Let the final outcomes be C = (c1, c2, c3) and suppose that a decision-maker has preferences over lotteries over C that are represented by a utility function U. Consider simple

lotteries 1 = (0,1,0), 2 = (0,0,1), 3 = (21, 12,0) and 4 = (61, 23, 16). Suppose also that

U(1) = 2, U(2) = 2, U(3) = 3 and U(4) = 7/3. Can the utility function U have the expected utility property? If so, provide a candidate utility function u over consequences.