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Interpreting, axiomatising and representing coherent choice functions in terms of desirability

Jasper De Bock (UGent) and Gert De Cooman (UGent)
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Abstract
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision making. We provide these choice functions with a clear interpretation in terms of desirability, use this interpretation to derive a set of basic coherence axioms, and show that this notion of coherence leads to a representation in terms of sets of strict preference orders. By imposing additional properties such as totality, the mixing property and Archimedeanity, we obtain representation in terms of sets of strict total orders, lexicographic probability systems, coherent lower previsions or linear previsions.

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MLA
De Bock, Jasper, and Gert De Cooman. “Interpreting, Axiomatising and Representing Coherent Choice Functions in Terms of Desirability.” International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, vol. 103, 2019, pp. 125–34.
APA
De Bock, J., & De Cooman, G. (2019). Interpreting, axiomatising and representing coherent choice functions in terms of desirability. In International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings (Vol. 103, pp. 125–134). Ghent.
Chicago author-date
De Bock, Jasper, and Gert De Cooman. 2019. “Interpreting, Axiomatising and Representing Coherent Choice Functions in Terms of Desirability.” In International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, 103:125–34.
Chicago author-date (all authors)
De Bock, Jasper, and Gert De Cooman. 2019. “Interpreting, Axiomatising and Representing Coherent Choice Functions in Terms of Desirability.” In International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, 103:125–134.
Vancouver
1.
De Bock J, De Cooman G. Interpreting, axiomatising and representing coherent choice functions in terms of desirability. In: International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings. 2019. p. 125–34.
IEEE
[1]
J. De Bock and G. De Cooman, “Interpreting, axiomatising and representing coherent choice functions in terms of desirability,” in International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, Ghent, 2019, vol. 103, pp. 125–134.
@inproceedings{8627069,
  abstract     = {Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision making. We provide these choice functions with a clear interpretation in terms of desirability, use this interpretation to derive a set of basic coherence axioms, and show that this notion of coherence leads to a representation in terms of sets of strict preference orders. By imposing additional properties such as totality, the mixing property and Archimedeanity, we obtain representation in terms of sets of strict total orders, lexicographic probability systems, coherent lower previsions or linear previsions. },
  author       = {De Bock, Jasper and De Cooman, Gert},
  booktitle    = {International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings},
  issn         = {2640-3498},
  language     = {eng},
  location     = {Ghent},
  pages        = {125--134},
  title        = {Interpreting, axiomatising and representing coherent choice functions in terms of desirability},
  url          = {http://proceedings.mlr.press/v103/de-bock19b/de-bock19b.pdf},
  volume       = {103},
  year         = {2019},
}