Under certainty, any increasing monotone transformation of a utility function is also a utility function representing the same preferences. Under uncertainty, we must re- strict this statement to linear transformations if we are to keep the same preference representation. Give a mathematical as well as an economic interpretation for this. Check this with the following example. Assume an initial utility function attributes the following values to three possible outcomes: B u(B) = 100 M u(M) = 10 P u(P) = 50 Check that with this initial utility function, the lottery L = (B, M, 0.5) is strictly preferred to P, that is L = (B, M, 0.5) > P