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Anyone with a sibling that has had to divide something equally to share it knows how to solve this. One group chooses the algorithm and the second group chooses which side they get to on.
The first group, who have the power to introduce bias disadvantaging one side cannot benefit from it, and worse, they'd hand the power to the second group. It forces the first group to choose a method with built in equality because the second group could force the first group to take the disadvantaged side.
In practice this would require the second group to basically have a switch that switches all voters' preferences. So I don't think that's gonna work here.
That wouldn't be the variable choice by the second group in what I'm suggesting.
In this scenario if the first party choices algorithmic weights which favor their voters, given them a controlling outcome, the second party would be able to substitute their own weights making the algorithm shift the districts to give the second party the control. The rules would forbid baking the weights into the algorithm meaning the first group would work very hard to produce an algorithm producing equal representation districts without being able to swing it either way by weighting it.
this seems to assume a baked-in 2 party system I would prefer not to continue to plan around
Unfortunately I don't think that's how algorithm development works, not if you want to make a fair one.