consider a decision maker who, when confronted with a choice between a lottery that would give her 4 for sure and a lottery that would give her 10 with probability, 4 with probability, and 0 with probability, would strictly prefer the first lottery and, when confronted with a choice between a lottery that would give her 4 with probability and 0 with probability and a lottery that would give her 10 with probability second lottery. and 0 with probability, would strictly prefer the Show that these preferences violate the independence axiom.