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Counterexamples to Some Characterizations of Dilation

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Abstract

We provide counterexamples to some purported characterizations of dilation due to Pedersen and Wheeler (Erkenntnis 79(6):1305–1342, 2014, ISIPTA ’15: Proceedings of the 9th international symposium on imprecise probability: theories and applications, 2015).

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Notes

  1. Note that there is a typo in their paper where they describe the direction of implication; “(iii) \(\Leftarrow \) (i)” should be replaced by “(iii) \(\Rightarrow \) (i)”.

References

  • Pedersen, A. P., & Wheeler, G. (2014). Demystifying dilation. Erkenntnis, 79(6), 1305–1342.

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  • Pedersen, A. P., & Wheeler, G. (2015). Dilation, disintegrations, and delayed decisions. In ISIPTA ’15: Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications. Aracne Editrice.

  • Seidenfeld, T., & Wasserman, L. (1993). Dilation for sets of probabilities. The Annals of Statistics, 21(3), 1139–1154.

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Authors and Affiliations

  1. Australian National University, Canberra, Australia

    Michael Nielsen

  2. Munich Center for Mathematical Philosophy, LMU Munich, Munich, Germany

    Rush T. Stewart

Authors
  1. Michael Nielsen
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  2. Rush T. Stewart
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Correspondence to Michael Nielsen.

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Nielsen, M., Stewart, R.T. Counterexamples to Some Characterizations of Dilation. Erkenn 86, 1107–1118 (2021). https://doi.org/10.1007/s10670-019-00145-y

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  • DOI: https://doi.org/10.1007/s10670-019-00145-y

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