We might be headed for another close election, which means your vote could really matter this time, right? Wrong. Your vote didn’t matter in 2000, it never mattered before 2000, and it’s very unlikely to start mattering now.
Last time around, everything came down to Florida, where Bush’s official margin was 537 votes. (Yes, yes, I know, if they’d been counted differently there’d have been a different margin and perhaps a different outcome. But that’s not what this column is about.) If any one of Florida’s 6 million voters had stayed home, Bush’s margin would have been 536 or 538 votes, and he’d still have won. Even if you voted in the most hotly disputed state in the mostly hotly disputed election in American history, your vote did not change the outcome.
Your individual vote will never matter unless the election in your state is within one vote of a dead-even tie. (And even then, it will matter only if your state tips the balance in the electoral college.) What are the odds of that? Well, let’s suppose you live in Florida and that Florida’s 6 million voters are statistically evenly divided—meaning that each of them has (as far as you know) exactly a 50/50 chance of voting for either Bush or Kerry—the statistical equivalent of a coin toss. Then the probability you’ll break a tie is equal to the probability that exactly 3 million out of 6 million tosses will turn up heads. That’s about 1 in 3,100—roughly the same as the probability you’ll be murdered by your mother.
And that’s surely a gross overestimate of your influence, because it assumes there’s no bias at all in your neighbors’ preferences. Even a slight change in that assumption leads to a dramatic change in the conclusion. If Kerry (or Bush) has just a slight edge, so that each of your fellow voters has a 51 percent likelihood of voting for him, then your chance of casting the tiebreaker is about one in 10 to the 1,046th power—approximately the same chance you have of winning the Powerball jackpot 128 times in a row.
For those of us who live in New York State, the situation is far worse. Last time around, about 6.5 million votes were cast for major party candidates in New York state and 63 percent of them went to Al Gore. Assuming an electorate of similar size with a similar bias, my chance of casting the deciding vote in New York is about one in 10 to the 200,708th power. I have a better chance of winning the Powerball jackpot 7,400 times in a row than of affecting the election’s outcome. Which makes it pretty hard to see why I should vote.
The traditional reply begins with the phrase “But if everyone thought like that … .” To which the correct rejoinder is: So what? Everyone doesn’t think like that. They continue to vote by the millions and tens of millions.
Even for the most passionate partisan, it’s hard to argue that voting is a good use of your time. Instead of waiting in line to vote, you could wait in line to buy a lottery ticket, hoping to win $100 million and use it to advance your causes—and all with an almost indescribably greater chance of success than you’d have in the voting booth.
Click here for the formulas that were used in this column.