Political Ignorance

Every Vote Does Count—But the Chance it Will Make a Difference is Still Ridiculously Low

A recent Virginia election decided by one vote has given new life to the mantra that "every vote counts." But the chance of a single vote making a difference remains extraordinarily low, and this reality incentivizes voters to be ignorant and biased.


A recent Virginia state legislative election which was decided by a single vote has stimulated predictable reassertions of the mantra that "every vote counts," and claims that a single vote has great power. The one vote margin not only determined the fate of a seat in the Virginia House of Delegates, but also likely ensured that the House would be equally split 50-50 between Democrats and Republicans, as opposed to having a 51-49 GOP majority [but see update below].

It is indeed true that every vote made a difference in this case and a handful of other elections decided by one vote. But focusing on such rare instances obscures the reality that the overwhelming majority of elections (well over 99.9%) are not decided by a single vote. In these cases, the absence of any one vote would not have made any difference.

In a certain way, it is indeed true that "every vote counts." Each vote is included in the total, and each has a tiny chance of being decisive. But this is true in the same sense that we can say that "every lottery ticket counts" because each ticket gets tallied and each has a tiny chance of winning the jackpot. In a US presidential election, the chance that any one vote will be decisive is roughly 1 in 60 million. The odds are better in congressional, state, or local elections. But they are still usually thousands or even millions to one.

Despite its misleading nature, the "every vote counts" mantra might be defended on the ground that it is a kind of "noble lie" that encourages civic participation. Even if most votes don't count in any meaningful sense, it might be desirable for citizens to think that they do, and act accordingly.

The problem is that, while "every vote counts" and similar slogans do encourage people to vote, they don't do much to ensure that we will do so in an informed way. Even a very low probability of casting a decisive ballot is often enough to make it rational to undertake the small effort of casting a ballot for the lesser of the available evils. But, as the persistence of widespread voter ignorance shows, it is not enough to incentivize most voters to invest the much greater time and effort needed to inform themselves about the candidates and issues at stake. While most people may not know the exact odds, they do have a sense that there is little payoff from spending large amounts of time studying political issues—at least not if the only reason is to cast a better vote. Thus, we end up with elections where millions vote, but the vast majority are ignorant about many of the issues at stake. Politicians, activists, and interest groups, are well aware of this reality, and routinely exploit public ignorance for their gain—and our loss.

In addition to being poorly informed, most voters also tend to be highly biased in their evaluation of the political information they do learn. Keeping our biases and prejudices under control is often difficult. Few people are willing to make the effort in situations where it is highly unlikely to make any difference to the outcome. For that reason, most people are far more biased in evaluating political information than otherwise similar information that relates to nonpolitical private sector decisions. Such behavior by individual voters is rational and understandable. The ignorance and bias of any one voter matters very little. But, sadly, ignorant voting is a situation where individually rational actions can lead to harmful collective outcomes. When all or most of entire electorate tends to be ignorant and biased, we end up with deeply flawed leaders, and harmful government policies.

If we want our choices to really count, in the sense of having a substantial chance of making a difference, we should make fewer decisions at the ballot box and more by "voting with our feet." When we choose what jurisdiction to live in in a federal system, or make choices in the private sector, the decisions we make really do affect outcomes for ourselves and our families, which gives us stronger incentives to seek out information and use it wisely. We can expand opportunities for foot voting by limiting and decentralizing government power, and by breaking down barriers to mobility—particularly those that inhibit the poor.

At best, "every vote counts" is a comforting distortion. At worst, it diverts attention away from the painful reality that individual votes don't count enough to ensure that we have a well-informed electorate. It also leads all too many citizens to overlook the need to empower people to make choices that really do count.

Constant invocations of "every vote counts" are usually motivated by a well-intentioned desire to increase turnout. But we should worry less about how many people turn up at the polls, and more about the quality of the decisions they make once they get there.

UPDATE: Soon after I posted the above, a court decision changed the result in the Virginia House of Delegates election by counting a vote in favor of the Republican candidate that had been previously been considered void. As a result, the election is now tied. If this ruling holds, the seat—and with it control of House of Delegates—will be decided by a coin toss or a drawing of lots. In in a sense every vote still did matter in this race, because all were necessary to ensure it was a tie rather than a one-vote victory for one side or the other.

The Washington Post describes the details of the court decision and its consequences here:

A three-udge panel declined to certify the recount of a key House race today, saying that a questionable ballot should be counted in favor of the Republican and tying a race that Democrats had thought they had won by a single vote.

"The court declares there is no winner in this election," said Newport News Circuit Court Judge Bryant L. Sugg, after the judges deliberated for more than two hours.

