Ordinal Subjective Foundations for Finite-domain Probability Agreement

Normative study of probability-agreeing orderings of propositions, much of it rooted in a false but evocative conjecture of Bruno de Finetti, has typically sought to abstract credal rationality claims familiarly made for numerical probabilities. It is now known that some probability-disagreeing orderings, e.g. possibilistic order, syntactically restate probability-agreeing orderings, and so share in any ordinal probabilistic ‘rationality.’ This paper explores what remains normatively distinctive about subjective probability agreement. A multiset partial ordering, characteristic of all transitive elementary orderings, helps provide succinct, apprehensible necessary and sufficient ordinal conditions for probability agreement.