I mispoke here, the signing by hashpower is for an on chain transaction, for example pegging out from the side chain to main. But this process is a simple poll vote by miners over time. 51% or more of global hash dominance has no bearing on who gets to vote or how much their vote is valued. The FAQ describes it better.

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Its getting late

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> But this process is a simple poll vote by miners over time. 51% or more of global hash dominance has no bearing on who gets to vote or how much their vote is valued.

It absolutely does! A 51% miner has the privilege of mining 100% of blocks because they can afford to ignore anyone else’s. Therefore, under BIP300, a 51% miner CASTS ALL VOTES.

Apologies for the emphasis caps, but I want there to be no mistake. In #Bitcoin, a 51% miner doesn’t just mine 51% of blocks. They mine ALL of the blocks.