He said the ballot in question contained a mark for Democrat Shelly Simonds as well as a mark for Republican Del. David Yancey but that the voter had made another mark to strike out Simonds' name….

The court's decision leaves the race for the 94th District tied at 11,608 votes each for Yancey and Simonds. And it leaves the balance of power in the state legislature at 49-51, in favor of Republicans—at least for now. In the case of a tie in a House race, state law says the winner is chosen by lot – essentially, a coin toss.

James Alcorn, the chairman of the state board of elections, said the winner will likely be chosen by drawing a name out of a glass bowl. He said he is conferring with staff to figure out the date and method.

But it doesn't end there. If the loser of the coin toss is unhappy with that result, he or she can seek a second recount.

NEXT: D.C. Allowed to Exclude Religious Ads from Buses

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  1. Moral: Just like buying lottery tickets, don’t cross the street to vote. Your chance of being killed by a car is 1 in 20 million.

  2. A three judge panel has ruled that a discarded ballot should be counted in favor of the Republican resulting in a tie vote.

    1. Barring further developments the race will be determined by lottery, so the votes didn’t count after all.

      1. Every vote still counted, because a change to any one vote would still produce a different result (a clear winner instead of a roll of the dice).

        1. Coin flip, not dice.

          1. Local reports have it as drawing names from a container which is the procedure for determining the ballot order.

        2. And you don’t think that in any such case, the result would still be decided judicially rather than by a count?

      2. Who was it who made the point some yrs. ago that if ever an election were decided by 1 vote, the result would never be allowed to stand. Case in point.

  3. Even those who follow politics closely can make mistakes. I seem to recall some law school professors enthusing about a Texas senatorial candidate named Cruz who they said was super bright and deserved to be sent to Washington. Maybe law school professors are more malevolent than I have realized.

    1. I haven’t seen an admission that this was a mistake.

      1. I always figured that ‘Libertarians for Ted Cruz’ stuff was a prank. How could anyone take it seriously?

      2. Of course you haven’t, that would not be typical for people who strive to be taken seriously.

  4. Many of the “ill-informed” are immigrants, both legal and illegal, that continue to register and vote in elections. Not to mention those “ill-informed” citizens that have no problem voting in multiple States, especially those States that do not check or cross-check with other States.

    1. Where is the proof of widespread voter fraud?

    2. You’re usually smart as heck, but will need to back up this narrative here before it approaches being an argument and not a nativist canard.

  5. Quote from Ilya: “In a certain way, it is indeed true that ‘every vote counts.’ . . . But this is true in the same sense that we can say that ‘every lottery ticket counts'”

    First, that’s a bad analogy. If 5% of would-be lottery-ticket purchasers are persuaded not to buy tickets, the aggregate consequences are trivial — it just ensures the lone winner won’t be one of those 5%. If 5% of would-be voters are persuaded not to vote by the belief that their vote doesn’t matter, resulting in a different candidate being elected, then the entire public will be impacted.

    Second, a vote does not have to be outcome-determinative to “count.” Votes count in the aggregate. The fact that you deem voting not worth your time, unless you have a high chance of being the deciding vote, merely reflects your personal preference not to participate in collective action unless your opinions control it — which is consistent with the expressly anti-democratic themes that have come to dominate your posts in the Trump era.

    Quote from Ilya: “If we want our choices to really count, in the sense of having a substantial chance of making a difference, we should make fewer decisions at the ballot box and more by ‘voting with our feet.'”

    This makes no sense. Under your theory that we’re all insignificant specks whose actions change nothing, a single person’s preferences typically won’t effectuate governmental change whether he’s voting or he’s moving from New York to New Jersey.

  6. If you look at the ballot, which is imaged in the Post’s article, you can see that the voter choose the Republican candidate for all the other contests, so it is reasonable to conclude that he/she meant to choose the Republican Yancey, but mistakenly marked the circle for the Democrat (which was first on the list).

    1. No, that is not reasonable to suppose. It is not reasonable because allowing a ballot like that invites corruption. How hard would it be for someone with access to ballots to find one where the voter happened to prefer the Democrat for one office, but Republicans for all the others? I vote like that (but for Republicans) in Massachusetts governors races all the time?Republican governor, all Democrats or blanks (plenty of blanks) otherwise. In that pattern, I’m joined by many others, as election outcomes demonstrate.

      So there are plenty of ballots like that. If someone with ballot access can alter an election outcome with a simple strike-through, that’s too great a risk to election integrity. It is shocking that a court even had power to make such a decision?the law should have taken that out of their hands by sufficiently defining a spoiled ballot. Assuming no such law did exist, the court should have called it a spoiled ballot and discarded it.

