logic & reasoning
a red ball, an unknown urn
two pairs of bets that feel obvious, and cannot both be obeyed by any coherent belief.
Before he became famous for the Pentagon Papers, Daniel Ellsberg designed an experiment that quietly broke a pillar of economics. An urn holds 90 balls. Exactly 30 are red. The other 60 are some mixture of black and yellow; in what proportion, you are not told. A ball will be drawn at random. Place two bets.
first bet: would you rather win on red, or on black?
You win £100 if the drawn ball is the colour you bet on. Red: there are exactly 30. Black: there are somewhere between 0 and 60.
further reading
- risk, ambiguity, and the savage axioms original paper
- ellsberg paradox wikipedia