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Uncertainty with Ordinal Likelihood Information

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Abstract

This paper proposes a new framework of choice under uncertainty, where the only information available to the decision maker is about the the ordinal likelihood of the di erent outcomes each action generates. This contrasts both with the classical models where the potential out- comes of each action have an associated probability distribution, and with the more recent complete uncertainty models, where the agent has no information whatever about the probability of the outcomes, even of an ordinal nature. We present an impossibility result in our framework, and some ways to circumvent it that result indiferent ranking rules.

Suggested Citation

  • Jorge Alcalde-Unzu & Ritxar Arlegi, 2007. "Uncertainty with Ordinal Likelihood Information," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0704, Departamento de Economía - Universidad Pública de Navarra.
    • Handle: RePEc:nav:ecupna:0704
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    References listed on IDEAS

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    1. Cohen, Michele & Jaffray, Jean-Yves, 1980. "Rational Behavior under Complete Ignorance," Econometrica, Econometric Society, vol. 48(5), pages 1281-1299, July.
    2. Barbera, S. & Barrett, C. R. & Pattanaik, Prasanta K., 1984. "On some axioms for ranking sets of alternatives," Journal of Economic Theory, Elsevier, vol. 33(2), pages 301-308, August.
    3. Ritxar Arlegi, 2003. "A note on Bossert, Pattanaik and Xu's “Choice under complete uncertainty: axiomatic characterization of some decision rules”," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 219-225, August.
    4. Bossert, Walter, 1989. "On the extension of preferences over a set to the power set: An axiomatic characterization of a quasi-ordering," Journal of Economic Theory, Elsevier, vol. 49(1), pages 84-92, October.
    5. Arlegi, Ricardo, 2007. "Sequentially consistent rules of choice under complete uncertainty," Journal of Economic Theory, Elsevier, vol. 135(1), pages 131-143, July.
    6. Prasanta K. Pattanaik & Yongsheng Xu & Walter Bossert, 2000. "Choice under complete uncertainty: axiomatic characterizations of some decision rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 295-312.
    7. Kelsey, David, 1993. "Choice under Partial Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(2), pages 297-308, May.
    8. Nitzan, Shmuel I. & Pattanaik, Prasanta K., 1984. "Median-based extensions of an ordering over a set to the power set: An axiomatic characterization," Journal of Economic Theory, Elsevier, vol. 34(2), pages 252-261, December.
    9. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
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    More about this item

    Keywords

    Uncertainty; Ordinal Likelihood; Nonprobabilistic models; Complete Uncertainty;
    All these keywords.

    JEL classification:

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

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