Economists sometimes use a model of voting that posits an equation-style relationship between different factors and a person’s decision to vote.

It says candidates promise a package of benefits to voters. That includes the policies they wish to enact and the more intangible things that voters like, such as the way they speak or their leadership style. Let’s call that B, for benefits.

In a winner-take-all election, most votes don’t “matter” in deciding the outcome, i.e., if a candidate wins by one vote or by a million votes, it’s a win all the same. That means the probability of your vote deciding the election is very low. One vote matters only if there’s a one-vote margin of victory, which has a probability, p, of basically zero.

There are other reasons people vote beyond the benefits they expect to receive, though: a feeling of obligation to democracy, honoring the sacrifice of soldiers who protected the right to vote, making their voices heard, setting an example for their children, and getting an “I Voted” sticker. We can lump that into the variable D, for democratic values.

Then there are costs to voting. You don’t have to pay to vote, of course, but going to the polling place might require getting up a little earlier or using a lunch break at work, and it takes time to get information about which candidates to vote for. Let’s call the costs C.

That means the voting equation looks like this:

Decision to vote = pB + D − C

Since p is basically zero, that term disappears, and all that’s left is:

Decision to vote = D − C

So people vote only if the good feelings they get from democratic values are greater than the costs of voting. This can lead to the conclusion that voting is fundamentally irrational since it’s really about warm fuzzies and not about actually choosing leaders.

That’s true in this analysis. But the weird thing about believing voting doesn’t matter is that it becomes less true as more people come to believe it.

It’s very unlikely that one person not voting would change the outcome of an election. But it’s less unlikely that 100 people not voting would change the outcome. And less unlikely that 10,000 people not voting would. And less unlikely that 100,000 people not voting would, etc.

So the greater the number of people who believe their vote doesn’t matter and behave rationally by not voting, the more likely it becomes that the outcome of the election could be changed by refusal to participate.