The Real Value of a Powerball Ticket
Alex Tabarrok has a fun post calculating the monetary value of a Powerball ticket. He estimates that, as of the most recent drawing, each $2 ticket carries an expected monetary value of roughly $2.73. Superficially then, it’s worthwhile to buy one. However, Tabarrok also points out this is only true for a simple expected value calculation; after accounting for taxes and the possibility of a shared prize, a ticket’s monetary value is actually substantially lower (around $.75), making it a poor investment.
So why do people buy them? Are consumers hapless rubes throwing away their hard-earned money in exchange for nothing? Not necessarily.
The reason is simple: there’s much more to valuation and choice than expected monetary value. In fact, I suspect almost no one buys a ticket with any such calculation in mind. Rather than a cold estimate of the probability of future returns, the Powerball actually illustrates the subjective theory of value.
There are many ways for people find value in the Powerball beyond its expected monetary payoffs. Tabarrok observes, for example, that people find pleasure in anticipating the drawing. Such excitement is actually a major attraction of games of chance, where players have no control over the outcome.
In fact, I doubt most people playing the Powerball seriously believe they’ll win. Instead, people treat a ticket as the price of daydreaming about what they’d do with an enormous pile of cash. You can’t win without playing, so people pay a small amount as a way to justify spending their scarce time imagining their own Scrooge McDuck scenarios. For these people, the benefit of the ticket is greater than its cost.
These are just two reasons people might find value in lottery tickets, but there are countless others. Incidentally, value subjectivity doesn’t imply anything about whether the values people actually hold are morally acceptable or even economically sensible; just because our values are subjective, doesn’t mean they’re above criticism. But it does mean they’re about more than a simple expected monetary return.
My point is that although it may be convenient to reduce value to a simple, objective measure, doing so can never capture the complexity of what, how, and why people value the things they do.
By the way, I don’t have a problem with the idea of calculating expected value, as it’s a useful way of thinking about how to place present monetary value on a contingent event. I do, however, take issue with the idea that expected value calculus is the way for an economist to think about these problems. Focusing too much on objective calculations of worth drains the richness from economics and helps turn it into a mechanical exercise inapplicable to actual human behavior.
If anything, the economic way of thinking should stress the diversity and complexity of human values. Economists would be better off taking a humble approach, acknowledging that we can’t always fit human decisions into neat little boxes for economists to analyze, much less to build policy proposals on.
Public policy is actually one important reason these seemingly simple examples matter quite a bit. It’s a short few steps, for example, from defining value as the expected monetary return of a ticket, to claiming that buying a ticket is irrational, and finally, to insisting consumers not be given a choice to buy one at all. (As a side note, this isn’t an endorsement of public lotteries.) Although it might seem odd, this kind of argument is increasingly common among behavioral economists. Human errors and biases are open doors waiting for paternalism to rush through. Subjectivity is a way to slam them shut.