Game Theory 101 Full Course - 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 versus Y, so whatever is determining his preference between the two lotteries must be his preference for those two outcomes. Independence is straightforward in this simple case, but individuals sometimes violate it when there are lotteries nested in these lotteries.