(Preferences over lotteries) There are three possible outcomes; in the outcome ai a decision-maker gains $ai, where a1 a2 a3. The decision- maker prefers a3 to a2 to a1 and she prefers the lottery (0.3, 0, 0.7) to (0.1, 0.4, 0.5) to (0.3, 0.2, 0.5) to (0.45, 0, 0.55). Is this information consistent with the decision maker's preferences being represented by the expected value of a payoff function?
If so, find a payoff function consistent with the information. If not, show why not. Answer the same questions when, alternatively, the decision-maker prefers the lottery (0.4, 0, 0.6) to (0, 0.5, 0.5) to (0.3, 0.2, 0.5) to (0.45, 0, 0.55).