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Utility in Case-Based Decision Theory

Author

Listed:
  • Itzhak Gilboa

    (Tel Aviv University [Tel Aviv])

  • David Schmeidler

    (Tel Aviv University [Tel Aviv], OSU - Ohio State University [Columbus])

  • Peter P. Wakker

    (UvA - University of Amsterdam [Amsterdam])

Abstract

This paper provides two axiomatic derivations of a case-baseddecision rule. Each axiomatization shows that, if preference orders over available acts in various contexts satisfy certain consistency requirements, then these orders can be numerically represented by maximization of a similarity-weighted utility function. In each axiomatization, both the similarity function and the utility function are simultaneously derived from preferences, and the axiomatic derivation also suggests a way to elicit these theoretical concepts from in-principle observable preferences. The two axiomatizations differ in the type of decisions that they assume as data.

Suggested Citation

  • Itzhak Gilboa & David Schmeidler & Peter P. Wakker, 2002. "Utility in Case-Based Decision Theory," Post-Print hal-00752278, HAL.
  • Handle: RePEc:hal:journl:hal-00752278
    DOI: 10.1006/jeth.2001.2858
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00752278
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    References listed on IDEAS

    as
    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
    3. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
    4. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    5. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Eichberger, Jurgen & Guerdjikova, Ani, 2007. "Multiple Priors as Similarity Weighted Frequencies," Working Papers 07-03, Cornell University, Center for Analytic Economics.
    2. Eichberger, Jürgen & Guerdjikova, Ani, 2010. "Case-based belief formation under ambiguity," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 161-177, November.
    3. Jordan Louviere & Kenneth Train & Moshe Ben-Akiva & Chandra Bhat & David Brownstone & Trudy Cameron & Richard Carson & J. Deshazo & Denzil Fiebig & William Greene & David Hensher & Donald Waldman, 2005. "Recent Progress on Endogeneity in Choice Modeling," Marketing Letters, Springer, vol. 16(3), pages 255-265, December.
    4. David Schmeidler, 2000. "Cognitive Foundations of Inductive Inference and Probability: An Axiomatic Approach," Working Papers 00-07, Ohio State University, Department of Economics.
    5. Lensberg, Terje & Schenk-Hoppé, Klaus Reiner, 2021. "Cold play: Learning across bimatrix games," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 419-441.
    6. Hensher, David A. & Rose, John M., 2007. "Development of commuter and non-commuter mode choice models for the assessment of new public transport infrastructure projects: A case study," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(5), pages 428-443, June.
    7. Rose, John M. & Hensher, David A. & Caussade, Sebastian & Ortúzar, Juan de Dios & Jou, Rong-Chang, 2009. "Identifying differences in willingness to pay due to dimensionality in stated choice experiments: a cross country analysis," Journal of Transport Geography, Elsevier, vol. 17(1), pages 21-29.
    8. Huirong Zhang & Zhenyu Zhang & Lixin Zhou & Shuangsheng Wu, 2021. "Case-Based Reasoning for Hidden Property Analysis of Judgment Debtors," Mathematics, MDPI, vol. 9(13), pages 1-17, July.
    9. Stephane Hess & John Rose, 2009. "Should Reference Alternatives in Pivot Design SC Surveys be Treated Differently?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 42(3), pages 297-317, March.
    10. Rose, John M. & Bliemer, Michiel C.J. & Hensher, David A. & Collins, Andrew T., 2008. "Designing efficient stated choice experiments in the presence of reference alternatives," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 395-406, May.
    11. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Case-based expected utility : preferences over actions and data," Papers 08-32, Sonderforschungsbreich 504.
    12. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    13. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Multiple Priors as Similarity Weighted Frequencies," Papers 08-07, Sonderforschungsbreich 504.
    14. Pavlo Blavatskyy, 2013. "A Simple Behavioral Characterization of Subjective Expected Utility," Operations Research, INFORMS, vol. 61(4), pages 932-940, August.
    15. Antonio Borriello & John M. Rose, 2021. "Global versus localised attitudinal responses in discrete choice," Transportation, Springer, vol. 48(1), pages 131-165, February.
    16. Gonzalo Valdés-Edwards & Salvador Valdés-Prieto, 2013. "A Tractable Theory of Choice Based on Cell Behavior," CESifo Working Paper Series 4424, CESifo.
    17. Itzhak Gilboa & David Schmeidler, 2004. "Subjective Distributions," Theory and Decision, Springer, vol. 56(4), pages 345-357, January.
    18. Denis Bouyssou & Thierry Marchant, 2011. "Subjective expected utility without preferences," Working Papers hal-00606939, HAL.
    19. Golosnoy, Vasyl & Okhrin, Yarema, 2008. "General uncertainty in portfolio selection: A case-based decision approach," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 718-734, September.
    20. Han Bleichrodt & Martin Filko & Amit Kothiyal & Peter P. Wakker, 2017. "Making Case-Based Decision Theory Directly Observable," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 123-151, February.
    21. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    22. 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.
    23. Dan Marsh & Lena Mkwara & Riccardo Scarpa, 2011. "Do Respondents’ Perceptions of the Status Quo Matter in Non-Market Valuation with Choice Experiments? An Application to New Zealand Freshwater Streams," Sustainability, MDPI, vol. 3(9), pages 1-23, September.
    24. Szwagrzak, Karol, 2021. "Weighing Sample Evidence," Working Papers 3-2021, Copenhagen Business School, Department of Economics.
    25. G Özerol & E Karasakal, 2008. "Interactive outranking approaches for multicriteria decision-making problems with imprecise information," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1253-1268, September.

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