Abstract
Granted a de Finetti style qualitative comparative probability relation on a Boolean algebra, necessary and sufficient conditions are given for the existence of an agreeing probability measure on the algebra in finite, countable and arbitrary situations. Partially ordered linear spaces and order-preserving linear functionals are used in proving the results and in explaining why the axiomatization of qualitative probability relations is bound to be complex. The inherent technical difficulites can be overcome by relying on nonstandard representations that are also provided. Extensive work done by Suppes in this area is also discussed, in conjunction with the problem of uniqueness and simplicity. The central aim of this work is to provide a more holistic setting for the axiomatization of comparative probability and its associated representational methodology.
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