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Imprecise sampling and direct decision making

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  • Christophe Gonzales
  • Jean-Yves Jaffray

Abstract

In decision theory, uncertainty is generally modeled through probabilities or probabilityintervals. Data however, when collected by sampling, do not provide probabilities (resp.,lower/upper probabilities) but frequencies (resp., lower/upper frequencies). Discrepanciesbetween the former and the latter are taken into account by the model presented: axiomaticrequirements are shown to imply that the ordering of the decisions must only depend on aquadruple (GEU, u, U, N), where GEU is the generalized expected utility evaluation of thedecision that would result from the assimilation of frequencies to lower/upper probabilities;u and U are the utility levels of, respectively, the worst and the best reachable outcomes;and N is the size of the sample. Additional axioms are given that ensure the existence of anadditive utility representing the ordering. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • Christophe Gonzales & Jean-Yves Jaffray, 1998. "Imprecise sampling and direct decision making," Annals of Operations Research, Springer, vol. 80(0), pages 207-235, January.
    • Handle: RePEc:spr:annopr:v:80:y:1998:i:0:p:207-235:10.1023/a:1018963914548
    DOI: 10.1023/A:1018963914548
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    Cited by:

    1. Ayala Arad & Gabrielle Gayer, 2012. "Imprecise Data Sets as a Source of Ambiguity: A Model and Experimental Evidence," Management Science, INFORMS, vol. 58(1), pages 188-202, January.
    2. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Multiple Priors as Similarity Weighted Frequencies," Papers 08-07, Sonderforschungsbreich 504.
    3. Eichberger, Jürgen & Guerdjikova, Ani, 2013. "Ambiguity, data and preferences for information – A case-based approach," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1433-1462.
    4. Eichberger, Jürgen & Guerdjikova, Ani, 2010. "Case-based belief formation under ambiguity," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 161-177, November.
    5. Dong-Ling Xu, 2012. "An introduction and survey of the evidential reasoning approach for multiple criteria decision analysis," Annals of Operations Research, Springer, vol. 195(1), pages 163-187, May.
    6. Eichberger, Jurgen & Guerdjikova, Ani, 2007. "Multiple Priors as Similarity Weighted Frequencies," Working Papers 07-03, Cornell University, Center for Analytic Economics.

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