Just in time for Election Day, Zach Barnett has a forthcoming proof that it's rational to vote in most elections.
Some people think it's not rational to vote because the chance of changing the outcome is so small. Of course, the stakes are very high (assuming you care about others). How do these factors trade off against each other?
Zach shows that your likelihood of deciding the outcome is usually more than one divided by the total number of voters. If there are a million voters aside from yourself, there are a million and one possible vote totals (1 million-to-zero.... 999,999-to-1... 999,998-to-2...). In a competitive election, the totals around the middle are much more likely than the ones at the edges. So an exact 500K to 500K tie, where your vote decides the election, is one of the more likely possibilities.
This means that in expectation, voting directs more than your share of tax dollars and government resources. If you could, you'd probably go to the trouble of voting to simply determine who directs your own share of all this (about $10,000 in annual revenue and $400,000 in assets, to divide the government's revenue and assets by the population). Your small chance to direct the $3.5 trillion federal budget and $124 trillion in assets is worth even more.
Humans being humans, I don't expect that Zach's argument is the key to converting many nonvoters into voters. But it's a nice formal explanation of why voting matters.
