October 21, 2005 12:18masterSheet number 111 Page number 95Expected Utility95A Discussion of the Plausibility of the vNM TheoryMany experiments reveal systematic deviations from vNM assump-tions. The most famous one is theAllais paradox. One version of it(see Kahneman and Tversky 2000) is presented here as follows.Choose betweenL1=0.25[3, 000] ⊕0.75andL2=0.2[4, 000] ⊕0.8and now choose betweenL3=1[3, 000]andL4=0.8[4, 000] ⊕0.2.Note thatL1=0.25L3⊕0.75andL2=0.25L4⊕0.75. AxiomIrequires that the preference betweenL1andL2be respectively thesame as that betweenL3andL4. However, a majority of people ex-press the preferencesL1≺L2and an even larger majority express thepreferencesL3L4. Among about 140 graduate students at Prince-ton, Tel Aviv, and NYU (in 2002–4), although they were asked torespond to the above two choice problems on line one after theother, 67% choseL2while 80% choseL3. This means that at least47% of the students violated propertyI.In my opinion, the last example demonstrates (again) the sensi-tivity of preference to the framing of the alternatives.When the
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