I was struck by the vagaries of the lottery while watching a report on ABC News. A wiley reporter asked several people if they would sell their Powerball ticket for $4 doubling the $2 they paid for it. Each person refused the offer and seemed quite incredulous that the reporter would even ask. I could not help thinking that it sounded like what Daniel Kahneman and Amos Tversky called loss aversion1. More about that in a moment.
The behavior does seem capricious. The odds were 1 out of 292 million to win $415 million2, but each person refused to sell claiming they might lose the millions. Apparently it never occurred to them to sell the ticket and buy two more effectively doubling their chances of winning. Nor did it make sense to them to sell the ticket and buy two additional tickets one with the same number they sold. That may require having to split the winnings, but would that be onerous if they won especially considering the almost unimaginable odds against winning?
The magnitude of the chance to win is difficult to put into perspective, but it helps me to think in terms of toothpicks. There are 250 toothpicks in a typical toothpick box and 73,000 give the requisite 292 million toothpicks needed to simulate the lottery odds. Imagine only one toothpick in the 73,000 boxes is colored red. If you could stack each box on top of one another, they would reach about 6,083 feet into the air – more than 800 feet higher than a mile. Picture all those boxes being emptied, you being blindfolded and asked to scramble through the pile, and coming out with just one. The odds of you picking the red toothpick are equivalent to you buying the winning lottery ticket.
But let’s get back to the original theme – loss aversion. Daniel Kahneman is a psychologist, and normally psychologists are not in line to win Nobel Prizes in economics. But he did in 2002 for his development of Prospect Theory, encompassing loss aversion, which attempts to explain the psychological impact of gains and loses. He summarized his work in his best selling book Thinking, Fast and Slow3. Prospect theory recognizes that humans are not completely rational. They are risk averse and weigh losses much more heavily than gains (that is, loss aversion).
Let’s take for example a wager on the toss of a coin. Tails you lose $100, heads you win $150. Common sense tells us that winning more than we lose is a good bet. After all, Vegas casinos make their livings on much less odds in their favor. But most people will not take the bet. They have a loss aversion. Most require to win at least $200 before they accept the odds.
No need to get into much more detail on loss aversion, but I highly recommend Kahneman’s book if you crave more detail. We can probably explain the unwillingness of some to sell their lottery tickets for double its’ worth because of loss aversion. There must be a heuristic that imparts a need to keep that potential winning ticket even in the face of mind-boggling odds. Perhaps loss aversion is hard-wired into our brains (that is, genetic). Many of the genetic characteristics that make us human evolved within small hunter-gatherer tribes thousands of years ago4.
If our hunter ancestors were cutting up the carcass of an animal too large to carry, and a lion saw them and charged, it does not take too much imagination to believe they would take what they could and run rather then fight for the remainder. They certainly would not be brain storming over what the rational decision would be. You don’t get your genes passed on by taking time to formulate a rational path of action under do or die circumstances.
- Kahnerman, D. and Tversky, A. (1992) Advances in prospect theory: Cumulative representation of uncertainty: J. Risk and Uncertainty , 5, 297-323. ↩
- The lump sum payout at $415 million is about $202 million after taxes which means paying for a $2 ticket is statistically a bad bet not that any of us would turn the money down. And this does not consider the possibility of sharing the winnings with other winners. ↩
- Kahneman, D. (2011) Thinking, Fast and Slow: Farrar, Straus and Giroux. ↩
- Pinker, S. (2002) The Blank Slate: New York: Penguin. ↩