Story by Yashowanto Ghosh, Staff Writer
Image courtesy of NBC
When the Powerball jackpot surged to ten digits, two kinds of articles proliferated in the media: first, explanations that it was still a losing proposition to buy a ticket; second, reports of long queues of people lining up to buy said tickets.
What you have heard is true: You would, on an average, lose money if you played. Why, then, do people play? And play they do, even when the jackpot is at a measly $40 million.
The reason is this: The same sum of money can be worth different amounts to different people.
You have probably seen an instance of this in the movie My Fair Lady: When Eliza Doolittle (Audrey Hepburn) offers to pay Professor Henry Higgins (Rex Harrison) a shilling an hour for phonetics lessons, Higgins says, “If you think of a shilling not as a simple shilling, but as a percentage of this girl’s income, it works out as fully equivalent to sixty or seventy pounds from a millionaire.” That argument does not, by itself, justify gambling—if you think of the jackpot as a percentage of your income, then you must also think of the price of a ticket as a percentage of your income, so all amounts would get multiplied by the same factor, and what was a losing proposition would remain a losing proposition. But it does show that the worth of money can be subjective. A valuation of how much something is worth to someone is called a utility function.
Real-valued utility functions of money have been studied (for example, by James O. Berger in his classic Statistical Decision Theory and Bayesian Analysis) and happen to be non-linear, which means (among other things) that the sum of the utilities of two dollars and five dollars need not equal the utility of seven dollars—as a result, what a Powerball ticket is worth to you can be different from its average cash value. The von-Neumann-Morgenstern utility theorem says a rational person will act to maximize their average utility, and this offers a first explanation of why people play: People are simply going by their subjective average utilities instead of the average cash value.
And there is more. The 30 years since Berger’s book have seen the introduction of non-Archimedean utility functions, where things can have not just real values, but also infinitely large or infinitely small values. For example, if you are a regular at Starbucks, then the price of a Powerball ticket may be negligible to you, just because it costs less than a tall latte from Starbucks; if you make $15,480 a year before taxes, then even a $40 million jackpot may be infinitely large to you. In either of those two cases, a Powerball ticket would be worth a positive amount to you.
And that’s the full explanation of why people play Powerball: It’s rational to play if $2 is negligible to you and/or $40 million is an astronomical sum of money to you.
About the Writer…
Yashowanto Ghosh is a senior with a major in communication and minors in journalism and writing. Jasho is also an alumnus of Aquinas (B.A. German ’11).