The technical term is sortition. And it is my pet unorthodox political position. The legislature should be replaced with an assembly of citizens picked by lottery.
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It would probably make sense to start with a new new "house" or something.
Might even make sense to have some quotas (at least 50% women etc.), so the whole things doesn't have to get to Chinese government size to reflect the populus.
That or pepple would have to be replaced with high frequency
If it comes out 10% female every sortition cohort, you know some funny business is going on.