OKAY, FINE, YOU CAN PLAY POWERBALL

OKAY, FINE, YOU CAN PLAY POWERBALL

Playing the lottery is almost always a poor choice in terms of expected dollars. Even when a ticket’s expected monetary value exceeds its cost, the value of a gamble to the buyer also depends on utility: how much the possible gains and losses matter to that person.

This leaves mathematically minded economists with one inconvenient fact to explain, the same one that baffled Adam Smith more than two hundred years ago: lotteries are very, very popular. The lottery is not the kind of situation Ellsberg studied, in which people face decisions against unknown and unknowable odds. The minuscule chance of winning the lottery is posted for all to see. The principle that people tend to make choices that more or less maximize their utility is a pillar of economics, and does an adequate job modeling behavior in everything from business practice to romantic choices. But not Powerball. This kind of irrational behavior is as unacceptable to a certain species of economist as the irrational magnitude of the hypotenuse was to the Pythagoreans. It doesn’t fit their model of what can be; and yet it is.

Economists are more flexible than Pythagoreans. Rather than angrily drowning the bearers of bad news, they adjust their models to fit reality. One popular account was offered by our old buddies Milton Friedman and Leonard Savage, who proposed that lottery players follow a squiggly utility curve, reflecting that people think about wealth in terms of classes, not numerical amounts. If you’re a middle-class worker who spends five bucks a week on the lottery, and you lose, that choice costs you a little money but doesn’t change your class position; despite the loss of money, the negative utility is pretty close to zero. But if you win, well, that moves you into a different stratum of society. You can think of this as the “deathbed” model—on your deathbed, will you care that you died with a little less money because you played the lottery? Probably not at all. Will you care that you retired at thirty-five and spent the rest of your life snorkeling off Cabo because you hit the Powerball? Yes. Yes you will.

In a bigger departure from classical theory, Daniel Kahneman and Amos Tversky suggested that people in general tend to follow a different path from the one the utility curve demands, not just when Daniel Ellsberg sticks an urn in front of them, but in the general course of life. Their “prospect theory,” for which Kahneman later won the Nobel Prize, is now seen as the founding document of behavioral economics, which aims to model with the greatest possible fidelity the way people do act, not the way that, according to an abstract notion of rationality, they should. In the Kahneman-Tversky theory, people tend to place more weight on low-probability events than a person obedient to the von Neumann-Morgenstern axioms would; so the allure of the jackpot exceeds what a strict expected utility calculation would license.

But the simplest explanation doesn’t require much theoretical heavy lifting at all. Simply: buying a lottery ticket, whether you win or not, is, in some small way, fun. Not Caribbean vacation fun, not all-night dance party fun, but one or two dollars’ worth of fun? Quite possibly so. There are reasons to doubt this explanation (for instance, lottery players themselves tend to cite the prospect of winning as their primary reason for playing), but it does an admirable job of explaining the behavior we see.

Economics isn’t like physics and utility isn’t like energy. It is not conserved, and an interaction between two beings can leave both with more utility than they started with. This is the sunny free-marketeer’s view of the lottery. It’s not a regressive tax, it’s a game, where people pay the state a small fee for a few minutes of entertainment the state can provide very cheaply, and the proceeds keep the libraries open and the streetlights on. Just as when two countries trade with each other, both parties to the transaction come out ahead.

So yes—play Powerball, if Powerball is fun for you. Math gives you permission!

There are problems with this view, to be sure. Here’s Pascal again, delivering a typically morose take on the excitement of gambling:

This man spends his life without weariness in playing every day for a small stake. Give him each morning the money he can win each day, on condition he does not play; you make him miserable. It will perhaps be said that he seeks the amusement of play and not the winnings. Make him then play for nothing; he will not become excited over it, and will feel bored. It is then not the amusement alone that he seeks; a languid and passionless amusement will weary him. He must get excited over it, and deceive himself by the fancy that he will be happy to win what he would not have as a gift on condition of not playing.

Pascal sees the pleasures of gambling as contemptible. And enjoyed to excess, they can of course be harmful. The reasoning that endorses lotteries also suggests that methamphetamine dealers and their clients enjoy a similar win-win relationship. Say what you want about meth, you can’t deny it is broadly and sincerely enjoyed.

But what about another comparison? Instead of strung-out tweakers, think about small-business owners, the pride of America. Opening a store or selling a service isn’t the same thing as buying a lottery ticket; you have some measure of control over your success. But the two enterprises have something in common: for most people, opening a business is a bad bet. It doesn’t matter how delicious you believe your barbecue sauce to be, how disruptively innovative you expect your app to be, how ruthless and borderline felonious you intend your business practices to be—you are much more likely to fail than to succeed. That’s the nature of entrepreneurship: you balance a very, very small probability of making a fortune against a modest probability of eking out a living against a substantially larger probability of losing your pile, and for a large proportion of potential entrepreneurs, when you crunch the numbers, the expected financial value, like that of a lottery ticket, is less than zero. Typical entrepreneurs (like typical lottery customers) overrate their chance of success. Even businesses that survive typically make their proprietors less money than they’d have drawn in salary from an existing company. And yet society benefits from a world in which people, against their wiser judgment, launch businesses. We want restaurants, we want barbers, we want smartphone games. Is entrepreneurship “a tax on the stupid”? You’d be called crazy if you said so. Part of that is because we esteem a business owner more highly than we do a gambler; it’s hard to separate our moral feelings about an activity from the judgments we make about its rationality. But part of it—the biggest part—is that the utility of running a business, like the utility of buying a lottery ticket, is not measured only in expected dollars. The very act of realizing a dream, or even trying to realize it, is part of its own reward.

That, at any rate, is what James Harvey and Yuran Lu decided. After the downfall of WinFall, they moved west and founded a Silicon Valley startup that sells an online chat system for businesses. (Harvey’s profile page coyly lists “non-traditional investment strategies” among his interests.) When I wrote this account, they were still looking for venture capital funding. Maybe they’ll get it. But if not, I’ll bet you’ll quickly find them starting again, expected value or no expected value, hoping the next ticket they try is a winner.