Theoretical Comparison of the Decision Theories of J. M. Keynes, Kahneman-Tversky, and Einhorn-Hogarth (original) (raw)

1991, Psychological Reports

It is demonstrated that J. M. Keynes in 1921 provided a complete decision rule that handles both the cases of nonlinear probability preferences and ambiguity or uncertainty. The 1979 Kahneman-Tversky approach deals only with risk (nonlinear probability preferences) and does not specify a decision rule. The 1985-1986 Einhorn-Hogarth anchoring and adjustment rule deals only with ambiguity or uncertainty and not risk. Only Keynes' rule does both. This paper is organized in the following way. After this brief historical introduction, we present Keynes' decision rule, Kahneman-Tversky's decision approach and Einhorn-Hogarth's decision rule. In another section, we demonstrate how Keynes' decision rule solves the Ellsberg Paradox and the Popper Paradox of Ideal Evidence quantitatively. One problem is presented for each paradox. A final section contains our conclusions. Keynes was concerned about the following questions: Whether. .. the 'mathematical expectation' of different courses of action accurately measures what our references ought to be-whether, that is to say, the undesirability of a given course of action increases in direct proportion to any increase in the uncertainty of its attaining its object, or whether some allowance ought to be made for 'risk,' its undesirability increasing more than in proportion to its uncertainty (Keynes, 1921, p. 313). Keynes then gives credit to D'Alembert for being the first scholar to recognize the fact that decision makers prefer high probability values to low probability values, given equal expected monetary values (emv). Thus, if emv, has a value of 90=p,.A,,wherep,=theprobabilityofsuccess=.9,q,=theprobabilityoffailure=.1,andA,=themonetaryoutcomeequals90 =p,. A,, where p, = the probability of success = .9, q, = the probability of failure = .1, and A, = the monetary outcome equals 90=p,.A,,wherep,=theprobabilityofsuccess=.9,q,=theprobabilityoffailure=.1,andA,=themonetaryoutcomeequals100, while ernv, also has a value of 90=p,.A,,wherep,=.I,q,=.9,andA,=90 = p ,. A,, where p, = .I, q , = .9, and A, = 90=p,.A,,wherep,=.I,q,=.9,andA,=900, a large majority of decision makers will choose emv, over ernv, if probability preferences are nonlinear. Only if probability preferences are linear will the decision maker be indifferent to emv, and ernv,. Brady and Lee (1989a, 1989b, 1989c) demonstrated that the type of problem discussed above, called by Kahneman and Tversky the "certainty effect" and by other researchers the AUais paradox or security level problem, is easily handled by Keynes' decision rule. Unfortunately, Keynes, in his discussion of applied decision making in 'Request reprints from Dr.