There are two preconditions that make your vote influential. Since the U.S. system is based on the electoral college, you need to be in a competitive state in order for your vote to really be decisive. Next, to cast the winning vote, the election in your state would have to end up tied.
Those two qualifications disbar a lot of states. In Oklahoma and Wyoming, for example, states that are both small and very unlikely to end up tied because they are so Republican, the chance of your vote deciding the election is 1 in 30 billion, Gelman calculates. In Maryland, Vermont and Idaho, other small and polarized states, the chance is 1 in 10 billion.
But in the country's swing states, the odds are much better. In New Hampshire and Colorado, the probability that your vote will be the decisive one in this election is roughly 1 in 1 million. In Nevada, Wisconsin and Pennsylvania, it’s 1 in 2 million. In Michigan, New Mexico, North Carolina and Florida it’s 1 in 3 million, while in Maine it’s 1 in 5 million.
Those might sound like distant odds. However, they’re far, far better than the odds of winning the lottery, which millions of Americans play all the time. (The odds of winning Powerball jackpot, for example, are 1 in 292 million.)
And there’s another important factor to consider: the potential payout on your vote. Think of it this way — if your vote turns out to be the decisive one, it could alter the course of many people’s lives. Since the federal government spends an astonishing amount of money each year, your vote is worth a large chunk of that.
“If your vote is decisive, it will make a difference for over 300 million people. If you think your preferred candidate could bring the equivalent of a $100 improvement in the quality of life to the average American — not an implausible number, given the size of the federal budget and the impact of decisions in foreign policy, health, the courts, and other areas — you’re now buying a $30 billion lottery ticket. With this payoff, a 1 in 10 million chance of being decisive isn’t bad odds.”
In fact, the federal government spent $3.7 trillion in fiscal 2015, so you could see the lottery ticket as even bigger than that. And the actions of the U.S. government don’t just affect Americans — their influence reverberates around the world. But setting those factors aside, even if you stick with Gelman’s $30 billion estimate, the amount of influence that swing-state voters wield might surprise you.
A 1 in 10 million chance at a $30 billion reward has an expected value of $3,000 — the long-run average of your payout if you made this gamble many times. In the swingiest of swing states, New Hampshire and Colorado, where your odds of casting the election’s deciding vote are 1 in 1 million, the expected payout rises to $30,000.
Thirty-thousand-dollars isn't bad for an hour’s work. In fact, you could see the hour you take to vote as the most influential hour you spend every four years. And it’s certainly far better than purchasing a $2 Powerball ticket, where the expected value is often negative money.
Of course, that value doesn't accrue to you — it goes to the United States overall. And then there's the issue of whether you're really right, if your candidate will indeed create more value than the other one. One valid reason not to vote would be if you really believe that the two presidential candidates will have a similar impact on the country. But since Hillary Clinton and Donald Trump have made dramatically different policy proposals, it's hard to believe that most Americans would not have a preference.
Even if you live in a state that is unlikely to decide the election, it’s still important to vote, Gelman says. For one thing, your vote still counts toward the popular vote total, which could give an incoming government more political legitimacy or help influence policy priorities in the years to come. But in swing states, you are giving up a lot of power if you don't make it to the polls.