November 6: The Day You Did Absolutely Nothing

As the elections were coming up, I noticed that many wanted to inflate their single vote with undeserved moral capital. I wasn’t having any of it, especially if they were doing so in order to smugly lecture others. 

So, what do the numbers say regarding your single vote? Georgetown’s Jason Brennan explains,

There is some debate among economists and political scientists over the precise way to calculate the probability that a vote will be decisive. Nevertheless, they generally agree that the probability that the modal individual voter in a typical election will break a tie is small, so small that the expected benefit (i.e., p[V(D)−V(R)]p[V(D)−V(R)]) of the modal vote for a good candidate is worth far less than a millionth of a penny (G. Brennan and Lomasky 1993: 56–7, 119). The most optimistic estimate in the literature claims that in a presidential election, an American voter could have as high as a 1 in 10 million chance of breaking a tie, but only if that voter lives in one of three or four “swing states,” and only if she votes for a major-party candidate (Edlin, Gelman, and Kaplan 2007). Thus, on both of these popular models, for most voters in most elections, voting for the purpose of trying to change the outcome is irrational. The expected costs exceed the expected benefits by many orders of magnitude.

While a 1-in-10 million chance is the most optimistic estimate, the average estimate is 1-in-60 million. Economist Steve Landsburg put it this way: “I have a better chance of winning the Powerball jackpot 7,400 times in a row than of affecting the election’s outcome. Which makes it pretty hard to see why I should vote.”1 

So maybe the presidential election is a long shot when it comes to making a difference as an individual voter. Surely the midterm elections are different, right? They certainly are, but it’s not something to get excited about. As economist Casey Mulligan explains,

An election of a United States senator, or a governor, has never in the history of the United States been decided by one vote. Charles Hunter, who earned a doctorate at the University of Chicago, and I studied almost 100 years of elections of members of Congress – almost 20,000 of them in which an aggregate two billion votes were cast – and only one election was determined by a single vote of the 40,000 cast (that was in the New York’s 36th Congressional District in 1910). And that election had a recount that determined the election was decided by a margin of six votes, rather than one.

Thus, when it comes to elections to federal office, history suggests that the chances that your vote…will change the winner of the election is less than one in 100,000; more people die in an election year in car crashes than cast a pivotal vote in a federal election.

Dr. Hunter and I also studied 21 years of elections to state legislatures in the 50 states. Our data included more than 50,000 elections with an aggregate of about a billion votes cast. Those elections were markedly smaller than the federal elections and therefore more likely to come down to one vote.

Still, only nine of these came down to one vote (before recounts), and included a grand total of less than 40,000 pivotal votes. So the probability of a pivotal vote in these elections was less than one in 25,000. (The odds are somewhat higher – one in 15,000 for the state elections and one in 89,000 for Congressional elections – if the election actually has more than one candidate; a number of elections do not, such as this year’s election in Florida’s 21st Congressional District).

Let’s check those stats again:

  • Presidential elections: 1-in-60 million on average; 1-in-10 million at best.
  • Federal elections: 1-in-100,000; 1-in-89,000 for Congressional elections.
  • State legislators elections: 1-in-25,000; 1-in-15,000 at best.

As one friend put it, if you’re trying to get into the Good Place, voting likely earns you 10 points total.2 That’s a blip on the moral scale.

However, these 10 points are probably cancelled out by:

  • The smugness that accompanies your “I Voted” sticker.
  • The terrible way you treat flesh-and-blood people who disagree with your politics.3
  • The likelihood that your Facebook status about the importance of voting is nothing more than moral grandstanding.4

But that’s still working off the assumption that voting is an inherent good. No one seems to care that voting imposes costs on others by means of legalized violence (government). Now, those costs and the accompanying legalized violence may be justified. But if you’re going to force something on to others, you’d better be damned sure it is in fact just and worth the cost. If you’re not sure (and the social science suggests you probably aren’t), stay away from the polls

Also, voters typically want to transmit all the goodness of their political picks to themselves, while ignoring the evil. For example, many Obama supporters probably see themselves as champions of the uninsured; crusaders for healthcare justice. However, they likely do not want his drone strikes or deportations on their conscience. “Turns out I’m really good at killing people” isn’t exactly the moral motto most voters want to trumpet.

