  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.
