Random selection is necessary to create stable meritocratic institutions

Haha, mine too.

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's truly random, it should already be 50-52% female.

If it comes out 10% female every sortition cohort, you know some funny business is going on.

Isn't this a question of how many people you select?

Sure.

My point is that so is the percentage of males in any sortition cohort.

Therefore, a consistent female census of 10% or less in all sortition cohorts, would be as unlikely as a consistent male census of 10% or less in all sortition cohorts.

In other words, having one sortition cohort result in 10% males would not be suspicious. Having every sortition cohort result in 10% males would be suspicious in the extreme. So much so that we should start looking for whoever is "putting their finger on the scale" so to speak.

If the sample size is low, it could come out at 10% purely at random, but that is still likely to undermine confidence in the system (in the immediate). Pragmatically, I think it makes sense to have quotas for a few protected classes, to maximize perception of fairness.