Welldefined Decision Scenarios
  Influence diagrams serve as a powerful tool for modelling symmetric decision
problems. When solving an influence diagram we determine a set of strategies
for the decisions involved. A strategy for a decision variable is in principle
a function over its past. However, some of the past may be irrelevant for the
decision, and for computational reasons it is important not to deal with
redundant variables in the strategies. We show that current methods (e.g. the
"Decision Bayes-ball" algorithm by Shachter UAI98) do not determine the
relevant past, and we present a complete algorithm.
  Actually, this paper takes a more general outset: When formulating a decision
scenario as an influence diagram, a linear temporal ordering of the decisions
variables is required. This constraint ensures that the decision scenario is
welldefined. However, the structure of a decision scenario often yields certain
decisions conditionally independent, and it is therefore unnecessary to impose
a linear temporal ordering on the decisions. In this paper we deal with partial
influence diagrams i.e. influence diagrams with only a partial temporal
ordering specified. We present a set of conditions which are necessary and
sufficient to ensure that a partial influence diagram is welldefined. These
conditions are used as a basis for the construction of an algorithm for
determining whether or not a partial influence diagram is welldefined.
