Ok, when I'm told all the information up front the complication of changing priors is removed.
But if we assume any symmetrical prior distribution the choices are still equivalent - I agree that (assuming statistical significance of the result) the experiment demonstrates a psychological tendency in humans, but their choices are not inconsistent with the assumption of a subjective prior, or with the principle of maximising expected utility. I expect it would be possible to set up an experiment along these lines to show that humans do in fact make choices inconsistent with the principle (e.g. removing one of the red balls may not change the result in situation A, or adding a red ball may not change the result in situation B), but like Allais' paradox that would only amount to a demonstration that humans exhibit risk averse behaviour. Konrad On Mon, 4 Aug 2003, Joseph Halpern wrote: > The arguably more interesting version of Ellsberg's paradox has > balls of three different colors in the urn: 30 reds, and 60 that are > some combination of blue and yellow. A ball is drawn. > > In situation A, you get to choose between betting on red and betting on > yellow (you get $1 if you guess right and 0 otherwise). In situation B, > you get to choose between between on red+blue or betting on yellow+blue. > (If you bet on red+blue, you get a dollar if the ball drawn is either > red or blue). > > Most people choose to bet on red in the first case and blue+yellow in > the second. That's inconsistent with having a subjective probability on > the balls (no matter what your attitude is to risk). > > Note that, unlike your discussion below, there's only one decision. > There is no second decision. > > -- Joe
