Generalized Qualitative Probability: Savage revisited

TL;DR

This paper revisits Savage's framework for preferences among acts, proposing a weaker set of rationality postulates that lead to a generalized qualitative probability, blending traditional and logical approaches.

Contribution

It introduces a partially ordered preference model with weaker postulates, deriving the Sure Thing Principle and characterizing a new form of generalized qualitative probability.

Findings

Weaker rationality postulates still derive the Sure Thing Principle.

The generalized qualitative probability unifies traditional and logical probability structures.

Preferences are modeled as partially ordered, expanding Savage's original framework.

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.