This paper is devoted to the extension of conditional assessments that satisfy some consistency criteria, such as weak or strong coherence, to further domains. In particular, we characterise the natural extension of a number of conditional lower previsions on finite spaces, by showing that it can be calculated as the limit of a sequence of conditional lower previsions defined by regular extension. Our results are valid for conditional lower previsions with non-linear domains, and allow us to give an equivalent formulation of the notion of coherence in terms of credal sets.
Keywords. Coherent lower previsions, weak and strong coherence, natural extension, regular extension, desirable gambles.
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Authors addresses:
Enrique Miranda
Dep. of Statistics and O.R.
University of Oviedo
C-Calvo Sotelo, s/n
33007 Oviedo (Spain)
Marco Zaffalon
Galleria 2
CH-6928 Manno
Switzerland
E-mail addresses:
| Enrique Miranda | mirandaenrique@uniovi.es |
| Marco Zaffalon | zaffalon@idsia.ch |