Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

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

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

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (46)

You are viewing a single comment's thread.

Comment author: AlexMennen 12 July 2011 02:58:54AM 1 point [-]

One thing I'm a bit confused about: How would weighted probabilities work when there are more than two possible outcomes? "sum Probability(x) = 1" does not imply "sum Weighted Probability(x) = 1", and furthermore, you can get a different weighted probability distribution by grouping similar outcomes and applying the weighting stepwise, first to groups of similar outcomes, and then to specific outcomes within the groups.

Comment author: k3nt 12 July 2011 05:09:38AM 1 point [-]

I think there's probably an interesting point in there but I can't quite parse the text. Can you give an example?

Comment author: AlexMennen 12 July 2011 06:55:46PM *  0 points [-]

Suppose there is a 90% chance of maintaining what the prospect theory agent perceives as the status quo, which means a 10% probability of something different happening, which looks like it might correspond to a weighted probability of around 25% according to the graph. But now suppose that there are 10 equally likely (1%) possible outcomes other than status quo. Each of the 10 possibilities considered in isolation will have a weighted probability of 10% according to the graph, even though the weighted probability of anything other than the status quo happening is only 25%

Comment author: Unnamed 13 July 2011 03:14:05AM 2 points [-]

You're getting into advanced questions; prospect theory was initially formulated to only deal with gambles with 2 (or fewer) possible outcomes so that it didn't have to deal with this sort of stuff. Eventually Tversky & Kahneman (1992) came out with a more complicated version of the theory, Cumulative Prospect Theory, which addressed this problem by being rank-dependent. Looking at the graph of w(p), basically what you do is rank the outcomes in order of their value, line them up along the probability axis in order giving each one a width equal to its probability, and weight each one by the change in w(p) over its width. So if the 10 outcomes each with probability .01 are all losses, then the largest loss gets the weight w(.01), the next-largest loss gets the weight w(.02)-w(.01), the next gets the weight w(.03)-w(.02), ... and the last one gets w(.10)-w(.09). So the total weight given to the 10 outcomes is still only w(.10), just as it would be if they were all combined into one outcome.

For more of the nitty gritty (like separating gains & losses), you can see the Tversky & Kahneman (1992) paper, or I found the explanation in this Fennema & Wakker (1997) paper easier to understand.

Tversky, A. & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297–323.