Similarly, we estimated a few years ago that the probability your vote is decisive in the presidential election is, at best, 1 in a million in a battleground state and much less in a noncompetitive state. The calculation is based on the chance that your state’s vote will be exactly tied, along with the chance that your state’s electoral votes are necessary for one party or the other to secure an electoral vote majority. Both of these conditions are necessary for your vote to be decisive.

So voting might at first not seem like such a good use of your time.

But here’s the good news. If your vote is decisive, it will make a difference for 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 hope, 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.