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Generalising the Pari-Mutuel Model

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Book cover Uncertainty Modelling in Data Science (SMPS 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 832))

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Abstract

We introduce two models for imprecise probabilities which generalise the Pari-Mutuel Model while retaining its simple structure. Their consistency properties are investigated, as well as their capability of formalising an assessor’s different attitudes. It turns out that one model is always coherent, while the other is (occasionally coherent but) generally only 2-coherent, and may elicit a conflicting attitude towards risk.

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Notes

  1. 1.

    It can be shown that a third, less relevant, submodel completes the family of NL models.

  2. 2.

    When \(b=1,\,a=0\), \(\mu \) is a probability. We shall hereafter neglect this subcase.

  3. 3.

    \(a+b>1\) in (k) could be relaxed to \(a+b\ge 1\), thus including the PMM as a special HB-PMM. We left out this case to focus on the ‘proper’ HB-PMMs.

References

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Authors and Affiliations

  1. University of Trieste (DEAMS), 34100, Trieste, Italy

    Chiara Corsato, Renato Pelessoni & Paolo Vicig

Authors
  1. Chiara Corsato
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  2. Renato Pelessoni
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  3. Paolo Vicig
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Corresponding author

Correspondence to Paolo Vicig .

Editor information

Editors and Affiliations

  1. CNRS, Heudiasyc, Sorbonne universités, Université de technologie de Compiègne, Compiegne, France

    Sébastien Destercke

  2. CNRS, Heudiasyc, Sorbonne universités, Université de technologie de Compiègne, Compiegne, France

    Thierry Denoeux

  3. Department of Statistics and Operational Research and Mathematics Didactics, University of Oviedo, Oviedo, Asturias, Spain

    María Ángeles Gil

  4. Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland

    Przemyslaw Grzegorzewski

  5. Department of Stochastic Methods, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Olgierd Hryniewicz

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Corsato, C., Pelessoni, R., Vicig, P. (2019). Generalising the Pari-Mutuel Model. In: Destercke, S., Denoeux, T., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Uncertainty Modelling in Data Science. SMPS 2018. Advances in Intelligent Systems and Computing, vol 832. Springer, Cham. https://doi.org/10.1007/978-3-319-97547-4_28

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