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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 wonder if a generalization exists for N paper l parties? Can you start with 4N districts, have party 2 combine, then party 3 combine again?
I’m guessing no, since in the extreme case you have log2(population) parties, the “define” party is forced to define 1-person districts and is effectively left out of the process…
@pganssle Problems "like this" get much more complex when there are N>2 players, and indeed even the definition of success is much more subtle. See https://en.wikipedia.org/wiki/Envy-free_cake-cutting and https://en.wikipedia.org/wiki/Proportional_division for an introduction.
But once you're in a political system with more than two parties, you should be thinking about how to move away from winner-take-all districts to multi-member representation and something like https://en.wikipedia.org/wiki/Single_transferable_vote.
@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
@Log3overLog2 It's interesting that they don't cite a 2017 paper that claims to give a protocol that solves this exactly. The solution in the paper you cited is only approximate.
@jdchristensen That work and others are cited and contrasted in Section 2, "Limitations of Current Partisan Gerrymandering Fixes".
@Log3overLog2 Oh, you're right, they do briefly mention that paper. But they don't really say much of substance about why that solution (or others) aren't adequate.
This is cool, but may not satisfy all legal requirements.
Although a lot of the weird maps you see are due to various biases, occasionally, some of them are actually a result of the civil rights regulations.
99% invisible did an episode on this:
https://99percentinvisible.org/episode/gerrymandering/
A more detailed link:
@beetle_b There is a whole section of the linked paper on VRA compatibility.
@Log3overLog2 The idea is interesting, but there is no reason to think that exactly one recombination makes up for the interests inherent in the initial proposal. Plus, in the contiguous case, the recombining party's options are highly constrained at the edges of the map. Despite the authors' claims to the contrary, the proposed method is itself a kind of bipartisan agreement that would require consent.
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@Log3overLog2 It seems to me that a more promising approach is to minimize an agreed measure of bias (e.g. disproportionality) across the historical votes in proposed districts: https://www.nature.com/articles/s41599-021-00809-7
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@Log3overLog2 coming from a country without such district effects (Sweden) due to us having a much simpler system makes it weird seeing people thinking hard about trying to fix gerrymandering. The problem is a lack of political will to fix it. Math can't approach that problem. But a super simple proportional counting system can. Easily.
@Log3overLog2 curious on your thoughts on this approach, @AustinLBuchanan .
@Log3overLog2
Possible evil strat: draw noncompact districts in areas with lots of opposing voters and compact districts in areas with yours, to make it more inconvenient for the other side to get to their polling place.
Possible patch: require subdistricts to be Voronoi cells, with a polling place at the generating point. Voters may use either of their district's two polling places.
#FBPE @Log3overLog2 How to embed the two party system even worse than it is already?