Weak Dutch Books versus Strict Consistency with Lower Previsions

Chiara Corsato, Renato Pelessoni, Paolo Vicig
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:85-96, 2017.

Abstract

Several consistency notions for lower previsions (coherence, convexity, others) require that the suprema of certain gambles, having the meaning of gains, are non-negative. The limit situation that a gain supremum is zero is termed Weak Dutch Book (WDB). In the literature, the special case of WDBs with precise probabilities has mostly been analysed, and strict coherence has been proposed as a radical alternative. In this paper the focus is on WDBs and generalised strict coherence, termed strict consistency, with imprecise previsions. We discuss properties of lower previsions incurring WDBs and conditions for strict consistency, showing in both cases how they are differentiated by the degree of consistency of the given uncertainty assessment.

Cite this Paper

BibTeX
@InProceedings{pmlr-v62-corsato17a, title = {{W}eak {D}utch {B}ooks versus Strict Consistency with Lower Previsions}, author = {Corsato, Chiara and Pelessoni, Renato and Vicig, Paolo}, booktitle = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {85--96}, year = {2017}, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien}, volume = {62}, series = {Proceedings of Machine Learning Research}, month = {10--14 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v62/corsato17a/corsato17a.pdf}, url = {https://proceedings.mlr.press/v62/corsato17a.html}, abstract = {Several consistency notions for lower previsions (coherence, convexity, others) require that the suprema of certain gambles, having the meaning of gains, are non-negative. The limit situation that a gain supremum is zero is termed Weak Dutch Book (WDB). In the literature, the special case of WDBs with precise probabilities has mostly been analysed, and strict coherence has been proposed as a radical alternative. In this paper the focus is on WDBs and generalised strict coherence, termed strict consistency, with imprecise previsions. We discuss properties of lower previsions incurring WDBs and conditions for strict consistency, showing in both cases how they are differentiated by the degree of consistency of the given uncertainty assessment.} }
Endnote
%0 Conference Paper %T Weak Dutch Books versus Strict Consistency with Lower Previsions %A Chiara Corsato %A Renato Pelessoni %A Paolo Vicig %B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2017 %E Alessandro Antonucci %E Giorgio Corani %E Inés Couso %E Sébastien Destercke %F pmlr-v62-corsato17a %I PMLR %P 85--96 %U https://proceedings.mlr.press/v62/corsato17a.html %V 62 %X Several consistency notions for lower previsions (coherence, convexity, others) require that the suprema of certain gambles, having the meaning of gains, are non-negative. The limit situation that a gain supremum is zero is termed Weak Dutch Book (WDB). In the literature, the special case of WDBs with precise probabilities has mostly been analysed, and strict coherence has been proposed as a radical alternative. In this paper the focus is on WDBs and generalised strict coherence, termed strict consistency, with imprecise previsions. We discuss properties of lower previsions incurring WDBs and conditions for strict consistency, showing in both cases how they are differentiated by the degree of consistency of the given uncertainty assessment.
APA
Corsato, C., Pelessoni, R. & Vicig, P.. (2017). Weak Dutch Books versus Strict Consistency with Lower Previsions. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 62:85-96 Available from https://proceedings.mlr.press/v62/corsato17a.html.

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