Finally, you may be risking more harm than good by simply driving to the polls on election day:

[S]uppose my favored candidate (who is worth $33 billion more to the common good) enjoys a slight lead in the polls. She has a very small anticipated proportional majority. The probability that any random voter will vote for her is 50.5 percent. This is an election we would describe as “too close to call.” Suppose also that the number of voters will be the same as in the 2004 U.S. presidential election: 122,293,332. I vote for my favored candidate. In this case, the expected value (for the common good) of my vote for the better candidate is $4.77 x 10^-2650 , that is, approximately zero. Even if the candidate were worth $33 billion to me personally, the expected value for me of my vote would be, again, a mere $4.77 x 10^-2650 . That is 2,648 orders of magnitude less than a penny. In comparison, the nucleus of an atom, in meters, is about 15 orders of magnitude shorter than I am. In meters, I am about 26 orders of magnitude shorter than the diameter of the visible universe. In pounds, I am about 28 orders of magnitude less heavy than the sun. Even if the value of my favored candidate to me were dramatically higher, say ten thousand million trillion dollars, the expected value of my vote in our example—for a close election—remains thousands of orders of magnitude below a penny. For an election in which the candidate has a sizable lead, the expected utility of an individual vote for a good candidate drops to almost zero.

The Beneficence Argument appeals to the public utility of individual acts of voting. However, suppose all you care about is maximizing your contribution to the common good. If so, voting would not merely fail to be worthwhile— it would be counterproductive. It turns out that the expected disutility of driving to the polling station (in terms of the harm a driver might cause to others) is higher than the expected utility of a good vote. This is not hyperbole.

Aaron Edlin and Pinar Karaca-Mandic have estimated the expected accident externalities per driver per year in the United States—that is, the amount of damage the average driver imposes on others from accidents and reckless driving. The expected accident externalities range from as little as $10 in low-traffic-density North Dakota to more than $1,725 in high-traffic-density California. Suppose a North Dakotan takes five minutes to drive to the polling station. The average expected accident externality of a five-minute drive in North Dakota is $9.5 x 10^-5 , much larger than the expected benefit of a good vote in the previous example. So the voter imposes greater expected harm on her way to the polls than she could compensate for by a good vote.5 

To review:

  • Mathematically speaking, your individual vote has probably never mattered and likely never will matter. It literally has no consequence on the planet.
  • Whatever goodness your single vote represents is likely cancelled out by a number of negative factors that are the byproduct of political participation.
  • In actuality, voting is a means of wielding legalized violence on others.
  • If you’re going to congratulate yourself on the good your chosen politician does, you have to condemn yourself for the bad as well.
  • The risk of harming others on election day is higher than the potential benefit.

Now, this isn’t an anti-voting post. I’m not saying you should refrain from voting.6 What I am saying is that before you start patting yourself on the back for supposedly righting the wrongs of the world through voting, you ought to realize that you probably did absolutely nothing.

So cool your jets. 

2 thoughts on “November 6: The Day You Did Absolutely Nothing”

  1. While I respect someone’s choice to stay home if they really don’t want to vote for any of the options, staying home because you don’t think your vote matters or because of laziness is not something I can condone.

    This post is why I hate the stock market and why I think there are significant limits to the utility of economics: if you can’t measure a gain it is of no worth. Nothing could be farther from the truth. Many of the things we do on a daily basis have little to no impact on our lives or the lives of those around us. However, if we stop making our meager contribution, we don’t stand still, we lose ground. It is our moral responsibility to make our contribution to society, however small it might be.

  2. Once again, this isn’t an anti-voting post. It’s a post encouraging people to stop acting like smug jackasses because they voted. More implicitly, it’s encouraging people to stop making politics the epitome of their moral framework. But to address your second paragraph:

    “Many of the things we do on a daily basis have little to no impact on our lives or the lives of those around us.”

    Like? I imagine the things you do on a daily basis have a small impact on you and those around you in the moment and a large impact over time. Yet, your single vote has likely never mattered and never will. And if you can list things that you do on a daily basis that literally have no impact whatsoever, then maybe you should find new daily activities. Or at least stop assuming those activities have any moral legitimacy.

    “It is our moral responsibility to make our contribution to society, however small it might be.”

    I agree. But once again, your single vote has likely never mattered and never will. If you voted the other way, the election would have come out the same. If you chose not to vote, it would have come out the same.

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