Question

Suppose that a decision-maker's preferences can be represented by the expected value of a utility function u. Find another utility function u' whose expected value represents the decision-maker's preferences and assigns a payoff of 1 to the best outcome and a payoff of 0 to the worst outcome.

Hint: Try to use this fact - Suppose there are at least 3 possible outcomes. The expected values of the Bernoulli payoff functions u and v represent the same preferences over lotteries (and certain outcomes) if and only if there exist numbers d and c, with c>0 such that v(x) = d + cu(x)