying $1000 would get their candidate elected, many would say yes. There’s plenty of people right now who’d also pay a lot to stop many of the current batch of candidates. So in that sense, I think people do in fact care about having their tribe/party win. And if their vote would be guaranteed to be augmented enough to swing things, then they would pay.

    In reality, we know that individual votes, or even 1000x votes won’t swing a presidential election, unless you’re talking Florida in 2000. Hence with priors saying votes won’t impact results, many wouldn’t pay unless their vote we’re million times baseline of 1. Not 1000x. And I think the abstractness of this question suppressed the innate tribalism behind voting. Most don’t understand marginal stats on a question like this.

    So in the end, agree we don’t mainly vote to change outcome. But I think the framing of paying to have the vote, where the delta is large enough to plausibly swing the election, would give a different result, with a much larger subset of people willing to pay.

    • Yes of course you could ask other price questions where people are more likely to offer higher prices. But I wanted to ask a question that best made clear why we usually vote.

  • Lord

    A lot of gaming going on here. Suppose being chosen, I offer my choice the opportunity to buy it for me. I am sure a candidate would pay much more and I could profit from it. While even $10 is a bit much, it’s marginal cost is close to zero as our free time is our own and no one pays us for that. Those that value it at $10 are probably the ones not voting. But no, most do so out of duty in hope of slightly better outcomes, even when that doesn’t include winning.

    • You can’t sell the kilo-vote because you can’t prove you have it.

      • Lord

        If you have to pay, you can.

  • Anon

    I’m new to this blog, but this post whets my curiosity. Are there other posts about why we vote if it is not about changing the outcome?

  • J.K.

    I’m about 20% convinced modern voting is simply an exercise in tribalism, rather like cheering a sports team. It is certainly isn’t rational, which becomes obvious when you try to get voters to analyze voting.

    I think the thought exercise, while interesting, has a critical flaw: that amount of money isn’t disposable for most people. I would wager that less than 30% of the population could come up with 10K on the spot. Of that 30% I would bet that less than half could do it without significant personal risk. Most people can come up with 30 minutes. Plus, it requires that people are balanced when evaluating risk/reward for long odds. People tend to be very risk avoidant with large expenses, but generous with cheap gambles (hence the continued existence of the lottery). I’m not sure how to get around those problems without introducing different ones. Even if we could get around that problem, I don’t disagree with your expected result.

    • sflicht

      Why only 20% convinced? That suggests you are not very convinced at all.

      • J.K.

        There is a strong civic culture around voting. We have incredibly low opinions of elected representatives, yet lots of people still vote. The value of voting is taken as an article of faith among a large swath of the population. If it is tribalism, it likely isn’t tribalism in regards to party for the true believers.

      • sflicht

        The standard riposte to “low opinions of elected representatives” is “except their own”. People view their own senator (assuming he or she is of their own party), for example, as the defender of their tribal values against insurgent attempts to overthrow them.

      • J.K.

        I don’t think tribalism is falsifiable from the tools that we have at our disposal.

    • Lord

      According to the Fed, 70% can’t come up with $400 without borrowing or selling something.

      • J.K.

        Interesting. My first thought was that probably less than 10% could come up with 10K on short notice. I increased the margin due to Hanson’s predilection towards taking wagers. $400 is a bit jarring though, considering I have half that just sitting on my desk right now.

      • Lord

        Yes, it was 48%. The cash account may be misleading though as it is usually offset by credit debt which would have to increase to maintain adequate levels.

    • How much do you think people would pay to secretly have ten votes instead of one?

      • J.K.

        If we stick to the original rules (only one person, can’t tell anybody, national election only), my gut would say $10-$15 on average. However, I’m probably discounting that a lot because:

        1: I am a cheapskate.

        2: I don’t think voting has a lot of value.

        Correcting for that, I would expect a national average of $35-$70, with a large variance. I would expect that the disposable income of the person asked, how contested the race is, and how partisan they are would all have a lot of impact on the individual’s price point.

  • right, voting is entertainment, just like amateur social media pundits are playing a recreational sport. but collectively, the group of people who tend to vote must be placated if you wish to attain office. (obviously correct) arguments like hanson’s are a good way to lower the average IQ per vote cast.

    • arguments like hanson’s are a good way to lower the average IQ per vote cast

      If we don’t in fact vote for instrumental reasons, arguments showing this enable moral pride in voting, increasing its likelihood.

      • Peter David Jones

        On the other hand , there are plenty of high IQ people who think only high IQ people should be allowed to vote.

  • Hanson doesn’t get voting because its moral structure is Kantian. We vote out duty, as is proven by the fact that those without much sense of duty in other respects don’t vote.

    If we voted for consequentialist reasons, high IQ folks would vote less than low IQ folks, who are more blind to the instrumental irrationality of voting.

