Majority stake enforces an independent and anonymous consensus policy $\pi$ (through a blockchain solution) that modifies the weights to minimize the expense $W_H$, which has been maximized by the cabal applying an objectively incorrect gratis self-weight $W_C$. Consensus aims to produce $\pi(\mathbf{W})\rightarrow (W'_H, W'_C)$ so that $W'_C=1-W'_H$, by correcting the error $\epsilon=W_C+W_H-1>0$. Note that the input cost $W_H$ remains fully expensed, and that $W'_H$ merely modifies the reward distribution that follows, but not knowing which players are honest or cabal (anonymous property).
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