Abstract
We study, from the standpoint of coherence, comparative probabilities on an arbitrary familyE of conditional events. Given a binary relation ⩽·, coherence conditions on ⩽· are related to de Finetti's coherent betting system: we consider their connections to the usual properties of comparative probability and to the possibility of numerical representations of ⩽·. In this context, the numerical reference frame is that of de Finetti's coherent subjective conditional probability, which is not introduced (as in Kolmogoroff's approach) through a ratio between probability measures.
Another relevant feature of our approach is that the family & need not have any particular algebraic structure, so that the ordering can be initially given for a few conditional events of interest and then possibly extended by a step-by-step procedure, preserving coherence.
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Coletti, G., Gilio, A. & Scozzafava, R. Comparative probability for conditional events: A new look through coherence. Theor Decis 35, 237–258 (1993). https://doi.org/10.1007/BF01075200
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DOI: https://doi.org/10.1007/BF01075200