Game Theory 101 (#48): Independence over Lotteries

Independence over lotteries is an axiom of expected utility theory that says the following. Let p be a probability (a number between 0 and 1), and X, Y, and Z be outcomes or probability distributions over outcomes. An individual weakly prefers receiving X with probability p and Z with probability 1 - p to receiving Y with probability p and Z with probability 1 - p if and only if he prefers X to Y. The reason is straightforward: the only difference between the first lottery and the second lottery is X versu