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DITTO comments on Prospect Theory: A Framework for Understanding Cognitive Biases - Less Wrong

66 Post author: Yvain 10 July 2011 05:20AM

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Comment author: DITTO 10 July 2011 02:01:44PM 4 points [-]

I'm learning about utitlity theory just now, but I hadn't heard about prospect theory before. Thanks for posting it.

I know the main point of the post was to introduce prospect theory, but I wanted to add a comment about standard utility theory. In the text you write that standard utility theory predicts Prospero should be indifferent between a certain $5,000 and a 50-50 chance of either $0 or $10,000. This isn't quite right, maximising expected utitlity isn't the same as maximising expected wealth.

In standard utility theory you have a utility function U(W), so Prospero has the choice between U(5,000) and a 50-50 chance of U(0) or U(10,000). The expected utility need not be the same for both cases. In fact, most investors are assumed to have a utility function such that each addttional dollar adds less utility than the previous one (diminishing marginal utility of wealth). E.g $10 adds less utility to a millionaire than it would to the same person if he were broke and homeless. An investor with diminishing marginal utility of wealth would always take the insurance since, taking the certain $5,000 as the base case, the 50% chance of losing that $5,000 would cost more utility than the 50% chance of the gain of an extra $5,000 would add.

In this case, what is the difference between standard theory and prospect theory? Taking the first graph, you could regard this as a plot of a standard utility function with wealth on the x axis and utility on the y axis. The differences seem to be: - in the second plot, it is shown that a prospect theory agent seems to behave as if small probabilities are larger than they actually are, and as if large probabilities are smaller than the actually are; - the fact that Prospero's utility function is different depending on how the question is framed; - the shape of the utility function has the form shown in the first graph, wheras in standard utility theory it can take a wider variety of possible shapes.

Comment author: jimmy 11 July 2011 06:36:59PM 2 points [-]

One difference is that in standard utility theory, while utility doesn't have to be linear in money, if you 'zoom in' enough it is very close.

In prospect theory the shape doesn't change. It generally makes sense to be risk averse when you're risking amounts near your total wealth, but prospect theory says that you'll be risk averse at the $1 level too.