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How to Assess Coherent Beliefs: A Comparison of Different Notions of Coherence in Dempster-Shafer Theory of Evidence

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Reflections on the Foundations of Probability and Statistics

Part of the book series: Theory and Decision Library A: ((TDLA,volume 54))

Abstract

Stemming from de Finetti’s work on finitely additive coherent probabilities, the paradigm of coherence has been applied to many uncertainty calculi in order to remove structural restrictions on the domain of the assessment. Three possible approaches to coherence are available: coherence as a consistency notion, coherence as fair betting scheme, and coherence in terms of penalty criterion. Due to its intimate connection with (finitely additive) probability theory, Dempster-Shafer theory allows notions of coherence in all the forms recalled above, presenting evident similarities with probability theory. In this chapter we present a systematic study of such coherence notions showing their equivalence.

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Acknowledgements

The authors are members of the INdAM-GNAMPA research group. The first author was supported by Università degli Studi di Perugia, Fondo Ricerca di Base 2019, project “Modelli per le decisioni economiche e finanziarie in condizioni di ambiguità ed imprecisione”.

Author information

Authors and Affiliations

  1. Department of Economics, University of Perugia, Perugia, Italy

    Davide Petturiti

  2. Department of MEMOTEF, La Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

Authors
  1. Davide Petturiti
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  2. Barbara Vantaggi
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Correspondence to Davide Petturiti .

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Editors and Affiliations

  1. Department of Statistics, Ludwig-Maximilians-University of Munich, Munich, Germany

    Thomas Augustin

  2. Universidade de São Paulo, São Paulo, Brazil

    Fabio Gagliardi Cozman

  3. Frankfurt School of Finance & Management, Frankfurt am Main, Germany

    Gregory Wheeler

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Petturiti, D., Vantaggi, B. (2022). How to Assess Coherent Beliefs: A Comparison of Different Notions of Coherence in Dempster-Shafer Theory of Evidence. In: Augustin, T., Cozman, F.G., Wheeler, G. (eds) Reflections on the Foundations of Probability and Statistics. Theory and Decision Library A:, vol 54. Springer, Cham. https://doi.org/10.1007/978-3-031-15436-2_8

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