Problem
Consider two experiments with an urn containing 5 balls: 2 balls are blue or green and 3 balls are red or white.
In experiment 1, assume that a person is offered two lotteries before drawing a ball from the urn: in lottery L1 she receives €100 if the ball is blue or green and €0 if it is red or white. In lottery L2 she receives €100 if the ball is white and €0 if it is blue, green, or red.
In experiment 2, assume that the same person is offered two other lotteries: in lottery L3 she receives €100 if the ball is blue, green, or red and €0 if it is white. In lottery L4 she receives €100 if the ball is red or white and €0 if it is blue or green.
1. If the person chooses lottery L1 in experiment 1, which lottery should she choose in experiment 2, if she makes decisions according to the Bernoulli principle? Please provide a formal explanation of your answer.
2. Suppose that in experiment 2 the person chooses the other lottery. Explain why this is plausible. Explain why this would violate the Bernoulli principle.