# Why rational to be indifferent between two urns, when urn A has 50-50 red and white balls, but you don't know urn B's ratio?

Please see the embolden sentence below. Assume that I'm risk adverse and "prefer the known chance over the unknown". Why's it irrational for me to choose A?

Also, there were problems on the probability side. One famous debate concerned a paradox posed by Daniel Ellsberg (of later fame due to publishing the Pentagon Papers) It involved multiple urns, some with known and some with unknown odds of drawing a winning ball. Instead of estimating the expected value of the unknown probability, and sticking with that estimate, most people exhibit strong aversion to ambiguity in violation of basic probability principles. A simpler version of the paradox would be as follows. You can choose one of two urns, each containing red and white balls. If you draw red you win $100 and nothing otherwise. You know that urn A has exactly a 50-50 ratio of red and white balls. In urn B, the ratio is unknown. From which urn do you wish to draw? Most people say A since they prefer the known chance over the unknown, especially since some suspect that urn B is perhaps stacked against them. But even if people can choose the color on which to bet, they still prefer A.

Rationally, you should be indifferent, or if you think you can guess the color ratios, choose the urn with the better perceived odds of winning. Yet, smart people would knowingly violate this logical advice.

Paul Slovic, *The Irrational Economist* (2010), p 56.

## 1 comment

Well, what probability do you assign to getting a red ball from urn B? If that differs from the probability of getting a white ball, why? If it doesn't, then the probabilities are the same in both cases. — Derek Elkins 17 days ago