January 11, 2013
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Lotteries and regret minimization
JDN 2456304 EDT 18:20
It’s long been a mystery in economic decision theory: Why do people play the lottery? Aren’t they risk-averse? They seem risk-averse when they buy insurance, but then when they play the lottery they seem massively risk-seeking. So what’s going on?
Well, I asked my mother why she plays the lottery, and she explained it thus: “I’d feel terrible if my numbers came up and I hadn’t played.” This reminded me of a principle in decision theory that doesn’t get a lot of attention: Regret minimization.“Regret” in this formal sense is the difference between what you got and what you could have gotten with your best-case alternative. Playing the lottery has, say, a 99.999,999,999% chance of losing $1 and a 0.000,000,001% chance of winning $100,000,000. The expectation value for this high-risk option is negative: -$0.90. But the regret is minimized if you play, because that’s a regret of $1 instead of a regret of $100,000,000.
The beautiful part is, this also works for insurance! If you buy insurance, you pay perhaps $10,000 a year in order to avoid a 5% chance of losing $100,000. Once again the expectation value is negative, but this time it’s a low-risk option: -$5,000. Yes, but the regret is only $10,000, whereas if you didn’t buy insurance your regret might be $100,000.
Regret minimization has one very big advantage: It’s independent of probability. So, since human beings are bad at estimating probabilities, our brains respond by avoiding the problem entirely, using heuristics that aren’t dependent on probability at all.
You can still be Dutch-booked this way (indeed, a lottery is arguably exactly that), but it’s a lot easier on your computational resources than actually trying to compute a full Bayesian risk assessment.
Therefore, we aren’t properly considered risk-seeking or risk-averse, and prospect theory doesn’t work either (because it says we should be risk-averse for gains but risk-seeking for losses, and lotteries are risk-seeking gains and insurance is risk-averse loss!); instead, we are regret minimizers.
Comments (3)
Yup. Damn skippy. I used that fact to my advantage in pitching business cases to upper management at my old company, and they were typically focused on regret minimization, so I could always get them to take my proposal seriously by pointing out the gravity of the risks of not acting as well as the benefits of acting. The thought of potential losses were often more motivating for them than the potential gains.
We can see that tendency at work in politics as well. The political response to the mass murder at Sandy Hook is a great example of how we tend to seek to minimize regret rather than doing proper risk assessments.
You sir are a very good writer. (Okay, maybe I am easily entertained.) I find very few blogs I enjoy reading. You strike me as being intelligent. Would you mind if I troll your blogs and study them? I feel as though I may find inspiration to further enlarge my own limited knowledge base. Maybe with some reviewing of my prior educational endeavors I can provide some worthy feedback. Smile
Maybe the prospect theorists have just learned to live without regrets!