Coherent combination of probabilistic outputs for group decision making: an algebraic approach

TL;DR

This paper introduces an algebraic method for combining probabilistic outputs from multiple expert panels in decision support systems, ensuring coherence and enabling efficient Bayesian multi-agent analysis across diverse models.

Contribution

The paper presents a novel algebraic framework that generalizes the combination of expert judgments in Bayesian decision analysis, allowing for partial model sharing and closed-form computations.

Findings

The approach guarantees coherence even with partial model sharing.

Closed-form formulas for joint moments in Bayesian networks are derived.

The method enhances computational efficiency in multi-agent decision systems.

Abstract

Current decision support systems address domains that are heterogeneous in nature and becoming progressively larger. Such systems often require the input of expert judgement about a variety of different fields and an intensive computational power to produce the scores necessary to rank the available policies. Recently, integrating decision support systems have been introduced to enable a formal Bayesian multi-agent decision analysis to be distributed and consequently efficient. In such systems, where different panels of experts oversee disjoint but correlated vectors of variables, each expert group needs to deliver only certain summaries of the variables under their jurisdiction to properly derive an overall score for the available policies. Here we present an algebraic approach that makes this methodology feasible for a wide range of modelling contexts and that enables us to identify the summaries needed for such a combination of judgements. We are also able to demonstrate that coherence, in a sense we formalize here, is still guaranteed when panels only share a partial specification of their model with other panel members. We illustrate this algebraic approach by applying it to a specific class of Bayesian networks and demonstrate how we can use it to derive closed form formulae for the computations of the joint moments of variables that determine the score of different policies.