    • What you (and most people) don’t get is that election outcomes depend on *influence*, which, unlike an individual’s vote, has statistical significance. No one knows whether or not I actually drop my ballot in the mail, but they know who I say I’m going to vote for and what arguments I make. And since I don’t want to lie and am a lousy liar anyway, along with duty and other psychological pressures, I usually actually do vote, despite my very high IQ. And I would note that people without much sense of duty not only don’t vote but spend no time trying to influence how others vote … they don’t care about the consequences and would be happy to convince others who had intended to vote to go party on election day instead.

  • James Babcock

    I see two resolutions to this inconsistency. The first is something analogous to timeless decision theory: we expect that if we ourselves vote or don’t vote, others whose votes correlate with ours will do the same.

    The second answer is that the “I voted” sticker they give you is worth >$10.

    • For your first, you have to also expect this correlated vote effect doesn’t happen with kilo-votes.

  • zarzuelazen

    If you want to know what the outcome is going to be, there’s no need for most people to vote at all: just take a poll on election day.

    In fact, you only need to consider a few hundred swing voters at the most to know the outcome!

    Take the US for instance: most states are already firmly either Democratic or Republician so we can eliminate them from consideration.

    Most districts in a state, we know what’s going to happen, so eliminate them.

    Most voters are already decided, eliminate them.

    Just poll 300 independent swing voters in the state of Florida on election day, that will accurately tell you the outcome.

  • DavidRHenderson

    Nicely stated.

  • AJ Li

    It could be argued that visibly voting changes the outcomes in ways that secret voting doesn’t, by influencing others to vote, superrationality-esque reasoning, etc. Whether visibly voting actually has additional effects or not doesn’t matter, as long as voters believe that it matters.

    An additional effect at play here is loss-aversion. $10,000 looks large to a lot of people. If you offer someone the chance to vote again paying $10 per vote, I’m sure a lot of people would take the offer.

    • What do you think people would pay to secretly haver ten votes, instead of one?

      • AJ Li

        For the same reason that people donate to political campaigns. It’s almost equally unverifiable, and while it’s not clear what the effect of the marginal dollar in campaign contributions has vs. another vote, the latter has more direct influence and IMO will appeal to people more.

        Combining the two, if such a system was in place, I’d imagine that campaign contributions will balloon because candidates can always use the excess dollar to vote for themselves.

        Edit: now that I think about it, this seems an excellent way for unpopular governments to raise money, since a lot more people would pay for votes when they want change.

    • “An additional effect at play here is loss-aversion.”

      Indeed. Since this is a very well known aspect of human psychology, it’s quite irrational and intellectually dishonest to draw the sort of inferences that Hanson does … but that’s what he so often does.

  • One local, not-particularly-contested election day, someone emailed a list for the Philadelphia start-up community encouraging everyone to go vote. I replied that as (generally) high-paid technologists, we should consider whether there may be better ways to altruistically spend our time than voting (in a very neutral, open-minded, non-trolling or accusing tone).

    This turned into quite the debate (50+ messages) and I ended up posting the following proposition the group. I would either:

    – Spend 2 hours* reading about the candidates, travelling to the polls, and voting.


    – Send $200 to the Against Malaria Foundation, with the estimated savings being 10 years of an adult life.

    I then put this as a poll to the group. ~80% of 50+ respondents said that voting was preferable**. So even when explicitly propositioned about the value of a vote, and told that I would either extend a life by 10 years or vote, most people picked voting.

    I felt bad at this outcome, but was also not shocked at all. As Robin knows better than anyone, voting is about signaling, not the act itself. For many, to not vote is to spit your gum on the sidewalk. It’s regarded as a completely lack of respect for your community.

    *I knew absolutely nothing about the candidates, don’t vote either R and D consistently, and there were ~20 to look at.

    **I did vote, but I gave to charity too.

    • If you’re an influential person, talking about how you’re going to vote has a greater effect than voting itself. So, I talk about who I’m going to vote for and who others should vote for, and then I usually go vote, myself, even though it’s statistically not significant.

      The reason that I wouldn’t pay $10,000 to be a kilo-voter is because I have the sort of human psychology explored in depth by Kahneman and Tversky, and so I don’t make “rational” statistical determinations of optimal cost/benefit; it has nothing to do with not wanting to change outcomes. Someone like Hanson should spend time on a political blog like DailyKos, where a lot of people there would do almost anything to get Bernie Sanders elected, but have never had $10,000 to their name.

    • Ken Arromdee

      People are not effective altruists and consider votes more important because voting affects people who are in your community and saving someone from malaria does not. Only to an EA are all people of equal value.

