The Algebra of Utility Inference

Title: The Algebra of Utility Inference

Research Question: Is there a logical way to express preferences in terms of logical operators of attributes, and can we update preferences in a unifying method similar to Richard Cox's axiomatic derivation for probable inference?

Methodology: The authors use the analogy between probability and utility to propose an axiomatic foundation for utility inferrence and the algebra of preferences. They show that consistency within these axions requires certain rules for updating belief. They discuss a class of utility functions that stems from the axioms of utility inferrence and show that this class is the basic building block for any general multi-attribute utility function. They use this class of utility functions together with the algebra of preferences to construct utility functions represented by logical operations on the attributes.

Results: The authors present an axiomatic derivation for utility inferrence that parallels Richard Cox's axiomatic derivation for probable inference. They provide notation and algebra needed to describe prospects of a decision situation in terms of their attributes. They show that the rules by which preference is updated over some attributes when we are guaranteed certain amounts of the others can be reduced to a harmonious schem

Link to Article: https://arxiv.org/abs/0310044v1 Authors: arXiv ID: 0310044v1