Possibility Theory: Searching for Normative Foundations

Savage has studied qualitative probability relations in order to justify the axioms of numerical probability from purely ordinal arguments, for the purpose of modeling subjective uncertainty judgments. Such an attempt is made here for possibility measures, in a finite setting. Axioms are suggested which a binary relation “at least as possible as” must satisfy, so that the only numerical uncertainty measures compatible with such a relation are possibility measures. Moreover a general notion of belief structure is proposed in order to encompass both probability and possibility theories within the same qualitative setting. This is done by relaxing the qualitative “additivity” axiom.

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