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The Invention of the Independence Condition for Preferences

Author

Listed:
  • Peter Fishburn

    (AT&T Bell Laboratories, Murray Hill, New Jersey 07974)

  • Peter Wakker

    (Medical Decision Making Unit, University of Leiden (AZL), Leiden, The Netherlands)

Abstract

This paper discusses the history and interrelations of three central ideas in preference theory: the independence condition in decision under risk, the sure-thing principle in decision under uncertainty, and conjoint independence for multiattribute decisions and consumer theory. Independence was recognized as an important component of decision under risk in the late 1940s by Jacob Marschak, John Nash, Herman Rubin, and Norman Dalkey, and first appeared in publication in Marschak (Marschak, J. 1950. Rational behavior, uncertain prospects, and measurable utility. Econometrica 18 111--141.) and Nash (Nash, J. F. 1950. The bargaining problem. Econometrica 18 155--162.). The sure-thing principle can be credited to Savage (Savage, L. J. 1953. Une Axiomatisation du Comportement Raisonnable Face à l'Incertitude. Colloq. Internal. Centre National Rech. Sci. 40 Econométrie 29--40; Savage, L. J. 1954. The Foundations of Statistics. Wiley, New York (2nd edn., Dover, New York, 1972.). Conjoint independence for consumer theory was introduced by Sono (Sono, M. 1943. The effect of price changes on the demand and supply of separable goods (in Japanese). Kokumin Keisai Zasshi 74 1--51.) and Leontief (Leontief, W. W. 1947a. A note on the interrelation of subsets of independent variables of a continuous function with continuous first derivatives. Bull. Amer. Math. Soc. 53 343--350; Leontief, W. W. 1947b. Introduction to a theory of the internal structure of functional relationships. Econometrica 51 361--373.); a form of it can also be recognized in Samuelson (Samuelson, P. A. 1947. Foundations of Economic Analysis. Harvard University Press, Cambridge, MA.), presented earlier in Samuelson (Samuelson, P. A. 1940. Foundations of analytical economics, the observational significance of economic theory. Ph.D. dissertation, Harvard University, Boston, MA.). Independence and the sure-thing principle are equivalent for decision under risk, but in a less elementary way than has sometimes been thought. The sure-thing principle for decision under uncertainty and conjoint independence are identical in a mathematical sense. The mathematics underlying our three preference conditions has an older history. The independence condition for decision under risk can be recognized in the characterization of "associative means," and conjoint independence for multiattribute decisions in solutions to the "generalized associativity functional equation."

Suggested Citation

  • Peter Fishburn & Peter Wakker, 1995. "The Invention of the Independence Condition for Preferences," Management Science, INFORMS, vol. 41(7), pages 1130-1144, July.
  • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:7:p:1130-1144
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    File URL: http://dx.doi.org/10.1287/mnsc.41.7.1130
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    References listed on IDEAS

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    1. JS Armstrong & Fred Collopy, 2004. "Causal Forces: Structuring Knowledge for Time-series Extrapolation," General Economics and Teaching 0412003, EconWPA.
    2. Fildes, Robert & Lusk, Edward J, 1984. "The choice of a forecasting model," Omega, Elsevier, vol. 12(5), pages 427-435.
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    5. Robert Carbone & Spyros Makridakis, 1986. "Forecasting When Pattern Changes Occur Beyond the Historical Data," Management Science, INFORMS, vol. 32(3), pages 257-271, March.
    6. Armstrong, J. Scott & Collopy, Fred, 1992. "Error measures for generalizing about forecasting methods: Empirical comparisons," International Journal of Forecasting, Elsevier, vol. 8(1), pages 69-80, June.
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    Citations

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    Cited by:

    1. Giancarlo Romano G, 2013. "Acerca de la condición normativa de la teoría de la decisión racional," REVISTA CUADERNOS DE ECONOMÍA, UN - RCE - CID, December.
    2. Dorian Jullien, 2016. "Under Uncertainty, Over Time and Regarding Other People: Rationality in 3D," GREDEG Working Papers 2016-20, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis.
    3. Luca Lambertini, 2013. "John von Neumann between Physics and Economics: A methodological note," Review of Economic Analysis, Rimini Centre for Economic Analysis, vol. 5(2), pages 177-189, December.
    4. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    5. Marc Le Menestrel & Luk Van Wassenhove, 2001. "The Domain and Interpretation of Utility Functions: An Exploration," Theory and Decision, Springer, pages 329-349.
    6. repec:hal:journl:halshs-00348818 is not listed on IDEAS
    7. Dorian Jullien, 2017. "Under Risk, Over Time, Regarding Other People: Language and Rationality Within Three Dimensions
      [Face au risque, dans le temps, par rapport aux autres : langage et rationalité dans trois dimensions
      ," Post-Print halshs-01651042, HAL.
    8. Dorian Jullien, 2013. "Asian Disease-type of Framing of Outcomes as an Historical Curiosity," GREDEG Working Papers 2013-47, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis.
    9. Li, Shu, 2003. "Violations of conjoint independence in binary choices: The equate-to-differentiate interpretation," European Journal of Operational Research, Elsevier, vol. 148(1), pages 65-79, July.
    10. Marc Le Menestrel & Bertrand Lemaire, 2002. "Additive utility with intransitive indifference and without independence: A homogeneous case," Economics Working Papers 628, Department of Economics and Business, Universitat Pompeu Fabra.
    11. L. Lambertini, 2000. "Quantum Mechanics and Mathematical Economics are Isomorphic. John von Neumann between Physics and Economics," Working Papers 370, Dipartimento Scienze Economiche, Universita' di Bologna.
    12. Han Bleichrodt & Chen Li & Ivan Moscati & Peter P. Wakker, 2016. "Nash was a first to axiomatize expected utility," Theory and Decision, Springer, pages 309-312.
    13. Marc Le Menestrel, 2001. "A Process Approach to the Utility for Gambling," Theory and Decision, Springer, pages 249-262.
    14. Robert F. Nau, 2003. "A Generalization of Pratt-Arrow Measure to Nonexpected-Utility Preferences and Inseparable Probability and Utility," Management Science, INFORMS, pages 1089-1104.
    15. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, pages 561-574.
    16. repec:hal:journl:halshs-00492170 is not listed on IDEAS
    17. Aurélien Baillon & Han Bleichrodt & Ning Liu & Peter P. Wakker, 2016. "Group decision rules and group rationality under risk," Journal of Risk and Uncertainty, Springer, vol. 52(2), pages 99-116, April.
    18. repec:hal:journl:halshs-00348814 is not listed on IDEAS

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