Really enjoyed this, and learning a little bit of combinatorics at the same time.

As danbruc mentions below we also would really like our networks to only ever split into sets such that there is at most one set which could include a leader; otherwise we might have a more durable consensus split.

That said, algebraic structures are a tool for working with consensus problems, but there’s also process. Together we get consensus protocols. So, for example, you could have a healing process step that privileges the larger group and forces a merge even if at some moment you had two candidates that believed they were a valid leader for their own split network view.