Because the choice of solution is consequential and left unspecified, we recommend that Team fractally add to their specification an additional constraint that specifies which solution to choose.
Ah, yeah we definitely could add it in writing somewhere, but the intention is that groups are always size 6, and we allow for groups of size 5 only when there aren't enough for a complete breakout room.
Barring other considerations, our recommendation for the Genesis Fractal is to always choose the solution to Equation 1 that maximizes the number of participants promoted to Round 2.
Interesting suggestion. Another benefit to meetings of 5 people that you didn't mention is that groups of 5 are psychologically more likely to be conversational & inclusive rather than dominated by one or two charismatic "leaders."
That said, it's not obvious to me that maximizing distributed respect on a given day is necessarily a benefit. Also it would change the constitution of the second meeting to being approximately the top half of the contributors in a community to being the top 60%. Also means more total man hours are required (more people need to do two rounds). These are not necessarily positive or negative, I'm just thinking of implications.
There's also other benefits to groups of size 6: consensus among 6 is 4/6 == 66%, which better approximates the BFT consensus threshold.
Anyway, I'm sure there's more to consider here.
Thanks, as always, for the thoughtful post @MattLangston.
RE: An Analysis of the Genesis Fractal's Group Structures and Random Processes