  • arch1

    If you plan to spread this more widely I think the description needs a bit of work. If they pay the fee, they become a kilo-voter, right? So how can they never learn that they were a kilo-voter? It seems that at most they could remain ignorant of the fact that they actually influenced the election (though kilo-voters would often learn that they *didn’t* influence the election, when their vote differed from the outcome).
    In any case, agree w/ your main thesis. Voting is a ritual.

    • “no one ever learns that they were the kilo-voter that year” means that no one *else* ever finds out.

      • arch1


  • free_agent

    Of course, the best way to determine why voters vote is to talk to voters in depth to determine why they vote.

    But it’s clear that voting is pitched as a virtue, so there are consequences to voting that come through other paths than the effect on the election. (My Boy Scout handbook had a chart of “rights of citizens” and “duties of citizens”; “voting” was the only item in both lists.)

    More interestingly is the fact that voting is a key part of the most competitive social systems that exist (most competitive against alternative systems, that is), and that part of making such a system work is getting people to vote, even though the direct benefits of voting don’t pay for the costs thereof. So how does one of these systems get people to vote?

  • dat_bro06

    There are lots of reasons people vote. One very simple one is that Election Day falls during the week, affording dithering white-collar workers a chance to cut an hour break from the usual 9-5 schedules to visit the polling station.

    Another: people assume a collective identity when they vote. Be that of a racial, socioeconomic, religious, partisan, or patriotic identity, a person voices a fractional vote on behalf of the group they psychologically affiliate with. Individual votes do not matter, but voting blocs certainly do. To me this is an ironic feature of Western democracy (not that it is unique to Western democracies), but given Western philosophical bend towards individualism.

    If Americans were as individualistic as they like to believe, they would never show up to vote.

  • Patrick LaVictoire

    Doesn’t change your point about normal human motivations (scope insensitivity, etc), but the one-in-sixty-million chance was for an election (2008) whose polls showed a clear lead for one side. If it were the 2000 election, my back-of-the-envelope calculation has the odds of a decisive vote more like one in 10^5 (given the polls going in, not even the crazy 500-vote margin in the deciding state). 2004 was almost as close. So if we average out across elections, maybe that’s only nine or ten coin flips for a kilovote.

    • You are going to have to give a lot more detail before I’ll be convinced your estimate is better.

      • Patrick LaVictoire

        Let’s look at 2012, since there Nate Silver was nice enough to do a model incorporating the chance of uniform bias in polls (which is what would have needed to be very true in 2008 in order for a close race in a tipping-point state).


        If you scroll down enough, he thinks that despite Obama having an advantage of ~2% in the tipping point states, there was still a 6.4% chance that at least one decisive state would be within 0.5%. Let’s be conservative and say this scenario is dominated by cases where the decisive state is a reasonably big state like Ohio, with a voting total of 5 million between the top 2 candidates.

        Then that’s a 6.4% chance that 25,000 votes decide the election, or a 1-in-400,000 chance that your vote is decisive if you live in a swing state.

        And that’s with what seemed to be a clear edge unless the polls were all biased by a few percentage points. In 2000 or 2004, you could plausibly get another factor of ten back by a higher chance of states being decided by small margins, including smaller states.

        How’s that?

      • So what is your estimate of the number that Gelman estimated, of the AVERAGE chance of being pivotal in the US?

      • Patrick LaVictoire

        Ah, OK. That’s another factor of 20 or so (since chance of being pivotal is weighted toward larger states). So for the 2012 election, my back-of-the-envelope calculation gives an average chance of 1 in 8 million, and for 2000 plausibly less than 1 in 1 million.

      • Sieben

        Let’s say there’s an election with 1,000 voters. Early polls say that 55% are voting one way. Assuming that each randomly selected person has a 55% chance to vote that way, the probability of the election being tied (i.e. one additional vote matters) is:


        = 1.6574e-04

        … or a 1/6000 chance.

        It’s difficult to compute higher N accurately, since nchoosek(1000,500) is already 2.7e299. There are approximations but I’m too lazy to do a full analysis.

        Anyway, the link is doing some misleading math. You can’t just divide by the number of votes and multiply the probabilities. It’s completely pointless to try and figure out the probability of the election being decided by within 25,000 votes, because for 25,000 coinflips to come up at exactly 12,500 heads is extremely low (and computable).

      • Patrick LaVictoire

        You’re making a key error that Gelman does not. When the polls say one candidate has a 10-point lead, the majority of the other candidate’s chances don’t come from winning way more coinflips than expected, they come from the poll having been wrong. And polls have standard error of a couple percentage points, not even counting sources of bias (nonresponse rates being the biggest).

        And if you do this as a probability problem where you have a noisy estimate of the true coinflip probability and a lot of coins, you find that the chance of a pivotal vote is basically the value of the probability density function (for the coinflip probability) at 0.5, divided by the number of voters.

  • Sieben

    Dumb question – failed to find this easily – how do the authors of your link determine the probability of influencing an election? My calculated probability is much smaller, but my assumptions are likely different.

