 Stirling formally defines representation theorems for three kinds of ordered utility functions: conditional utility, concordant utility and conditional concordant utility. These may be applied recursively, i.e. to individuals, to teams and to teams of teams. Then the core of the formal development is the theory that aggregates individuals’ conditional concordant preferences to build models of team choice that are not exogenously imposed on team members, but instead derive from their several preferences. In stating Stirling’s aggregation procedure in the present context, it is useful to change his terminology, and therefore paraphrase him rather than quote directly. This is because Stirling refers to “groups” rather than to “teams”. Stirling’s initial work on CGT was entirely independent of Bacharach’s work,so was not configured within the context of team reasoning (or what we might reinterpret as team-centred choice). But Bacharach’s ideas provide a natural setting in which to frame Stirling’s technical achievement as an enrichment of the applicability of game theory in social science (see  Hofmeyr and Ross (2019)).  We can then paraphrase his five constraints on aggregation as follows: