If you purchased Powerball or Mega Millions lottery tickets like I did yesterday, you’re not stupid, despite the snotty comments of our betters that playing the lottery is a “tax on stupid people.” Sure, we don’t expect to win billions of dollars. Nor do we expect that a two dollar ticket for a ride at the amusement park is a smart investment. We are paying for the thrill, which as my Dad used to say, “ain’t nothing.”
I’m often exasperated by economists who look down on the behavior of people without Ph.D.s, as if they are analyzing animals at zoo for signs of irrationality. They build a toy model of utility-maximizing behavior, then observe real behavior that doesn’t fit the model, and declare humans to be irrational. Could it be that the simplistic models are the problem?
The analytical problem stems from the narrowly defined “utility” in the standard model as encompassing money and money only. What about hope? Can you put a price on hope?
Yes, in fact, you can. A Powerball ticket cost me two bucks. A medicine with a 10% chance to cure cancer may cost you $100,000, but it buys you more than a statistical probability. It buys you hope.
The numbers
The odds of winning the Powerball grand prize are 1 in 292,201,338. All you have to do is correctly select “five numbers between 1 and 69 for the white balls, then select one number between 1 and 26 for the red Powerball.” As of March 25, 2024, the next Powerball grand prize is worth around $865 million dollars, which is actually less than half that if the winner takes the cash payout. With this information, we can calculate the expected value of single Powerball ticket. It’s basically the prize value (416m) divided by the odds denominator (292m), which equals $1.40.
Anyone paying $2.00 for a piece of paper with an expected value of $1.40 is essentially throwing sixty cents in the trash. Who does that? According to the standard model, people who are bad at math do that. However, like most other trades where you pay cash for a service, you are not making a financial investment even though you don’t get anything tangible. In fact, most purchases of tickets have an expected return of zero! Movie tickets are not worth more than their price the day after you watch the film, are they? Tickets to an NFL game or a ballet performance can’t be turned in for a penny years afterwards. Heck, most tickets nowadays are electronic, so there’s not even a possibility of selling the old ticket as a collector’s item. So why buy them? It’s the same logic as buying a lottery ticket: you are paying for an emotional experience.
The Curse of the Lottery
There is a legend that lottery winners are cursed. Since the first American lotteries (conducted in the 1600s to raise funds for colonial infrastructure) there have been true stories of ill fortune befalling the winners. It’s undeniably more than just coincidence that many lottery winners die early from drug and alcohol overdoses, heart attacks, drownings, even murders. Some researchers found that bankruptcy is just as likely among lottery winners as everyone else, which just goes to show that bankruptcy isn’t about money.
Jonathan Cohen recounts the myth of the lottery curse growing in the public consciousness alongside the growth state-run jackpots that went from relatively small-dollar thousands of dollars in the 1950s to millions in the 1980s and billions today. The legend is real, and it’s also old. “From the 18th through the 20th century, newspapers in the United States recounted the misfortunes of lottery winners from across the globe: A baker and his pregnant wife murdered for his winnings by an employee (Paris, France, 1765). A squandered jackpot invested in a failed shipping venture (Newburyport, Massachusetts, 1883). A winner dying of a heart attack immediately upon hearing news of his windfall (Bilbao, Spain, 1934).”
What cemented the myth of the cursed lottery winner is - as you must suspect - bad research. An influential paper published in the August 1978 issue of the Journal of Personality and Social Psychology found that lottery winners were no happier than non-winners. The study also found no long-term change in happiness among victims of major traumatic accidents who became paralyzed. Lead author Philip Brickman cautioned that the finding needed more scrutiny, but it was a bombshell because it was interesting and also because it reinforced Brickman’s 1971 theory that human beings are stuck on a “hedonic treadmill,” meaning that individuals quickly return to their own personal level of happiness regardless of major positive or negative events or life changes. This isn’t just a rehash of the ancient trope that happiness is relative. It’s a discovery that internal personalities are more important than external events.
There’s a massive academic literature on happiness that is a slight quagmire for the point I’m trying to get to. Friends will often mention it when I talk about my “value of nothing” book, and I have to explain that happiness and utility aren’t exactly the same. Indeed, they’re very different. In a nutshell, happiness research, per se, is bounded both by the metrics used to study it and by the human mind. The metrics are usually surveys that ask people to self-evaluate their state of happiness on a ten point scale which by definition has an upper bound. Mind goes to eleven? No, and forgive the pun, the human mind probably has an upper bound on happiness. Utility, however, is unlimited. Think of the exponential growth curve that describes per capita GDP since the dawn of history. Happiness is to human height as Utility is to human flight.
It turns out Brickman was wrong. Not about happiness, but definitely about lotteries. Jonathan Cohen recounted the myth of the lottery curse in his 2022 article in SLATE only to puncture it. In our time, there are enough lotteries and lottery winners to provide systematic data for scrutiny. Guess what? “Research into winners in Germany, Singapore, and Britain found that winning the lottery does, in fact, make people happier,” says Cohen.
Whoa! Happier?
Yes. It turns out the Brickman’s 1978 paper had some major caveats. Its claims were based on 22 lottery winners who were interviewed at a single point in time. The control group was nothing more than neighbors randomly drawn from a phone book. There was no assessment of happiness before the lottery win or how happiness changed over time. Later studies confirmed Brickman’s hypothesis that individuals have a “set point” for their outlooks, some have a gloomier equilibrium and some have a perennially sunny attitude, though the later work also found that set points often shift to a higher or lower equilibrium.
A 2006 study by Jonathan Gardner and Andrew Oswald of the University of Warwick in England, found that winners of medium-sized lotteries (up to $200,000) exhibited measurably better psychological wellbeing than non-winners and small-scale winners. They asked a controlled sample of nearly 5000 Britons a battery of twelve questions two years before and two years after playing the lottery. The twelve questions rated happiness, confidence, stress, concentration, worry, and self-worth. Not only were the medium-size winners boosted to a higher set-point, the most intriguing finding was that the sense of wellbeing took a J-curve, meaning that stress increased in the first year after a financial windfall, but decreased when the new financial and psychological equilibriums were settled.1
An extraordinary 2020 study by Erik Lindqvist from the Stockholm School of Economics, Robert Ostling from Stockholm University and David Cesarini from New York University surveyed every winner of three of Sweden’s major lotteries over many years with the cooperation of the Swedish government. They were able to track details of the winners’ lives in contrast with thousands of similar Swedes who lost or won smaller amounts. The scholars discovered that happiness, per se, did not rise significantly with lottery wins, but another dimension of wellbeing did rise — the self-reported satisfaction with their lives. In sum, the Swedish study confirms common sense that money matters, and importantly, the effect does not diminish over time.2
Now let me encourage you to go buy lottery tickets. Just don’t play numbers 3-16-20-28-68-P17. Only a stupid person would play those numbers.
Money and Mental Wellbeing: A Longitudinal Study of Medium-Sized Lottery Wins, Jonathan Gardner Andrew J. Oswald, July 2006, IZA Discussion Paper No. 2233.
Long-Run Effects of Lottery Wealth on Psychological Well-Being, Erik Lindqvist, Robert Östling, David Cesarini, The Review of Economic Studies, Volume 87, Issue 6, November 2020, Pages 2703–2726.
This stuff just keeps getting better and better!!!