Unformatted text preview: one of the proposed alternatives to expected utility theory. Consider a world with the prizes z , z 1 ,…, z K . A decision maker attaches a number v ( z k ) to each z k such that v ( z ) = < v ( z 1 ) < v ( z 2 ) < . . . < v ( z K ) and eval-uates each lottery L by the number U ( L ) = 6 K k = 1 f ( G L ( z k )) [ v ( z k ) − v ( z k − 1 ) ] , where f : [ 0, 1 ] → [ 0, 1 ] is a continuous increasing function and G L ( z k ) = 6 j ≥ k L ( z j ) . ( L ( z ) is the probability that the lottery L yields z and G L is the “anti-distribution” of L .) a. Verify that for f ( x ) = x , U ( L ) is the standard expected v-utility of L . b. Show that the induced preference relation satis±es the continuity ax-iom but may not satisfy the independence axiom. c. What are the dif±culties with a functional form of the type 6 z f ( p ( z )) u ( z ) ?...
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- Fall '10