    Given that the data is given in terms of polls, I always thought you should model the rest of the voters as weighted coinflips. So for example, if there are 10,000 voters, and the polls show 55/45% split, the probability of a tie is (10,000 choose 5,000)(0.55^5000)(0.45)^(5000). Of course, this is extremely hard to compute, but using approximations, my estimation for a tie in the national popular vote was ~10^-42.

    I did this a long time ago so I can’t remember my exact inputs and method, but it always surprises me when people say the probability of influencing the election is on the order of 10^-7. That’s almost roughly a uniform distribution, or something.

    • They are using the Electoral College structure in the US, not a simple national vote.

      • Sieben

        Aware. Was just doing a back of the envelope. But I can’t imagine they use the binomial distribution within electorates. The estimated probability would likely be a lot smaller.

  • Thomas_L_Holaday

    The duty is to demonstrate your willingness to accept the judgment of the majority.

  • bluto

    I think the kilovoting question is interesting but wonder if the value is reduced by phrasing it as willingness to pay rather than willingness to accept. I’d reject an offer much higher than I could pay if it meant getting cash to instead of my vote being the kilovote.

  • Brian Slesinsky

    It’s one thing if you happen to decide the election if the voters are split 50-50 and quite another to thwart the majority decision in a landslide. One of the points of an election is to make sure the losers accept that the decision was made fairly. Unless the polls were close, this can’t be hidden.

    So, I don’t think I would want to accept the responsibility of being a kilovoter even if it were offered for free. Even if it’s a secret, I’d still bear a heavy responsibility for the resulting chaos.

  • This exemplifies the failure of economists to grasp reality.

    • Anon

      You took the time to comment here, but didn’t take the time to explain your reasoning or even highlight any of the points you disagreed with. I guess you’re a busy guy with only enough time to get a nice, satisfying dig in before you get back to work.

      • I wrote more extensive comments elsewhere on this page, you hypocritical jackass.

      • R Hugh Sirius

        Savvy Humanist: One who does not know his/her
        asshole from a hole in the ground.

      • R Hugh Sirius

        I once saw an enlarged live picture of an asshole and guess what was at
        the very center? That’s right, Jim Balter hanging from an ass hair. I
        waved, but he ignored me.

      • Wow. I blocked this thing on twitter and now it’s stalking me on Discus. Fortunately Discus has added a block feature, so away with it.

      • R Hugh Sirius

        Using that new brain medication your doctor recommended? Colon-block?

  • Mordy

    We know that while individual voters do not determine elections, large groups of voters certainly do. But large groups of voters do not exist without the individual voters who comprise them. So while your vote doesn’t matter individually, your participation in the group phenomenon of voting does matter.

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  • Jason Abaluck

    Robin, your argument illegitimately assumes no income effects. Think of it this way – suppose voting in a Presidential election is like giving $10,000 to charity. I think this comparison is pretty reasonable – you have about a 1/10^8 chance of being pivotal, and it’s plausible in many presidential elections that the difference in social welfare between the candidates is on the order of a trillion dollars (compare to cost of Iraq War). See, e.g. Andrew Gelman’s work on voting as a rational decision.

    Then your argument amounts to saying – suppose that I am willing to pay $500 in order to give $10,000 to charity. Then I must also be willing to pay $500,000 to give $10,000,000 to charity. But that is ridiculous. You might not even have $500K. There are income effects.

    • Anon

      Jason, you’re correct in that the marginal value of each dollar you have decreases as your wealth grows. $10,000 is worth more to me than it is to Bill Gates. This is a non-linear relationship and doing back-of-the-handkerchief math with non-linear relationships is hard.

      No need to throw up your hands and give up though, you can reasonably ignore these non-linear effects when the range of values you are dealing with is small (linearization). Is $10 to $10,000 a small enough interval? I’m not so sure, but Robin does openly hedge here by stating “As long as these numbers are both small compared to a voter’s wealth…”. If you wanted to you could research the marginal value per dollar for the typical US voter and scale the $10,000 based on that. I think actuaries measure that sort of stuff.

      • Jason Abaluck

        Anon, firstly, $10K is not remotely small compared to the average voters’ total wealth! (about 50% of the population has essentially zero wealth). Secondly, there is a second relevant non-linearity here I didn’t mention before – diminishing returns to charitable giving. For both reasons, if there were a charitable matching program where a person could pay $50 to give $1,000 to charity, we wouldn’t say, “Therefore, because $50 is small as a fraction of your total wealth, you are irrational not to also pay $100 to give $2,000″ to charity.” That is what Robin’s example amounts to saying. (As an aside, to perform the exercise you propose where you measure the marginal value of a dollar one would need a third good as a numeraire that could be compared to both dollars and votes).

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