The typical case, in which there may be a practical connection between weight and probable error, may be illustrated by the two cases following of balls drawn from an urn. In each case we require the probability of drawing a white ball ; in the first case we know that the urn contains black and white in equal proportions; in the second case the proportion of each colour is unknown, and each ball is as likely to be black as white. It is evident that in either case the probability of drawing a white ball is 0.5, but that the weight of the argument in favour of this conclusion is greater in the first case.
Friday, January 23, 2009
Keynes and Ellsberg's Paradox
Ellsberg's Paradox is a famous conundrum in decision theory. At the Wikipedia website, they noted a reference to Keynes in the Ellsberg entry. As I have seen just about every idea attributed to Keynes, I figured this was a typical overstatement. But then I check the entry, and lo and behold, I think Keynes articulates the Ellsberg paradox pretty well. From Keynes Treatise on Probability: