A Foundational Approach to Generalising the Maximum Entropy Inference Process to the Multi-Agent Context

Abstract

The present paper seeks to establish a logical foundation for studying axiomatically multi-agent probabilistic reasoning over a discrete space of outcomes. We study the notion of a social inference process which generalises the concept of an inference process for a single agent which was used by Paris and Vencovská to characterise axiomatically the method of maximum entropy inference. Axioms for a social inference process are introduced and discussed, and a particular social inference process called the Social Entropy Process, or SEP, is defined which satisfies these axioms. SEP is justified heuristically by an information theoretic argument, and incorporates both the maximum entropy inference process for a single agent and the multi–agent normalised geometric mean pooling operator.

Keywords

• inference process
• maximum entropy
• social entropy
• Kullback-Leibler
• probabilistic reasoning
• pooling operator
• discrete probability function
• probabilistic merging
• multi-agent reasoning