### Transcript (PDF)

In the greatest democracy on earth, voter turnout is typically around 100%.[1]

In lesser democracies, the numbers are usually less fantastic. For example, for the US presidential elections, only 57.8% of eligible voters show up. For the midterm elections, the number is a rather more woeful 41.7%.[2]

To the concerned citizen, these numbers are too low. Because, y’know, “robust voter turnout is fundamental to a healthy democracy” — and other clichés.

But strangely enough, for economists, these numbers are too high! For economists, the puzzle is not why voter turnout is so low, but why it’s so high.

That’s because to economists, voting is irrational. Irrational in the narrow sense that it fails a simple cost-benefit analysis — the **cost of voting** exceeds its **expected benefit**.

To see why, let’s first look at a simple example of cost-benefit analysis. Say a lottery ticket gives you a 1% chance of winning $500. Then its expected benefit is simply the “probability of winning”, times the “value of winning”. That’s $5.

So if the ticket costs $1, the expected benefit exceeds the cost and it would be rational to buy it. But if it costs $20, the cost exceeds the expected benefit and it would be irrational to buy it.[3]

For voting, the cost-benefit analysis is exactly analogous. We’ll start by examining the cost of voting.

These days, you can send strangers money and your most intimate pics — all while taking a dump. But voting still isn’t that convenient. To vote, you still have to haul your posterior to some polling station. Where there might even be a long and painful queue. All of this takes time. And as Mother Teresa once said, “Time is money.”

And oh, you might even have to pay a little for transport.

So, the cost of voting may be small. But it ain’t zero.

Let’s say your time is worth only the US minimum wage — $7.25 an hour.

Let’s say the polling station is within walking distance, so that you pay nothing for transport. Also, the polling station has no queue. Altogether, voting takes only 10 minutes.

Even with these generous assumptions, voting still costs you one-sixth of an hour, times $7.25 an hour, or $1.21. Let’s just round down and say that at the very least, the cost of voting is $1.

Next. The expected benefit of voting.

For some, the point of voting is to fulfill some sacred, mystical, patriotic, civic duty-thing. To others, it’s to get one of those “I Voted” stickers. To the economist, these are nonsensical reasons for voting. To the economist, the only reason for voting is that your vote might matter — there’s a slim chance your vote swings the election result.

To see when your vote matters,[4] imagine we count all votes *except* yours. Then there are four possibilities. One, your preferred candidate’s winning. Two, he’s *exactly* tied with the frontrunner. Three, he’s losing by *exactly* 1 vote. Four, he’s losing by more than 1 vote.

These are the *only* possible scenarios. Either your man’s winning, exactly tied, down 1, or down by more than 1.

Now, it turns out that in Scenarios 1 and 4, your vote doesn’t matter.

In Scenario 1, without your vote, he wins. With your vote, he also wins. So your vote makes no difference.

And in Scenario 4, without your vote, he loses by more than 1 vote. With your vote, he *still* loses by at least 1 vote. So again your vote makes no difference.

In Scenarios 2 and 3, your vote matters.

In Scenario 2, without your vote, he’s exactly tied. Assuming ties are broken by a simple coin-flip, this means he has a 50% chance of winning. With your vote, you break the tie and so increase his chances to 100%.

And in Scenario 3, without your vote, he’s down 1. Meaning he has 0% chance of winning. With your vote, you create a tie. Meaning the election is now decided by a coin-flip and you’ve increased his chances to 50%.

Altogether then, your vote matters only if, counting all votes except yours, he’s exactly tied or down 1.

Now, here’s the thing. These scenarios are *wildly* improbable. Especially if there are millions of voters. A study[5] of the 2008 election found that the probability a vote would matter was at most 1 in 10M in some states. But in other states, it was less than 1 in 10B!

Here’s another thing. Even when your vote matters, all it does is to increase your man’s chances of winning by 50 percentage points.[6]

And so, by analogy to our lottery example, the “expected benefit of voting” equals the “probability your vote matters”, times the “value of increasing your man’s chances by 50 percentage points”.

For the “probability your vote matters”, let’s use the high-end figure from the 2008 study. Let’s say it’s 1 in 10M.

Next. As you know from an earlier video, value is purely subjective and personal. So. Imagine the Devil offers to increase your man’s chances of winning by 50 percentage points. What would you be willing and able to pay for this offer? This figure is the value you place on increasing your man’s chances by 50 percentage points.

If you’re like most people, the figure is probably fairly modest. Maybe 1K. Or maybe even 10K tops.

But let’s exaggerate and say that to increase your man’s chances by 50 percentage points, you’re willing and able to pay an incredible $1M.

Now, even with this incredible figure, the “expected benefit of voting” still works out to be only 1 in 10M, times $1M, or 10¢.

That’s less than the cost of voting, which we said is at least $1.

And here, we’ve clinched the argument. The cost of voting exceeds its expected benefit. Therefore, voting is irrational.

Why then do people vote? Are they simply stupid? Or are there flaws in our argument? In the next video, we’ll look at various explanations.

#### Footnotes

[1] According to *The Guardian*, voter turnout for both the 2011 and 2015 elections was 99.97%.

[3] Strictly speaking, these statements depend on one’s degree of risk aversion. For someone who’s extremely risk-averse, it may be rational to *not* buy the ticket, even if it costs only $1. Conversely, for someone who’s extremely risk-loving, it may be rational to buy the ticket, even if it costs $20. But for simplicity, both here and also later on, I gloss over the whole risk-aversion thing. I implicitly assume that you’re neither “too” risk-averse nor “too” risk-loving.

[4] Or in economistic jargon, when your vote is *pivotal* or *decisive*.

[5] Gelman, Silver, and Edlin (2012).

[6] For simplicity, I assume you’re indifferent between “increasing your man’s chances from 0 to 50%” and “increasing your man’s chances from 50 to 100%”. This need not generally be the case. (If it isn’t the case, the analysis will be slightly more complicated, but the conclusion will still be the same.)