(SMPS 2026), Sept 2026.
IJAR Best Paper Award.We study sets of desirable gamble sets, which are closely related to choice functions, from the perspective of information algebras, which is a framework for reasoning with partial information in a multivariate setting. We show that closed sets of desirable gamble sets, as well as their representations consisting of sets of closed sets of desirable gambles, form information algebras. For a natural map between these algebras, the marginalisation and combination operators commute. Finally, we prove that this mapping is indeed a homomorphism, guaranteeing that the two algebras contain the same information and induce the same marginalisation and combination operators.