Prospect Theory and Loss Aversion
Another stimulating lunch today. Loss aversion means not just that the person prefers no gamble to a 50-50 win-lose gamble, but that they strictly prefer no gamble even for vanishingly small risks. Here are three graphs that represent different ways of modelling loss aversion. In each, I suppose the person’s underlying utility function is risk neutral, to represent this idea that people shouldn’t care about trivial risks.
One graph is for prospect theory, which says that people treat the probability of a loss as being greater than its objective value and the probability of a gain as being less than its objective value. Prospect theory does not ask why this is true; it just accepts it as a given.
Another graph is for a regret cost model. In this story, people suffer a fixed cost utility loss from losing a gamble, in addition to the money they lose, but no fixed-benefit gain from winning.
The third aph, the top one, is for an adjustment cost model. In this story, people need to incur some thinking costs to adjust their behavior when they either win or lose. This means that (a) there is a fixed cost of losing, similar to regret, and (b) there is no gain from winning until the amount won exceeds the adjustment cost (I assume the person can just not collect the winnings if he doesn’t want to bother with them.)
Experiments could distinguish between these three model. Prospect theory, for example, says that if someone prefers (a) to (b) in
(a) no gamble
(b) 50% probability of winning $10, 50% probability of losing $9,
then he will also prefer (a) to (b) in
(a) Losing $100 for sure
(b) 50% probability of losing $90, 50% probability of losing $109