Criminals, by and large, must be risk-lovers–otherwise they’d be car-wash attendants instead of criminals. Lottery players, by and large, must be risk-lovers–otherwise they’d buy Treasury bonds instead of lottery tickets. You might be tempted to conclude that criminals and lottery players are often the same people. That’s probably the wrong conclusion. After all, risk-lovers enjoy having all their eggs in one basket, which suggests they should pursue either crime or the lottery, but not both.
Still, if you want to understand what attracts people to crime, it pays to understand what attracts people to risky activities more generally, so it pays to understand what attracts people to the lottery.
Lotteries are attractive when they offer big prizes or (relatively) good odds. If you’re running a lottery and you’re going to pay out $10 million, you can offer a single $10 million jackpot or you can offer 10 prizes of $1 million each. Which is more appealing to the players? Usually, the former. For the most part, lottery players prefer a small chance of a big payout to a bigger chance of a smaller payout. That’s because the people who prefer a bigger chance of a smaller payout are buying certificates of deposit, not lottery tickets. So if you want to make the lottery more attractive, it’s better to double the size of the jackpot than to double the number of winners.
(More precisely, doubling the number of winners makes the lottery more attractive to the sort of person who never buys lottery tickets anyway, while doubling the jackpot makes it more attractive to the sort of person who might actually be tempted to play.)
Now let’s apply the same reasoning to criminal deterrence. For the most part, criminals prefer a small chance of a big punishment to a big chance of a small punishment. That’s because the people who prefer a big chance of a small punishment go into punishing careers like construction work or coal mining instead of crime. So if you want to make crime less attractive to criminals, it’s better to double the odds of conviction than to double the severity of the punishment.
Add 10 percent to the length of the average jail sentence and crime will fall. Add 10 percent to the conviction rate instead and crime will fall even further. Like any risk-lovers, criminals are out to beat the odds, so they get particularly demoralized when the odds turn against them.
So much for the theory; now to the facts. What’s true of the lottery should be true at the racetrack. And gambling consultant Maury Wolff confirms that if you’re designing a complicated bet like a trifecta, the way to generate the most action per dollar’s worth of prize money (and hence the most profit for the track) is to offer very large prizes at very long odds. Why, then, do the tracks continue to offer bets with much smaller payoffs? According to Wolff, it’s because big prize winners take their money and go home while small prize winners plow their winnings back into the next race. That sets up an interesting trade-off for the track owner: One big prize maximizes profit on the current race, while several small prizes maximize the action on the next race. Interesting as that trade-off may be, it’s largely irrelevant to the main point, which is that players like big prizes and long odds. (On another interesting tangent, Wolff asked me whether there’s something inherently corrupt about a system where the proceeds from state lotteries are used to fund school systems that then have an incentive to produce the kind of students who will go out and play the lottery.)
With regard to crime, let’s consider the most spectacular of all crimes, murder. Here the expert is Professor Isaac Ehrlich, who, in the mid-’70s, pioneered the use of sophisticated statistical techniques to measure deterrent effects of conviction and punishment. Together with Professor Zhiqiang Liu, Ehrlich has recently revisited the subject, refuting his most vocal critics and offering new evidence in support of his original conclusion: Increase the number of convictions by 1 percent and (to a very rough approximation) the murder rate falls by about 1 percent. Increase the number of executions by 1 percent (which amounts to increasing the severity of the average punishment) and (again to a very rough approximation) the murder rate falls by about half a percent. (These numbers are based on evidence from the 1940s and 1950s. Capital punishment studies tend to focus on decades with more executions and hence more data.) As the theory predicts, convictions matter more than punishments.
T hat’s not to say that punishments don’t matter. Executions may be a less-effective deterrent than convictions, but they are nevertheless an extremely powerful deterrent; according to Ehrlich’s numbers, one additional execution in 1950 could well have prevented over 20 murders.
I am grateful to Ehrlich for that amazingly strong result, because I use it to illustrate three points that I’m always eager to drive home to my students. First, incentives matter, even to murderers. Second, economic theory predicts that some incentives matter more than others, and the data confirm the theory: Executions prevent murders, but convictions prevent even more murders. And finally, if you want to give policy advice, it’s not enough to know your numbers. You’ve also got to know your values. Isaac Ehrlich, the man who proved to the satisfaction of the economics profession that capital punishment works, is a passionate opponent of capital punishment.