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Generalized Invariant Preferences: Two-parameter Representations of Preferences


  • Robert G. Chambers

    () (Dept of Agricultural and Resource Economics, University of Maryland, College Park)

  • John Quiggin

    () (Department of Economics, University of Queensland)


In this paper, we generalize the model of Quiggin and Chambers (2004) to allow for ambiguity, and derive conditions, referred to as generalized invariance, under which a two argument representation of preferences may be obtained independent of the existence of a unique probability measure. The first of these two arguments inherits the properties of standard means, namely, that they are upper semi-continuous, translatable and positively linearly homogeneous. But instead of being additive, these generalized means are superadditive. Superadditivity allows for means that are computed (conservatively) with respect to a set of prior probability measures rather than a singleton probability measure. The second argument of the preference structure is a further generalization of the risk index derived in Quiggin and Chambers (2004). It is sublinear in deviations from the generalized mean discussed above.

Suggested Citation

  • Robert G. Chambers & John Quiggin, 2008. "Generalized Invariant Preferences: Two-parameter Representations of Preferences," Risk & Uncertainty Working Papers WPR08_1, Risk and Sustainable Management Group, University of Queensland.
  • Handle: RePEc:rsm:riskun:r08_1

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    References listed on IDEAS

    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Epstein, Larry G, 1985. "Decreasing Risk Aversion and Mean-Variance Analysis," Econometrica, Econometric Society, vol. 53(4), pages 945-961, July.
    3. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005. "Certainty Independence and the Separation of Utility and Beliefs," Journal of Economic Theory, Elsevier, vol. 120(1), pages 129-136, January.
    4. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    7. Quiggin, John & Chambers, R.G.Robert G., 2004. "Invariant risk attitudes," Journal of Economic Theory, Elsevier, vol. 117(1), pages 96-118, July.
    8. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty


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