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Cases and States

Author

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  • Ani Guerdjikova

    (GAEL - Laboratoire d'Economie Appliquée de Grenoble - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

  • Jürgen Eichberger

    (Universität Heidelberg [Heidelberg] = Heidelberg University)

Abstract

In this paper, we provide a novel framework for decision making under uncertainty based on information available in the form of a data set of cases. A case contains information about an action taken, an outcomes obtained, and other circumstances that were recorded with the action and the outcome. The set of actions, the set of outcomes and the set of possibly relevant recorded characteristics are derived from the cases in the data set. The information from the data set induces a belief function over outcomes for each action. From a decision maker's preferences over belief functions one can derive a representation evaluating outcomes according to the α-max min criterion. New data affects behavioral parameters, such as awareness, ambiguity and ambiguity attitude, and may suggest a classifications of data into states.

Suggested Citation

  • Ani Guerdjikova & Jürgen Eichberger, 2023. "Cases and States ," Working Papers hal-03962412, HAL.
    • Handle: RePEc:hal:wpaper:hal-03962412
    Note: View the original document on HAL open archive server: https://hal.science/hal-03962412v1
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    References listed on IDEAS

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    1. Grant Simon & Guerdjikova Ani & Quiggin John, 2021. "Ambiguity and Awareness: A Coherent Multiple Priors Model," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 571-612, June.
    2. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2012. "Probabilities as Similarity-Weighted Frequencies," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 7, pages 169-184, World Scientific Publishing Co. Pte. Ltd..
    3. Eichberger, Jürgen & Guerdjikova, Ani, 2010. "Case-based belief formation under ambiguity," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 161-177, November.
    4. Karni, Edi & VierÃÿ, Marie-Louise, 2010. ""Reverse Bayesianism": A Choice-Based Theory of Growing Awareness," Queen's Economics Department Working Papers 273757, Queen's University - Department of Economics.
    5. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    6. Gilboa, Itzhak & Minardi, Stefania & Samuelson, Larry, 2017. "Cases and Scenarios in Decisions Under Uncertainty," HEC Research Papers Series 1200, HEC Paris.
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    8. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, March.
    9. Itzhak Gilboa & Stefania Minardi & Larry Samuelson & David Schmeidler, 2020. "States and Contingencies: How to Understand Savage without Anyone Being Hanged," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 365-385.
    10. Edi Karni & Marie-Louise Vier?, 2013. ""Reverse Bayesianism": A Choice-Based Theory of Growing Awareness," American Economic Review, American Economic Association, vol. 103(7), pages 2790-2810, December.
    11. Eichberger, Jürgen & Pasichnichenko, Illia, 2021. "Decision-making with partial information," Journal of Economic Theory, Elsevier, vol. 198(C).
    12. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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