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Axioms for Measuring without mixing apples and Oranges

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  • O'Callaghan, Patrick

Abstract

A mixture set is path-connected via a suitable collection of paths, the most common example being a convex set. Yet in many economic settings, there are pairs of prospects that are not connected by a path of mixtures. Consider the thought experiment of von Neumann and Morgenstern involving a glass of milk, a glass of tea and a cup of coffee: we are often asked to choose between convex combinations of milk and tea, yet the same cannot be said of tea and coffee. We introduce partial mixture sets (which need not be path-connected) and provide a formal extension of the well-known axiomatisation of cardinal, linear utility by Herstein and Milnor. We show that partial mixture sets encompass a variety of settings in the literature and present a novel application to cardinal, nonlinear utility on a stochastic process.

Suggested Citation

  • O'Callaghan, Patrick, 2017. "Axioms for Measuring without mixing apples and Oranges," MPRA Paper 81196, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:81196
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    File URL: https://mpra.ub.uni-muenchen.de/81196/1/MPRA_paper_81196.pdf
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    References listed on IDEAS

    as
    1. Karni, Edi & Safra, Zvi, 2000. "An extension of a theorem of von Neumann and Morgenstern with an application to social choice theory," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 315-327, November.
    2. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    3. Simon Grant & Atsushi Kajii & Ben Polak & Zvi Safra, 2010. "Generalized Utilitarianism and Harsanyi's Impartial Observer Theorem," Econometrica, Econometric Society, vol. 78(6), pages 1939-1971, November.
    4. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    5. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, April.
    6. Chew, S H & Epstein, Larry G & Segal, U, 1991. "Mixture Symmetry and Quadratic Utility," Econometrica, Econometric Society, vol. 59(1), pages 139-163, January.
    7. Chew, Soo Hong & Epstein, Larry G & Segal, Uzi, 1994. "The Projective Independence Axiom," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 189-215, March.
    8. Ball, Clifford A. & Torous, Walter N., 1983. "Bond Price Dynamics and Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(04), pages 517-531, December.
    9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    10. Edi Karni, 2009. "A theory of medical decision making under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 1-16, August.
    11. Back, Kerry, 1992. "Insider Trading in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
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    More about this item

    Keywords

    Utility; Preferences; mixtures;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D0 - Microeconomics - - General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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