Clarify unified cabal

Author: opentaco

docs/consensus.md

@@ -37,6 +37,7 @@ Yuma Consensus is adversarially-resilient when majority stake is honest, via sta
 We consider a two-team game between (protagonist) honest stake ($0.5< S_H\le 1$) and (adversarial) cabal stake ($1 - S_H$), with $|H|$ honest and $|C|$ cabal players, that have $S_H = \sum_{i\in H}S_i$ honest stake and $1-S_H = \sum_{i\in C}S_i$ cabal stake. They compete for total fixed reward $E_H + E_C = 1$, with honest emission $E_H$ and cabal emission $E_C$, respectively. Then the stake updates to $S_H'=S_H+\tau E_H$ and $S_C'=(1 - S_H)+\tau E_C$, where $\tau$ decides the emission schedule. We normalize stake after the emission update, so that $\sum S'=1$. The honest objective $S_H\le E_H$ at least retains scoring power $S_H$ over all action transitions in the game, otherwise when $E_H\le S_H$ honest emission will erode to 0 over time, despite a starting condition of $0.5\lt S_H$.
 
 We assume honest stake sets objectively correct weights $W_H$ on itself, and $1 - W_H$ on the cabal, where honest weight $W_H$ represents an ongoing expense of the honest player such as utility production, sustained throughout the game. However, cabal stake has an action policy that freely sets weight $W_C$ on itself, and $1 - W_C$ on the honest player, at no cost to the cabal player.
+Independent smaller cabals will downweight each other thereby weakening overall adversarial power, so we consider the worst-case of a unified cabal.
 Specifically, honest players $i\in H$ set $W_H = \sum_{j\in H}W_{ij}$ self-weight and $1-W_H = \sum_{j\in C}W_{ij}$ weight on cabal players, while cabal players $i\in C$ set $W_C = \sum_{j\in C}W_{ij}$ self-weight and $1-W_C = \sum_{j\in H}W_{ij}$ weight on honest players.
 
 The cabal has the objective to maximize the required honest self-weight expense $W_H$ via