      1. They need to additional instructions:

        If you mark more candidates than allowed for the office your vote for that office will not be counted.
        If you make a mistake request a new ballot.

        Ballots are inserted into a machine at the polling location. I guess the machines don’t do basic checks for overvoting.

  7. This is why local control and weaker decentralized governments are a good thing.

    1. Except see Jim Crow. And the short life of the poor America pre-New Deal. And the kind of personal corruption specific to what smaller and thus less scrutinized institutions can do.

      There are costs as well as benefits to local control. The key is the position of the line, not it’s momentum.

  8. A coin toss seems so unsatisfying. The method should be at least as fun as rock, paper, scissors…

  9. Another mantra “If you didn’t vote, you can’t complain”, is the reason I vote.

    On November 8th, 2016, congressional disapproval stood at approximately 75%, while the voter turn out was at 55%, which nets to 20% disapproving but not voting.

    Skimming through the report below, I found it interesting that, 89% “would like to see the media report
    more on the issues and actual policy discussions in Congress”, while only 7% “would like to see the media report on the personalities in Congress”

    It appears politically active voters now approach politics as a sporting event, and the major new outlets are only giving the people what they want.


    1. “If you didn’t vote, you can’t complain”, is the reason I vote.

      I vote (major party, minor party, write in) so my opinion doesn’t get thrown in with the apathetics. Low turnout is less of a statement than a candidate winning with less than 50% of the vote. It is an explicit rejection of the candidates to write in “none of the above”.

      1. Quite true. Election day should be a national holiday, to shame people into voting. If people who never voted take a look at the ballet, it may surprise them how much else is being decided for them.

        1. 1. No it shouldn’t
          2. Thanks for another day’s lost output, and either reduced wages (if the workers don’t get paid) or reduced profits (if they do)
          3. How nice of you to want to shame people for not doing what you’s like them to do. I hope they get to return the compliment. Daily.
          4. Ballet is rather an acquired taste

      2. Besides being pointless and childish, writing in “none of the above” is not a vote. It’s not voting, but with more effort. Nobody cares about your none-of-the-above “statement”, and it accomplishes nothing except maybe an uptick in undeserved smugness. Moreover, “they’re all bums” may be very self-satisfying, but it’s also untrue and how we ended up where we are today.

        1. For the record, I always pick the least bad candidate. If someone else doesn’t know who the least bad candidate is, then rather than do a coin flip at the booth, it would only make sense to right in “none of the above’ and move on to the other questions on the ballot.

  10. How do you feel about multidistrict voting and encouraging more ways to break the first past the post system? Our current voting system has seemed to calcify our democracy and provides little pressure on parties as a whole to offer compelling/competing visions that they can sell to the populace.

    I have been quite inspired by the effect smaller parties have had in countries like Germany in recent elections to force the big parties to adapt or die. We have no such mechanism here.

    1. I beg to differ. It is the continental European proportional systems that are calcified. Elections rarely change much about the support for parties and all the horse trading gets done by the politicians after the election. True, after decades of this calcification, some newer smaller parties have emerged as havens for protest voters, but with the exception of Austria, none of them have made it into even a share of government. They have been frozen out by the political establishment. Besides which, in Europe, 80% of government policy is determined by the EU Commission which is immune from interference by the voters.

      Whereas the FPTP system does at least allow the electorate to throw the bums out. The bums were thrown out pretty vigorously in 2006 and again in 2010. And as like as not, again in 2018.

      1. Something for me to think about. Thanks for your opinion.

  11. Somin’s repeated critique of vote significance is less persuasive than he supposes. In an election determined by a single vote, it isn’t just one vote that determines the outcome, it’s every single vote cast, on both sides. So even if that kind of close race is rare, when it happens there are a great many voters whose vote individually determined the outcome. Somin seems to understand that, although he’s a little tacit about it.

    Now consider that at the next level?Bush and Gore in Florida. That outcome, which swung the national election, was determined by a 537 vote margin (plus Supreme Court meddling, whatever you think of it). Extending the 1-vote reasoning to Florida, every voter who cast a ballot in Florida’s election?not just 537 of them?had a 1/537th share in determining the national race for President?thus distributing an almost-grandiose share of national power to each among millions of Florida voters.

    The error in Somin’s reasoning comes from supposing the opposite of what he tacitly (and correctly) concedes when he notes that in a single-vote election every vote is determinative. He nevertheless goes on to reason as if that were not so?or not approximately so to a lesser-but-still-noteworthy degree?in elections determined by wider margins. He invites voters in those cases to suppose that all the votes cast outside of the margin of victory were simply inconsequential. That is a mistake in reasoning, and Somin should stop repeating it.

