# Nisan comments on Self-Integrity and the Drowning Child

• Ah, great! To fill in some of the details:

• Given agents and numbers such that , there is an aggregate agent called which means “agents and acting together as a group, in which the relative power of versus is the ratio of to ”. The group does not make decisions by combining their utility functions, but instead by negotiating or fighting or something.

• Aggregation should be associative, so .

• If you spell out all the associativity relations, you’ll find that aggregation of agents is an algebra over the operad of topological simplices. (See Example 2 https://​​arxiv.org/​​abs/​​2107.09581.)

• Of course we still have the old VNM-rational utility-maximizing agents. But now we also have aggregates of such agents, which are “less Law-aspiring” than their parts.

• In order to specify the behavior of an aggregate, we might need more data than the component agents and their relative power . In that case we’d use some other operad.