The marginal problem for sets of desirable gamble sets

Justyna Dąbrowska, Arthur Van Camp, Erik Quaeghebeur
Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 290:103-114, 2025.

Abstract

We study the marginal problem for sets of desirable gamble sets (SoDGSes), which is equivalent to studying this problem for choice functions. More specifically, given a number of marginal SoDGSes on overlapping domains, we establish conditions under which they are compatible in the sense that they can be derived from a common joint SoDGS. We do so for SoDGSes that admit a concrete finite representation. Our main result is that such SoDGSes are compatible if they are pairwise compatible and if a running intersection property is satisfied.

Cite this Paper

BibTeX
@InProceedings{pmlr-v290-dabrowska25a, title = {The marginal problem for sets of desirable gamble sets}, author = {D\k{a}browska, Justyna and Van Camp, Arthur and Quaeghebeur, Erik}, booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {103--114}, year = {2025}, editor = {Destercke, Sébastien and Erreygers, Alexander and Nendel, Max and Riedel, Frank and Troffaes, Matthias C. M.}, volume = {290}, series = {Proceedings of Machine Learning Research}, month = {15--18 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v290/main/assets/dabrowska25a/dabrowska25a.pdf}, url = {https://proceedings.mlr.press/v290/dabrowska25a.html}, abstract = {We study the marginal problem for sets of desirable gamble sets (SoDGSes), which is equivalent to studying this problem for choice functions. More specifically, given a number of marginal SoDGSes on overlapping domains, we establish conditions under which they are compatible in the sense that they can be derived from a common joint SoDGS. We do so for SoDGSes that admit a concrete finite representation. Our main result is that such SoDGSes are compatible if they are pairwise compatible and if a running intersection property is satisfied.} }
Endnote
%0 Conference Paper %T The marginal problem for sets of desirable gamble sets %A Justyna Dąbrowska %A Arthur Van Camp %A Erik Quaeghebeur %B Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2025 %E Sébastien Destercke %E Alexander Erreygers %E Max Nendel %E Frank Riedel %E Matthias C. M. Troffaes %F pmlr-v290-dabrowska25a %I PMLR %P 103--114 %U https://proceedings.mlr.press/v290/dabrowska25a.html %V 290 %X We study the marginal problem for sets of desirable gamble sets (SoDGSes), which is equivalent to studying this problem for choice functions. More specifically, given a number of marginal SoDGSes on overlapping domains, we establish conditions under which they are compatible in the sense that they can be derived from a common joint SoDGS. We do so for SoDGSes that admit a concrete finite representation. Our main result is that such SoDGSes are compatible if they are pairwise compatible and if a running intersection property is satisfied.
APA
Dąbrowska, J., Van Camp, A. & Quaeghebeur, E.. (2025). The marginal problem for sets of desirable gamble sets. Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 290:103-114 Available from https://proceedings.mlr.press/v290/dabrowska25a.html.

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