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Lexicographic Choice Functions Without Archimedeanicity

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Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

We investigate the connection between choice functions and lexicographic probabilities, by means of the convexity axiom considered by Seidenfeld et al. (Synthese 172:157–176, 2010 [7]) but without imposing any Archimedean condition. We show that lexicographic probabilities are related to a particular type of sets of desirable gambles, and investigate the properties of the coherent choice function this induces via maximality. Finally, we show that the convexity axiom is necessary but not sufficient for a coherent choice function to be the infimum of a class of lexicographic ones.

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Acknowledgments

The research reported in this paper has been supported by project TIN2014-59543-P.

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Authors and Affiliations

  1. Ghent University, Data Science Lab, Technologiepark-Zwijnaarde 914, 9052, Zwijnaarde, Belgium

    Arthur Van Camp & Gert de Cooman

  2. Department of Statistics and Operations Research, University of Oviedo, Oviedo, Spain

    Enrique Miranda

Authors
  1. Arthur Van Camp
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  2. Enrique Miranda
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  3. Gert de Cooman
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Corresponding author

Correspondence to Arthur Van Camp .

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Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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Van Camp, A., Miranda, E., de Cooman, G. (2017). Lexicographic Choice Functions Without Archimedeanicity. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_59

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_59

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42971-7

  • Online ISBN: 978-3-319-42972-4

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