Abstract
Let $\mathscr{J}$ be a Boolean algebra of subsets of a state space $S$ and let $\succ$ be a binary comparative probability relation on $\mathscr{J}$ with $A \succ B$ interpreted as "$A$ is more probable than $B$." Axioms are given for $\succ$ on $\mathscr{J}$ which are sufficient for the existence of a finitely additive probability measure $P$ on $\mathscr{J}$ which has $P(A) > P(B)$ whenever $A \succ B$. The axioms consist of a necessary cancellation or additivity condition, a simple monotonicity axiom, an axiom for the preservation of $\succ$ under common deletions, and an Archimedean condition.
Citation
Peter C. Fishburn. "Weak Comparative Probability on Infinite Sets." Ann. Probab. 3 (5) 889 - 893, October, 1975. https://doi.org/10.1214/aop/1176996277
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