Comparative probability for conditional events: A new look through coherence |
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Authors: | Giulianella Coletti Angelo Gilio Romano Scozzafava |
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Institution: | (1) Dipartimento di Matematica, Università, Via Vanvitelli 1, 06100 Perugia, Italy;(2) Dipartimento di Metodi e Modelli Matematici, Università La Sapienza , Via A. Scarpa 16, 00161 Rome, Italy |
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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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Keywords: | conditional events comparative probability coherence management of uncertainty |
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