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Unnamed 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: Unnamed 16 July 2011 07:40:21PM 3 points [-]

The other big difference is that the prospect theory value function is defined relative to a reference point (which typically represents the status quo) while the EU theory utility function is defined based on total wealth. So (as jimmy said) the nonlinearity of the prospect theory curve has a big effect on pretty much any decision (since any change from the current state is taking you through the curviest part of the curve), but the nonlinearity of EU theory curve is relatively minor unless the stakes are large relative to your total wealth. Under those conditions, EU theory (based on the utility of total wealth) is essentially equivalent to expected value.

Let's say that you have $30,000 in total wealth and you're given a choice of getting $10 for sure or getting $21 with p=.5. On the EU curve, the relationship between U($30,000), U($30,010), and U($30,021) should be nearly linear, so with any reasonable curve EU theory predicts that you prefer the 50% chance at $21 (indeed, you'd even prefer a 50% chance at $20.01 to $10 for sure as long as your curve is something like the square root function or even the natural log function). But on the prospect theory curve, V($0), V($10), and V($21) are very nonlinear, so even if we just treat probabilities as probabilities (rather than using the probability weighting function) prospect theory predicts that you'll prefer the certain $10 (at least, it will if the V(x) curve is the square root function, or x^.88 as is commonly used).

When people are actually given choices like $10 for sure vs. $21 w. p=.5, they tend to choose $10 for sure just as prospect theory predicts (and EU theory does not). That's paying rent in anticipated experiences. Prospect theory was developed by asking people a bunch of questions like that one, seeing what they did, and fitting curves to the data so that predictions about hundreds of similar decisions could be made based on a model with only a few parameters. That research produced a lot of data which was inconsistent with expected value (which, for these types of gambles, implies that it was also inconsistent with EU theory based on utility-of-wealth) and so Kahneman & Tversky developed a relatively simple model that did fit the empirical data, prospect theory.

Comment author: Academian 23 July 2011 09:22:46AM *  1 point [-]

The main descriptive difference between prospect theory and EU theory is that for monetary decisions, EU theory uses one curve (utility function), whereas prospect theory uses two curves (a value function and weight function) as well as a framing variable

The other big difference is that the prospect theory value function is defined relative to a reference point

That's what Yvain and I are calling framing.

When people are actually given choices like $10 for sure vs. $21 w. p=.5, they tend to choose $10 for sure just as prospect theory predicts (and EU theory does not).

What you're calling EU theory is a very restricted version of EU theory, where you require utility to be a function of total monetary wealth, or total material wealth. You might call it "Expected Utility of Wealth" theory. EU theory is actually much more general, and assigns utility to outcomes rather than amounts of money or even lists of possessions. This is all discussed in

http://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem , and

http://lesswrong.com/lw/244/vnm_expected_utility_theory_uses_abuses_and/

But for predictive purposes, EU theory is so ridiculously general (there are so many situational parameters) that, as far as anyone knows, it has almost no predictive power. So for the purposes of prediction, I think you're justified in talking about "EUW" theory, because without a highly restrictive assumption like utility being a function of wealth, EU theory has no chance of making predictions.

Nonetheless, I want to encourage you, and anyone else, to make explicit the assumption "utility is a function of wealth" when you're making it. My reason is that, in toy decision-theory problems, EU theory is usually part of the framework, and it's a reasonable framework provided we don't impose the restrictions that make it predictively meaningful and false.