Characterizing the set of coherent lower previsions with a finite number of constraints or vertices

Erik Quaeghebeur
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:465-472, 2010.

Abstract

The standard coherence criterion for lower pre- visions is expressed using an infinite number of linear constraints. For lower previsions that are es- sentially defined on some finite set of gambles on a finite possibility space, we present a reformula- tion of this criterion that only uses a finite number of constraints. Any such lower prevision is coher- ent if it lies within the convex polytope defined by these constraints. The vertices of this polytope are the extreme coherent lower previsions for the given set of gambles. Our reformulation makes it possible to compute them. We show how this is done and illustrate the procedure and its results.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-quaeghebeur10a, title = {Characterizing the set of coherent lower previsions with a finite number of constraints or vertices}, author = {Quaeghebeur, Erik}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {465--472}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/quaeghebeur10a/quaeghebeur10a.pdf}, url = {https://proceedings.mlr.press/r8/quaeghebeur10a.html}, abstract = {The standard coherence criterion for lower pre- visions is expressed using an infinite number of linear constraints. For lower previsions that are es- sentially defined on some finite set of gambles on a finite possibility space, we present a reformula- tion of this criterion that only uses a finite number of constraints. Any such lower prevision is coher- ent if it lies within the convex polytope defined by these constraints. The vertices of this polytope are the extreme coherent lower previsions for the given set of gambles. Our reformulation makes it possible to compute them. We show how this is done and illustrate the procedure and its results.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Characterizing the set of coherent lower previsions with a finite number of constraints or vertices %A Erik Quaeghebeur %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-quaeghebeur10a %I PMLR %P 465--472 %U https://proceedings.mlr.press/r8/quaeghebeur10a.html %V R8 %X The standard coherence criterion for lower pre- visions is expressed using an infinite number of linear constraints. For lower previsions that are es- sentially defined on some finite set of gambles on a finite possibility space, we present a reformula- tion of this criterion that only uses a finite number of constraints. Any such lower prevision is coher- ent if it lies within the convex polytope defined by these constraints. The vertices of this polytope are the extreme coherent lower previsions for the given set of gambles. Our reformulation makes it possible to compute them. We show how this is done and illustrate the procedure and its results. %Z Reissued by PMLR on 04 October 2026.
APA
Quaeghebeur, E.. (2010). Characterizing the set of coherent lower previsions with a finite number of constraints or vertices. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:465-472 Available from https://proceedings.mlr.press/r8/quaeghebeur10a.html. Reissued by PMLR on 04 October 2026.

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