Stumbling and Mumbling: Risk aversion on Deal or No Deal

January 09, 2007

Risk aversion on Deal or No Deal

Given a choice between £44,000 for sure and a 50-50 chance of either £3,000 or £250,000, which would you choose?
On Deal or No Deal, Laura Pearce chose the gamble, and won £250,000.
A few observations:
1. Even people who are quite risk averse or loss averse might have made Laura's choice. The expected value of the gamble is £126,500, which is far above the certain £44,000.
Laura's gamble seems consistent with the average behaviour on Deal or No Deal described here. Perhaps the Banker made Laura a low offer, figuring that the possible loss to the programme of £250,000 would be recouped by good publicity.
2. However, Laura's choice is inconsistent with the simplest utility function which generates risk aversion - the log wealth function. She's less risk-averse than this suggests.
3. Laura doesn't seem regret-averse. Many would take the £44,000, for fear of kicking themselves for losing £41,000 if we'd gambled and got only £3,000.
4. Laura's choice seems - at the empirical level only - to rescue expected utility theory from the complaint made against it by Rabin and Thaler here (pdf) - that people who rejected modest gambles would also reject very favourable gambles.
5. Are there non-linearities in wealth that make the gamble attractive? I would have taken the gamble - despite being risk-averse in many ways - because a 50% chance of £250,000 is more valuable to me than a 100% chance of £44,000. £250,000 would allow me to move out of London in some comfort, thus raising my utility substantially. £44,000 would not quite do this. There isn't always diminishing marginal utility of wealth, so sometimes gambles can be attractive.