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Abstract
We consider coherent choice functions under the recent axiomatisation proposed by De Bock and De Cooman that guarantees a representation in terms of binary preferences, and we discuss how to define conditioning in this framework. In a multivariate context, we propose a notion of marginalisation, and its inverse operation called weak (cylindrical) extension. We combine this with our definition of conditioning to define a notion of irrelevance, and we obtain the irrelevant natural extension in this framework: the least informative choice function that satisfies a given irrelevance assessment.
Keywords
Choice functions, coherence, sets of desirable gambles, natural extension, conditioning, epistemic irrelevance

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Citation

Please use this url to cite or link to this publication:

MLA
Van Camp, Arthur, and Enrique Miranda. “Irrelevant Natural Extension for Choice Functions.” International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, edited by Jasper De Bock et al., vol. 103, 2019, pp. 414–23.
APA
Van Camp, A., & Miranda, E. (2019). Irrelevant natural extension for choice functions. In J. De Bock, C. P. de Campos, G. De Cooman, E. Quaeghebeur, & G. Wheeler (Eds.), International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings (Vol. 103, pp. 414–423). Ghent, Belgium.
Chicago author-date
Van Camp, Arthur, and Enrique Miranda. 2019. “Irrelevant Natural Extension for Choice Functions.” In International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, edited by Jasper De Bock, Cassio P. de Campos, Gert De Cooman, Erik Quaeghebeur, and Gregory Wheeler, 103:414–23.
Chicago author-date (all authors)
Van Camp, Arthur, and Enrique Miranda. 2019. “Irrelevant Natural Extension for Choice Functions.” In International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, ed by. Jasper De Bock, Cassio P. de Campos, Gert De Cooman, Erik Quaeghebeur, and Gregory Wheeler, 103:414–423.
Vancouver
1.
Van Camp A, Miranda E. Irrelevant natural extension for choice functions. In: De Bock J, de Campos CP, De Cooman G, Quaeghebeur E, Wheeler G, editors. International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings. 2019. p. 414–23.
IEEE
[1]
A. Van Camp and E. Miranda, “Irrelevant natural extension for choice functions,” in International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, Ghent, Belgium, 2019, vol. 103, pp. 414–423.
@inproceedings{8623856,
  abstract     = {{We consider coherent choice functions under the recent axiomatisation proposed by De Bock and De Cooman that guarantees a representation in terms of binary preferences, and we discuss how to define conditioning in this framework. In a multivariate context, we propose a notion of marginalisation, and its inverse operation called weak (cylindrical) extension. We combine this with our definition of conditioning to define a notion of irrelevance, and we obtain the irrelevant natural extension in this framework: the least informative choice function that satisfies a given irrelevance assessment.}},
  author       = {{Van Camp, Arthur and Miranda, Enrique}},
  booktitle    = {{International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings}},
  editor       = {{De Bock, Jasper and de Campos, Cassio P. and De Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}},
  issn         = {{2640-3498}},
  keywords     = {{Choice functions,coherence,sets of desirable gambles,natural extension,conditioning,epistemic irrelevance}},
  language     = {{eng}},
  location     = {{Ghent, Belgium}},
  pages        = {{414--423}},
  title        = {{Irrelevant natural extension for choice functions}},
  url          = {{http://proceedings.mlr.press/v103/}},
  volume       = {{103}},
  year         = {{2019}},
}