All votes are thrown away, so vote sincerely

Virginians go to the polls tomorrow to select a new governor. To be more precise: a modest minority of eligible voters—maybe about 35 percent—will go to the polls to select a new governor. The rest will stay at home, work late, or spend time with loved ones.

Seventh grade civics teachers and mothers everywhere wonder why more people don’t exercise their precious right to vote. Public choice economists wonder why anyone does.

Here is how I typically talk about the vote decision in my public choice classes. Perhaps it will help you think through how you’d like to spend your day tomorrow.

Let’s start with a simple model and add complexity as we go.

We are going to be “modeling” an individual’s decision to vote based on the idea that voting brings some satisfaction. We call this satisfaction “utility” and say that people will vote so long as the utility from voting is positive.

Utility from voting = a function of stuff

But what should we put on the right hand side? We know people vote so we know utility from voting is positive. What gives them this satisfaction from voting?

Let’s begin with the assumption that people vote because they want to affect the outcome, to make a difference. They derive some joy from the outcome of the election. Let’s call this joy B for benefit:

Utility from voting = B + other things

B is equal to the difference in benefits the voter obtains when one outcome beats another. B could be the benefit of a government job that the voter expects to have once his brother-in-law becomes mayor. Or it could be the benefit he expects to enjoy once the entire economy improves as a result of a candidate’s policies. It need not be personal benefits. It could also include the joy one might obtain from seeing more redistribution from one group to another. And, of course, it could be all of these. The point is that B captures the expected gain in utility from one outcome prevailing over the alternatives. Note that if you think that there is essentially no difference between the candidates, B will be zero since it represents the difference in benefits obtained from one outcome prevailing over the others.

We can say more. Voting is costly. When you vote, you have to give up time you could have spent working, reading public choice books, or playing with your children. Voting is also risky. You risk being selected for a boring jury pool, you risk getting your finger jammed in the voting machine, and you risk sustaining a life-threatening accident on the way to the polls. To account for these costs, we subtract a term called C:

Utility from voting = B – C + other things

But there is still more. Remember that the B term represents the difference in utility you obtain from seeing your preferred outcome prevail. But what if you expect to see your outcome prevail whether you vote or not (think: those who voted for Reagan in ’84)? Or what if you expect to see your outcome lose whether you vote or not (think: those who voted for Gary Johnson in 2012)? The point is that if you vote in order to make a difference, then your chance of making a difference is important in your decision to vote. So we should include that as part of the gross utility term. If P is the probability that your vote will make a difference then we can write:

Utility from voting = P*B – C

In words: the utility from voting is equal to the chance that one’s vote will make a difference, multiplied by the difference in benefits one expects to obtain from one outcome beating the others, minus whatever costs are incurred in the act of voting. So long as P*B > C, people will vote.

We call this the “instrumental theory of voting” because it describes a voter who uses her vote as an “instrument” to affect the outcome. Unfortunately, there is a problem with it.

It turns out that P is small, vanishingly small. By one estimate, the chance of casting a decisive vote in the 2008 presidential election was 1 in 60 million. Why so low? Your vote only makes a difference when the rest of the electorate is evenly split. In the case of a presidential election, you’d need your state to be the decisive state in the Electoral College and you’d need all the other citizens of your state to be exactly evenly divided. That’s not terribly likely. Of course, you have a greater chance of casting a decisive vote in a smaller election such as a governorship. But even in these cases, the probabilities are extraordinarily small. I estimate that there have been over 2,000 gubernatorial elections in the U.S. Not one has come down to a single vote (the closest was Washington state’s 2004 election which came down to 133 votes but even in this case no single vote could be said to have “made a difference”).

It turns out that the chance of sustaining a life-threatening accident on the way to the polls (an element of C) is actually greater than 1 in 60 million. So this leaves us with two conclusions:

  1. Perhaps B is so great that even when multiplied by a very tiny P, it is still enough to overcome C. In other words, perhaps people are willing to risk life and limb to obtain their preferred outcome in the election. This seems less than plausible.
  2. Perhaps people obtain some benefit from voting that has nothing to do with changing the outcome. In this case, we need to add something to our model, another gross benefits term that is not affected by P. Let’s call this “D”:

Utility from voting = P*B – C + D

Here, D represents some benefit from the act of voting that has nothing to do with changing the outcome. Different authors have suggested different ideas of what D might be. It might be the sense of pride one obtains in fulfilling one’s civic duty. Or it might be the joy one gets from “cheering” on one’s side even if it doesn’t make a difference. Think of fans at a football game. They “vote” by cheering even though they know that their own cheer won’t produce a victory. This is known as the “expressive theory of voting” since it captures the notion that people vote to express opinions, not necessarily to change the outcome.

Expressive Voter

Expressive Voter


So what is the implication of all of this? Some say that the implication is that it is irrational to vote. It is costly and has almost no chance of making a difference, which gives voting about the same ROI as a sacrifice to the rain gods.

I disagree.

There’s nothing dumb about someone feeling that they have a civic duty. There’s nothing irrational about cheering on a cause even if you know it won’t make a difference. It is no more irrational to vote than it is to cheer for the Redskins (okay, so maybe it’s a little irrational).

It is irrational, however, for someone to believe that their vote makes a difference. Despite what MTV says, not every vote matters. In fact, the only time any one vote “matters” is when the electorate is perfectly split. And in that case, the only vote that really matters is Anthony Kennedy’s.

Some of you may find this depressing. It means you don’t matter. Worse, it means that you and your fellow voters have little incentive to gather or to process information about the issues, which means we are all destined to be uninformed and irrational when we step into that voting booth.

But there is some good news here: freed from any concerns that your miniscule vote will make a difference, you should feel free to vote your conscience. So if your conscience compels you to vote for a third (or fourth or fifth) party candidate, don’t listen to the nonsense that you are “throwing your vote away.” ALL votes (except for Anthony Kennedy’s) are thrown away. So, if you’d like to express your opinion, to cheer for a cause, then vote sincerely for the candidate that you think is best.

Then go home and spend time with your loved ones.