One of the first things I learned about as a political science student was the “paradox of voting,” which is simply the observation that the cost associated with voting (i.e., the opportunity cost of taking the time to vote) outweighs the expected benefit.
While the outcome of a political race may be highly consequential, it is extremely unlikely that you will have any impact on that outcome. The reason for this is that unless your vote is decisive,it has no effect on who wins. And in an election where millions of people are casting ballots—as is typical in a high-stakes election—the odds of your vote being decisive are extraordinarily low.
Even though I have some minor issues with the above argument, I still believed that the core of the argument was correct. In other words, in cost-benefit terms, I thought it was probably true that the cost of voting exceeds the expected benefit.
However, once I actually tried to calculate the expected value of a single vote, I changed my mind entirely. In fact, according to the cost-benefit model, I’m now convinced that the so-called “paradox” of voting isn’t a paradox at all. This is because I now believe that, in most elections, the expected benefit from voting far exceeds the associated cost.
How can this be? Let’s look at a hypothetical two-way election to sketch out the argument:
Assume two candidates are running for president. Because politicians are not all the same, let’s assume that Candidate A is more desirable than Candidate B. Why? Well, with Candidate A in office instead of Candidate B, the $4 trillion national budget will be 10% better every year for 4 years. As such, the expected value of Candidate A defeating Candidate B is $1.6 trillion.
Of course, in reality the president affects far more than just the national budget. The president also significantly shapes the social fabric, the foreign policy landscape, and many other important things. However, for my argument, I will just stick to national budget effects because—at least relatively speaking—they are easiest to quantify.
Assume that 150 million people are expected to vote in this election. Also assume that the election will be close, probably within the range of 5 percentage points. A plausible final tally would be 78 million votes for the winner and 72 million for the loser. Of course, it could also be much closer, with the winner earning only a couple thousand more votes than the loser.
But what are the odds that this election is decided by a single vote? Alas, my math skills are not good enough to precisely answer this question. But if we assume that the election will be decided by at most 8 million votes, then I’ll assume the odds that the election is decided by a single vote are roughly 1 in 8 million.
Now that we have everything we need to calculate expected value, let’s calculate it. Fortunately, my math skills are good enough to make this calculation: $1.6 trillion divided by 8 million = $200,000.
Are you shocked at how high the expected value is? I certainly was. But even if you were to assume (which I don’t) that this figure is off by an order of magnitude, a single vote would still be worth $20,000. Even if it were off by two orders of magnitude, a vote would still be worth $2,000. Before doing any math, I would have guessed a single vote was worth around $50. Turns out I was off by a factor of 400.
When I saw these numbers, I immediately thought a few things. First, I should definitely vote this election cycle. Secondly, I should definitely remind all of my friends to vote. Hell, I should definitely canvass for a close Senate race to get out as many people to vote as possible.
If I assumed that every 20 hours of helping to “get out the vote” would convince 1 person to vote who would not have otherwise, what would be the expected value of an hour of my work? The answer: $10,000! That’s a pretty extraordinary use of my time. Again, even if I assumed that my calculation was off by two orders of magnitude, each hour would still be worth $100. That’s still more valuable than probably >99% of my hours.
Of course, I sketched out an extremely broad argument here. But I don’t think it’s unreasonable to say that most of its logic applies to the upcoming US midterm elections, which will (probably) be close and highly consequential.
Does this mean that everyone should stop everything they’re doing right now and work for a campaign? Probably not, although I hope at least some people do this! So what should you do? Well, you should definitely vote. And you should probably encourage all of your friends to vote. And you should possibly encourage as many people as you reasonably can to vote.
P.S. A caveat to this argument is that you should not merely encourage people to vote, but encourage people to vote for the better choice. Fortunately, in the upcoming election, I don’t think it’s especially hard to discern the better choice.
How Important is “Getting Out the Vote?”
One of the first things I learned about as a political science student was the “paradox of voting,” which is simply the observation that the cost associated with voting (i.e., the opportunity cost of taking the time to vote) outweighs the expected benefit.
While the outcome of a political race may be highly consequential, it is extremely unlikely that you will have any impact on that outcome. The reason for this is that unless your vote is decisive, it has no effect on who wins. And in an election where millions of people are casting ballots—as is typical in a high-stakes election—the odds of your vote being decisive are extraordinarily low.
Even though I have some minor issues with the above argument, I still believed that the core of the argument was correct. In other words, in cost-benefit terms, I thought it was probably true that the cost of voting exceeds the expected benefit.
However, once I actually tried to calculate the expected value of a single vote, I changed my mind entirely. In fact, according to the cost-benefit model, I’m now convinced that the so-called “paradox” of voting isn’t a paradox at all. This is because I now believe that, in most elections, the expected benefit from voting far exceeds the associated cost.
How can this be? Let’s look at a hypothetical two-way election to sketch out the argument:
Assume two candidates are running for president. Because politicians are not all the same, let’s assume that Candidate A is more desirable than Candidate B. Why? Well, with Candidate A in office instead of Candidate B, the $4 trillion national budget will be 10% better every year for 4 years. As such, the expected value of Candidate A defeating Candidate B is $1.6 trillion.
Of course, in reality the president affects far more than just the national budget. The president also significantly shapes the social fabric, the foreign policy landscape, and many other important things. However, for my argument, I will just stick to national budget effects because—at least relatively speaking—they are easiest to quantify.
Assume that 150 million people are expected to vote in this election. Also assume that the election will be close, probably within the range of 5 percentage points. A plausible final tally would be 78 million votes for the winner and 72 million for the loser. Of course, it could also be much closer, with the winner earning only a couple thousand more votes than the loser.
But what are the odds that this election is decided by a single vote? Alas, my math skills are not good enough to precisely answer this question. But if we assume that the election will be decided by at most 8 million votes, then I’ll assume the odds that the election is decided by a single vote are roughly 1 in 8 million.
Now that we have everything we need to calculate expected value, let’s calculate it. Fortunately, my math skills are good enough to make this calculation: $1.6 trillion divided by 8 million = $200,000.
Are you shocked at how high the expected value is? I certainly was. But even if you were to assume (which I don’t) that this figure is off by an order of magnitude, a single vote would still be worth $20,000. Even if it were off by two orders of magnitude, a vote would still be worth $2,000. Before doing any math, I would have guessed a single vote was worth around $50. Turns out I was off by a factor of 400.
When I saw these numbers, I immediately thought a few things. First, I should definitely vote this election cycle. Secondly, I should definitely remind all of my friends to vote. Hell, I should definitely canvass for a close Senate race to get out as many people to vote as possible.
If I assumed that every 20 hours of helping to “get out the vote” would convince 1 person to vote who would not have otherwise, what would be the expected value of an hour of my work? The answer: $10,000! That’s a pretty extraordinary use of my time. Again, even if I assumed that my calculation was off by two orders of magnitude, each hour would still be worth $100. That’s still more valuable than probably >99% of my hours.
Of course, I sketched out an extremely broad argument here. But I don’t think it’s unreasonable to say that most of its logic applies to the upcoming US midterm elections, which will (probably) be close and highly consequential.
Does this mean that everyone should stop everything they’re doing right now and work for a campaign? Probably not, although I hope at least some people do this! So what should you do? Well, you should definitely vote. And you should probably encourage all of your friends to vote. And you should possibly encourage as many people as you reasonably can to vote.
P.S. A caveat to this argument is that you should not merely encourage people to vote, but encourage people to vote for the better choice. Fortunately, in the upcoming election, I don’t think it’s especially hard to discern the better choice.