The Marginal Problem for Sets of Desirable Gamble Sets
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
Text
Dąbrowska et al. "The Marginal Problem for Sets of Desirable Gamble Sets." Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, 2025.Markdown
[Dąbrowska et al. "The Marginal Problem for Sets of Desirable Gamble Sets." Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, 2025.](https://mlanthology.org/isipta/2025/dabrowska2025isipta-marginal/)BibTeX
@inproceedings{dabrowska2025isipta-marginal,
title = {{The Marginal Problem for Sets of Desirable Gamble Sets}},
author = {Dąbrowska, Justyna and Van Camp, Arthur and Quaeghebeur, Erik},
booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications},
year = {2025},
pages = {103-114},
volume = {290},
url = {https://mlanthology.org/isipta/2025/dabrowska2025isipta-marginal/}
}