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Yes, Virginia, it can be rational to vote!

Carl Shulman correctly thought I’d be interested in this news item, “A single vote leads to a rare tie for control of the Virginia legislature”:

A Republican seat flipped Democratic in a wild recount Tuesday – with the Democrat winning by a single vote – creating a rare 50-50 tie between the parties in the House of Delegates and refashioning the political landscape in Richmond.

Democrat Shelly Simonds emerged from the recount as the apparent winner in the 94th District of the House of Delegates, seizing the seat from Republican incumbent David Yancey. . . .

The final tally: 11,608 for Simonds to 11,607 for Yancey.

As Edlin, Kaplan, and I wrote, it can be rational to vote, as long as you’re doing so out of concern with general social welfare.

P.S. This update makes the story even better:

Control of the Virginia House could depend on which old film canister an election official pulls out of a glass bowl.

A three-judge panel certified the 94th District in Newport News as tied on Wednesday, a day after a dramatic recount appeared to give Democrat Shelly Simonds a victory over Del. David Yancey by a single vote.

By state law, the winner of the tie will be determined “by lot.”

A win by the Democrat would make the house evenly split between parties.

Virginia Board of Elections Chairman James Alcorn said the board will likely pick the winner the same way it picks ballot order. He said each candidate’s name is placed into a separate film canister. The canisters are placed into a glass bowl and shaken up. The canister containing the winner’s name is pulled out at random by a board member.

I think they should decide it with a game of Horse. Or a penalty shoot-out. That would be more fun.


  1. TN says:

    That small Virginia election is hardly a Black Swan event. Tie votes in small state/local elections are not rare — North Carolina had several in past two years. Of course, the smaller the election… the less its relative importance and value of individual votes. Tie votes usually signal a defect in the balloting & ballot counting system, rather than true electorate action.

    Point to a large national/statewide election where a single voter determined the outcome.

    • Andrew says:


      I agree with you that the Virginia election is no “black swan.” It’s an amusing news item, and potentially consequential for certain outcomes in the state of Virginia, but from a statistical point of view this particular election is nothing special. I’ve written about this in various articles, also on the blog, and even in a homework problem in one of my books! To estimate the probability of an election being decided by 1 vote, one could just as well take the proportion of elections that are decided by less than 1000 votes, and divide that proportion by 1000.

      There’s no reason whatsoever to say that a tie vote (or, in this case, an election decided by 1 vote) signals “a defect in the balloting & ballot counting system.” There has to be some vote margin, and just by chance the margin will sometimes happen to be 0 or 1.

      The larger the election, the lower the chance of a tie—we also discuss this in several of our papers! Also, as discussed in the above-linked article, the stakes are higher in big elections, hence it can still be rational to vote in an election that is predicted to be close. The “large national/statewide election where a single voter determined the outcome” has not happened yet, and it may never happen—but it could. Multiply the probability of this happening by the stakes of the election and you can get a reasonably large number.

      • Allan C says:

        Wouldn’t a better way of estimating the probability of an election being tied by a given number of votes be to model individual voting behavior directly, simulate and then take the frequency of occurrence of given vote counts over the number of simulations? Naturally you’d have to check the simulations to see if you recover the parameters/data per usual before going forward. Or is voting behavior too unpredictable for this to have much benefit over rudimentary estimates such as the one you propose?

        • Andrew says:


          For any particular election, I think the best way to estimate Pr(tie) is to construct a forecasting model. For the aggregate question of how frequently do we expect to see tied elections, it can make sense to use a simpler and more crudely empirical approach.

  2. Zack says:

    Having just read your paper on voting rationality, one thing, in particular, stands out to me:

    In larger elections, social motivations dominate, but in smaller elections, selfish motivations become more influential.

    So, people voting for members of Congress would be doing so rationally for (perceived) societal gain, *but* members of Congress would be comparatively more inclined to vote (still rationally) according to their own selfish interests.

    I understand that the paper was more concerned with motivation to vote at all as opposed to voting preferences, but that’d seem like a logical extension of the general reasoning behind your model.

    Do you think I’m extrapolating too far from/misinterpreting the conclusions of the paper?

    • Andrew says:


      Yup, I do think that when voting in a small legislature, your probability of decisiveness can be high enough that it can make sense to do so for selfish interests. As always, it can be difficult to disentangle selfish from general interests. For example, a congressmember might selfishly want to be reelected, while also feeling that his or her reelection will benefit the country more generally.

      • Zack says:

        That’s true; what is altruistic and what is selfish (from the perspective of the voter) can, at least in some circumstances, have significant overlap.

        With that in mind, do you think your model could potentially be feasibly adapted to apply to a group like Congress, where that entanglement is more prevalent, rather than just the general public?

        I, for one, would *love* to see even just a reasonable attempt at that sort of model. Though, that entanglement issue may present an unsolvable roadblock to creating it.

        (As an irrelevant side note: I’m a *huge* fan of your work; I’ve honestly learned more about how to *do* statistics from your blog than I did getting my undergraduate stats degree. So, please, for the good of the humanity, keep it up!)

  3. Fran says:

    Follow up: (Now it’s a tie)[]!

  4. Terry says:

    He said each candidate’s name is placed into a separate film canister. The canisters are placed into a glass bowl and shaken up. The canister containing the winner’s name is pulled out at random by a board member.

    What’s a film canister? One of these things?

    Doesn’t sound very practical.

  5. Jonathan (another one) says:

    I think they should decide the election by replicating an experiment with a p value of 0.05 and seeing if the result is statistically significant.

  6. I love this blog!

    Quick question about this topic: in my understanding of the way economists use the word “rational”, one of the things that keeps it from degenerating into tautology is that the utility function has to be stable — it can’t for example be radically changing from action to action.

    Do we have any evidence that that is the case here? That is, are there any other actions that people habitually take in which they demonstrate the same level of concern for the general social welfare that you hypothesize they do when they vote?

    • Andrew says:


      Here’s another example, which we mention in our paper: small dollar-value contributions to political campaigns. If you give $100,000 to a campaign you might be buying influence, but not if you give $20.

      Also, it’s not quite that I’m “hypothesizing” that people care about the general social welfare when they vote. This is also what people tell survey interviewers when asked why they are voting.

  7. Larisom says:

    …and what do people tell survey interviewers when asked why they are not voting ?

  8. Sorry, but it’s still irrational to vote in most circumstances. Your paper “Voting as a Rational Choice” employs the highly unrealistic unbounded utility function

    B_self + α N B_soc

    where B_self is the personal benefit, B_soc the social benefit, N the size of the affected population, and α > 0. Unbounded utility functions have long been known to be problematic. For example, the unbounded utility function above implies that, if N is large enough, you would be willing to see yourself and everyone you love slowly tortured to death just to secure a small increase in the probability of electing a slightly better candidate.

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