So let’s go back to the original question posed by Anthony Downs. Suppose you were deciding whether to vote in the 2008 election. When, given all this, does it make rational sense to vote?
First, you have to put a value on the difference between a McCain presidency and an Obama presidency. One way to arrive at this value is to ask yourself, How much would I be willing to pay to be the only person who gets to choose whether McCain or Obama is president? You can go to the bank and withdraw any amount you like. How much would you hand over to be the kingmaker, the one person who chooses who runs the country for the next four years? One dollar? Ten dollars? One million dollars? When undergraduates answer this question, they usually give amounts of less than $10, which is astonishing since this is probably the greatest value anyone could get for a $10 purchase. However, for the sake of argument, let’s say you think it is a very important decision and you are willing to spend $1,000 of your own money to be the only person who chooses the next president of the United States.
Second, you have to account for the fact that, by voting, you get the opportunity to determine the election’s outcome only when there is an exact tie. Otherwise, the outcome will not change whether you vote or not. So the value of voting is not $1,000; instead, it is a 1 in 10 million chance to obtain the $1,000 value.
Third, and finally, you have to compare your anticipated benefit to the costs of voting. Most people say that the costs of gathering information and going to the polls are not that great, so for convenience let’s assume they are $1. They could be much higher, of course, but they are almost certainly greater than zero.
Hence, now that we have your costs and benefits all worked out, the rational analysis of voting suggests that the decision to vote equates roughly with the decision to pay $1 for a lottery ticket that gives you a 1 in 10 million chance of winning a $1,000 prize. Las Vegas would love to sell these tickets. If they could sell 10 million tickets, they would make $10 million dollars and owe just $1,000 in prize money. But even the most ardent gambler would probably refuse to buy them, knowing that the odds are extremely unfair. The average person would probably need other inducements to buy a ticket, because slot machines, blackjack tables, and roulette wheels all have vastly better odds. Even state lotteries that use funds from ticket sales to provide public services rather than prize money typically offer people millions of dollars in winnings, not thousands, for odds like these. And so we are left with the same puzzle we began with. Why do millions of people vote in spite of these odds and payoffs? What is it about elections that make them different from lotteries?
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