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Gert De Cooman, Enrique Miranda

Independent natural extension for sets of desirable gambles


We investigate how to combine a number of marginal coherent sets of desirable gambles into a joint set using the properties of epistemic irrelevance and independence. We provide formulas for the smallest such joint, called their independent natural extension, and study its main properties. The independent natural extension of maximal sets of gambles allows us to define the strong product of sets of desirable gambles. Finally, we explore an easy way to generalise these results to also apply for the conditional versions of epistemic irrelevance and independence.


Epistemic irrelevance, epistemic independence, independent natural extension, strong product, coherent set of desirable gambles.

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Authors’ addresses

Gert De Cooman
Technologiepark - Zwijnaarde 914
9052 Zwijnaarde

Enrique Miranda
Dep. of Statistics and O.R.
University of Oviedo
C-Calvo Sotelo, s/n
33007 Oviedo (Spain)

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Gert De Cooman
Enrique Miranda

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