266 PROBLEM 2: Choose between The data show that 82 per cent of the subjects ent of the subjects chose C in Problem 2. Each of these preferences is significant at the 01 level, as denoted by the asterisk. Moreover, the analysis of individual hoice indicates that a majority of respondents(61 per cent)made the Dice in both problems. This pattern of preferences violates expected y in the manner originally described by Allais. According to that th u(0)=0, the first preference implies (2,400)>33(2,500)+66(2,400)or34(2,400)>33(2,500) while the second preference implies the reverse inequality. Note that Problem 2 is obtained from Problem 1 by eliminating a. 66 chance of winning 2400 from both prospects under consideration. Evidently, this chang tion in desirability when it alters the character of the prospect from a sure gain to a probable one, than when both the original and the reduced prospects are A simpler demonstration of the same phenomenon, involving only two- outcome gambles is given below. This example is also based on Allais [2] A:(4,00,80),orB:(3,000) [80] C:(4,000,20),orD:(3,00025), 95[65] [35 In this pair of problems as well as in all other problem-pairs in this section, over half the respondents violated expected utility theory. To show that the modal attern of preferences in Problems 3 and 4 is not compatible with the theory, set (0)=0, and recall that the choice of B implies u(3, 000)/u(4,000)>4/5 whereas the choice of C implies the reverse inequality. Note that C=(4,000,. 20)can be expressed as (A, 25), while the prospect D rewritten as(B,. 25). The substitution axiom of utility theory asserts that ferred to A, then any(probability)mixture(B, p)must be preferred to the (A, p). Our subjects did not obey this axiom. Apparently, reducing the bability of winning from 1.0 to 25 has a greater effect than the reduction from Reproduced with permission of the copyright owner. Further reproduction prohibited without pemission.Reproduced with permission of the copyright owner. Further reproduction prohibited without permission