Robert Wiblin in 80,000 Hours:
Could one vote — your vote — swing an entire election? Most of us abandoned this seeming fantasy not too long after we learned how elections work.
But the chances are higher than you might think. If you’re in a competitive district in a competitive election, the odds that your vote will flip a national election often fall between 1 in 1 million and 1 in 10 million.
That’s a very small probability, but it’s big compared to your chances of winning the lottery, and it’s big relative to the enormous impact governments can have on the world.
Each four years the US federal government allocates $17,500,000,000,000, so a 1 in 10 million chance of changing the outcome of a US national election gives you some degree of influence over $1.75 million, on average.