## Comparative probability for conditional events: A new look through coherence.(English)Zbl 0785.90006

Summary: We study, from the standpoint of coherence, comparative probabilities on an arbitrary family $$\mathcal E$$ of conditional events. Given a binary relation $$\prec\cdot$$, coherence conditions on $$\prec\cdot$$ 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 $$\prec\cdot$$. 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 $$\mathcal E$$ 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.

### MSC:

 91B08 Individual preferences 91B16 Utility theory

### Keywords:

conditional events; comparative probability; coherence
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### References:

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