Generalized Qualitative Probability: Savage Revisited

TL;DR

This paper revisits Savage's framework for preferences among acts, weakening some rationality postulates, and introduces a generalized qualitative probability that unifies traditional and logical probability structures.

Contribution

It weakens Savage's rationality postulates, derives the Sure Thing Principle in a partially ordered setting, and characterizes a new generalized qualitative probability.

Findings

Derived the Sure Thing Principle under weaker assumptions.

Unified qualitative probability with ranked logical structures.

Provided a new framework for preferences among acts.

Abstract

Preferences among acts are analyzed in the style of L. Savage, but as partially ordered. The rationality postulates considered are weaker than Savage's on three counts. The Sure Thing Principle is derived in this setting. The postulates are shown to lead to a characterization of generalized qualitative probability that includes and blends both traditional qualitative probability and the ranked structures used in logical approaches.