Generalized Qualitative Probability: Savage Revisited

Title: Generalized Qualitative Probability: Savage Revisited

Research Question: How can we weaken Savage's postulates while still maintaining a coherent model of decision-making under uncertainty?

Methodology: The author proposes a model where 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:

1. Preference is not required to be a simple order (contrary to expectations). This allows for situations where a decider may be undecided between two acts and also undecided between another act and the first, but definitely prefers the second act to the third. 2. The Sure Thing Principle is derived in this setting. 3. The postulates lead to a characterization of generalized qualitative probability that includes and blends both traditional qualitative probability and the ranked structures used in logical approaches.

Results: The author shows that a set of postulates concerning rational decisions in the face of uncertainty implies that the decider acts as if he/she were maximizing the expectation of some utility function. The postulates are shown to lead to a characterization of subjective probabilities that obey the laws of the calculus of probabilities.

Implications: This work is a first step in exploring the possibilities of analyzing preference among acts as a partial ordering, which could shed real light on the question. It also allows for events that are null relatively to other events, addressing a disputable aspect of Savage's treatment of null events. The results provide a coherent model of decision-making under uncertainty that is more flexible and realistic than previous approaches.

Link to Article: https://arxiv.org/abs/0202030v1 Authors: arXiv ID: 0202030v1