    1. I think you are mistaken.

      In an election won by one vote, Mr X who voted for the winner, can say his vote was decisive. Because if he had voted the other way the election would have gone the other way. Now let us look at Ms Y, who also voted for the winner. She can also say her vote was decisive for exactly the same reason. Consequently everyone who voted for the winner can say their vote was decisive, because the condition {if I had voted the other way the result would have changed} applies to each voter individually.

      If the election is won by 3 votes*, however (or 537 if you prefer) neither Mr X nor Ms Y, nor any voter can say {if I had voted the other way the result would have changed} ? consequently none of the voters’ votes was decisive.

      Now you may wish to generate a different test for “my vote was decisive” such as my vote counts as fractionally decisive to the extent of a fraction of 1/x, where x is the minimum number of people, including me, who if we had all voted differently, would have flipped the result.

      This definition hardly trips off the tongue, and with the best will in the world, I don’t think this more complicated formula can be described as a reasonable interpretation of “my vote was decisive.”

      * I say 3 because a single vote flip where there is a two vote win would force a draw which would be a different result.

      1. Can you bring yourself to suggest that all the votes cast outside the margin of victory were inconsequential? If not, I suggest you join me in my disagreement with Somin.

        1. All the votes cast outside the margin of victory are indeed inconsequential.We know that because looking at any particular vote, if we suddenly discovered it was invalid and disallowed it, the consequences wouldn’t change.

          The concept you are grappling with without stating clearly is that each vote has a probabalistic connection with the result. After you know the result, and it’s a win by more than 2 votes, you know that your vote made no difference. But before you vote, you don’t know how the vote is going to turn out. There’s some probability that it will be decisive, and the probability is greater, the closer the district.

          What you can also say – if the result is a win by 537 – is that {those 269 votes} were decisive – but unless you have a very large family, or you’re running a mail in vote fraud, it’s not a very meaningful thing to say. Because those other 268 votes are not within your control, they’re not acting in concert.

  12. Whew, here we almost had an incredibly rare moment wherein we could show a notoriously lazy and uninvolved voting population that, yes, in fact voting can and does matter. Fortunately, we have Prof. Somin to reassure us that, by the odds, it really doesn’t.

    That was close.

  13. Volucre: “This makes no sense. Under your theory that we’re all insignificant specks whose actions change nothing, a single person’s preferences typically won’t effectuate governmental change whether he’s voting or he’s moving from New York to New Jersey.”

    Not being able to +1 comments like this is one of the losses of this blog moving.

    The “voting with your feet” meme Somin has blogged about is pretty interesting, but he has latched onto it way too tight, ignoring or wildly downplaying any negatives or counterarguments. I have voted in almost every election (including local ones) for many years. I often research the candidates, and the sum energy I have put into all of those dozens of elections combined is far less than the time or energy of moving just once. I know my votes have sometimes counted, as several times ballots have been won/lost by less than 10 votes. I strongly doubt my moving has ever made the tiniest difference in any municipal or state policy.

    1. But it made a difference in your life, which is more than you can say about election voting.

  14. The problem is not with any particular individual vote not being important to the outcome. The problem is the cumulative effect of lots and lots of people not voting. If 80,000 people in three states who didn’t vote, but who would have voted for Clinton, had shown up at the polls last year, Donald Trump would not now be president.

    It’s like I keep trying to tell the spendthrift I’m married to. The problem is not a $20 purchase here or a $50 purchase there. The problem is that they all add up until all of a sudden, we have a thousand dollar credit card bill. Same principle applies here.

    1. The spending adds up, but only if it’s from the same acc’t. There’s no way someone’s voting can add up like that.

  15. The author seems to have a problem understanding corporate decision-making. In such a system, every vote counts not because it is individually “decisive”, but because it adds to the collective without which the collective would not win. The first such vote is as important as the 11,608th vote in this system. Not only does your vote matter, but so does everyone’s vote.

  16. But this is true in the same sense that we can say that “every lottery ticket counts” because each ticket gets tallied and each has a tiny chance of winning the jackpot. In a US presidential election, the chance that any one vote will be decisive is roughly 1 in 60 million. The odds are better in congressional, state, or local elections. But they are still usually thousands or even millions to one.

    No no no no no no. There is at least some forces pushing all elections to regress to approximately 50/50 — in fact that’s the natural Nash equilibrium in a 2-party FPTP system. So the odds are not like the lottery where all outcomes are equally probable and so the average is a simple division. Rather, it’s far more likely (theoretically and empirically) that elections will be close and so the probability of a decisive single vote has to be calculated against the expected margin of victory.

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