KAHNEMAN AND A. TVERSKY ProblEM 2: Choose between C: 2, 500 with probability .33, D: 2, 400 with probability .34 0 with probability .67 0 with probability 66. [83]* The data show that 82 per cent of the subjects chose B in Problem 1, and 83 per cent 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 patterns of choice indicates that a majority of respondents(61 per cent)made the modal choice in both problems. This pattern of preferences violates expected utility theory in the manner originally described by Allais. According to that leory, with u(0)=0, the first preference implies (2,400)>,33(2,500)+.66(2,400)or,34u(2,400)>,33(2,500) while the second preference implies the reverse inequality. Note that problem 2 is btained from Problem 1 by eliminating a 66 chance of winning 2400 from both prospects under consideration. Evidently, this change produces a greater reduc- 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 PROBLEM 3 A:(4,000,80), B:(3,000 N=95[20] [80J PROBLEM 4 C:(4,000,20),orD:(3,000,25) N=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 pattern of preferences in Problems 3 and 4 is not compatible with the theory, set u(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 the prospect C=(4,000,20)can be expressed as(A, 25), while the prospect D=(3, 000, 25) can be rewritten as(B,. 25). The substitution axiom of utility theory asserts that if B is preferred to A, then any (probability)mixture (B, p) must be preferred to the mixture(A, p). Our subjects did not obey this axiom. Apparently, reducing the probability of winning from 1.0 to, 25 has a greater effect than the reduction from