 Under these restrictions, Stirling proves an aggregation theorem which follows a general result for updating utility in light of new information that was developed by  Abbas (2003, Other Internet Resources).  Individual team members each calculate the team preference by aggregating conditional concordant preferences. Then the analyst applies marginalization. Let \(X^n\) be a team. Let \(X^m=\{X_{j1},\ldots,X_{jm}\}\) and \(X = \{X_{i1},\ldots, X_{ik}\}\) be disjoint sub-teams of \(X^n\). Then the marginal concordant utility of \(X^m\) with respect to the sub-team \(\{X^m, X^k\}\) is obtained by summing over \(\mathcal{A}^k\), yielding 