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{"ops":[{"insert":"Let X = {x1, x2, x3} be the set of three alternatives and \u2206X = {(q1, q2, q2) | q1 + q2 + q3 = 1, q1, q2, q3 > 0} be the set of corresponding lotteries. Moreover, let u : X \u2192 R be a utility function on X and let U : \u2206X \u2192 R be a utility function on the set of lotteries of X. \n\nExercise 1. (5%) Let % be the preference relation represented by U. Verify or falsify the following statements: The preference relation % is (a) complete; (b) transitive; (c) acyclic. Exercise 2. (5%) Assume that U(1, 0, 0) = U(0, 0.5, 0.5) = 1 and U(0, 1, 0) = U(0.5, 0, 0.5) = 0. Is it possible that the preference relation represented by U satisfies the independence axiom?\n"}]}
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