**Max weight supported by $\kappa$-majority stake**: We can plot a consensus graph for each active miner by ordering weights (y-axis) set on the target miner and recording cumulative stake (x-axis) of the source validators. The weight read at $x=1-\kappa$ ratio of total active stake is the stake-based median, which means that at least $\kappa$ stake supports that weight decision. Typically $\kappa=0.5$, which means that 50% of stake needs to agree on the relative utility of a miner, and we clip excess weight above this median to encourage validators to vote fairly and uphold consensus.
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