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Wow, this proposed approach to drawing districts without gerrymandering is fascinating! In the spirit of "I cut you choose", the proposal is "One party defines 2N equal-population sub-districts, and the other party chooses pairs of adjacent sub-districts to combine, to form N districts."
The analysis in the body of the paper focuses on simulations of each party's optimal strategy in the context of some real-world maps of US voting precincts, while an appendix proves a few theorems giving bounds in the alternate context where the pairs of districts that get combined don't need to be geographically adjacent. (If this idea catches on, I'd bet someone will produce theoretical bounds in the presence of the geography constraint.)
A Partisan Solution to Partisan Gerrymandering: The Define–Combine Procedure
@Log3overLog2 I've always wondered this, but can someone explain why you can't just do some kind clustering algorithm? Just distribute n dots on the map and let them each grow towards an even size. Like how is gerrymandering is even a thing if you just have "this house has 2 people, this house has 4, etc". Do politicians actually get to see race and other info for each building? If that's true then FFS that should stop if not how the hell is this so complicated?
For one possible answer to why we (the U.S. or its individual states) can't just rely on tidy algorithms for districting, see @beetle_b's comment here:
https://mastodon.xyz/@beetle_b/111937812188418377