The 1 Urn Paradox
Suppose you have an urn containing 30 red balls and 60 other balls that are either black or yellow. You don't know how many black or how many yellow balls there are, but that the total number of black balls plus the total number of yellow equals 60. The balls are well mixed so that each individual ball is as likely to be drawn as any other. You are now given a choice between two gambles:
| Gamble A | Gamble B |
|---|---|
| You receive $100 if you draw a red ball | You receive $100 if you draw a black ball |
Also you are given the choice between these two gambles (about a different draw from the same urn):
| Gamble C | Gamble D |
|---|---|
| You receive $100 if you draw a red or yellow ball | You receive $100 if you draw a black or yellow ball |
This situation poses both Knightian uncertainty – whether the non-red balls are all yellow or all black, which is not quantified – and probability – whether the ball is red or non-red, which is ⅓ vs. ⅔.
Read more about this topic: Ellsberg Paradox
Famous quotes containing the word paradox:
“The conclusion suggested by these arguments might be called the paradox of theorizing. It asserts that if the terms and the general principles of a scientific theory serve their purpose, i. e., if they establish the definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretive statements establishing such a connection should then be replaceable by a law which directly links observational antecedents to observational consequents.”
—C.G. (Carl Gustav)