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Influence diagrams provide a compact graphical representation of decisionproblems. Several algorithms for the quick computation of their associatedexpected utilities are available in the literature. However, often they rely ona full quantification of both probabilistic uncertainties and utility values.For problems where all random variables and decision spaces are finite anddiscrete, here we develop a symbolic way to calculate the expected utilities ofinfluence diagrams that does not require a full numerical representation.Within this approach expected utilities correspond to families of polynomials.After characterizing their polynomial structure, we develop an efficientsymbolic algorithm for the propagation of expected utilities through thediagram and provide an implementation of this algorithm using a computeralgebra system. We then characterize many of the standard manipulations ofinfluence diagrams as transformations of polynomials. We also generalize thedecision analytic framework of these diagrams by defining asymmetries asoperations over the expected utility polynomials.

A symbolic algebra for the computation of expected utilities in multiplicative influence diagrams