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Lexicographic choice functions without archimedeanicity

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Abstract
We investigate the connection between choice functions and lexicographic probabilities, by means of the convexity axiom considered by Seidenfeld, Schervisch and Kadane (2010) 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.
Keywords
maximality, archimedeanicity, choice functions, lexicographic probabilities

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Citation

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Chicago
Van Camp, Arthur, Enrique Miranda, and Gert De Cooman. 2017. “Lexicographic Choice Functions Without Archimedeanicity.” In Soft Methods for Data Science , ed. Maria Brigida Ferraro, Paolo Giordani, Barbara Vantaggi, Marek Gagolewski, Mariá Ángeles Gil, Przemysław Grzegorzewski, and Olgierd Hryniewicz, 456:479–486. Switzerland: Springer International Publishing.
APA
Van Camp, Arthur, Miranda, E., & De Cooman, G. (2017). Lexicographic choice functions without archimedeanicity. In M. B. Ferraro, P. Giordani, B. Vantaggi, M. Gagolewski, M. Á. Gil, P. Grzegorzewski, & O. Hryniewicz (Eds.), SOFT METHODS FOR DATA SCIENCE (Vol. 456, pp. 479–486). Presented at the 8th International Conference on Soft Methods in Probability and Statistics (SMPS) , Switzerland: Springer International Publishing.
Vancouver
1.
Van Camp A, Miranda E, De Cooman G. Lexicographic choice functions without archimedeanicity. In: Ferraro MB, Giordani P, Vantaggi B, Gagolewski M, Gil MÁ, Grzegorzewski P, et al., editors. SOFT METHODS FOR DATA SCIENCE . Switzerland: Springer International Publishing; 2017. p. 479–86.
MLA
Van Camp, Arthur, Enrique Miranda, and Gert De Cooman. “Lexicographic Choice Functions Without Archimedeanicity.” Soft Methods for Data Science . Ed. Maria Brigida Ferraro et al. Vol. 456. Switzerland: Springer International Publishing, 2017. 479–486. Print.
@inproceedings{8079477,
  abstract     = {We investigate the connection between choice functions and lexicographic probabilities, by means of the convexity axiom considered by Seidenfeld, Schervisch and Kadane (2010) 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.},
  author       = {Van Camp, Arthur and Miranda, Enrique and De Cooman, Gert},
  booktitle    = {SOFT METHODS FOR DATA SCIENCE },
  editor       = {Ferraro, Maria Brigida and Giordani, Paolo and Vantaggi, Barbara and Gagolewski, Marek and Gil, Mari{\'a} {\'A}ngeles and Grzegorzewski, Przemys\unmatched{0142}aw and Hryniewicz, Olgierd},
  isbn         = {978-3-319-42972-4},
  issn         = {2194-5357},
  keyword      = {maximality,archimedeanicity,choice functions,lexicographic probabilities},
  language     = {eng},
  location     = {Rome, Italy},
  pages        = {479--486},
  publisher    = {Springer International Publishing},
  title        = {Lexicographic choice functions without archimedeanicity},
  url          = {http://dx.doi.org/10.1007/978-3-319-42972-4\_59},
  volume       = {456},
  year         = {2017},
}

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