Wesley Pegden, Ariel D. Procaccia, Dingli Yu
2017 · arXiv
We design and analyze a protocol for dividing a state into districts, where parties take turns proposing a division, and freezing a district from the other party's proposed division. We show that our protocol has predictable and provable guarantees for both the number of districts in which each party has a majority of supporters, and the extent to which either party has the power to pack a specific population into a single district.
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Some mathematicians worked out a way to fairly do districting, similar to having one kid cut the cake and the other kid gets first choice: "A partisan districting protocol with provably nonpartisan outcomes" by Wesley Pegden, Ariel D. Procaccia, Dingli Yu https://arxiv.org/abs/1710.08781
Yes, and it works really well for two parties if both parties are equally informed and competent. https://arxiv.org/abs/1710.08781 For n>2 the simple I-cut-you-choose stops working.
"A Partisan Districting Protocol with Provably Nonpartisan Outcomes" https://arxiv.org/abs/1710.08781 Very cool. Though it does freeze in the two-party nature.
This problem has been solved by mathematicians: A partisan districting protocol with provably nonpartisan outcomes https://arxiv.org/abs/1710.08781 by Wesley Pegden, Ariel D. Procaccia, Dingli Yu
Any attempt to completely automate this process is destined to fail, for all the reasons given in this thread. Weighting factors matter, and it is naive to assume that nobody is going to attempt to subvert a nonpartisan board, when so much power is at stake. Don't despair! There's an alternative that generates an equitable outcome between two parties that are trying to screw their rivals: Cake Cutting. https://arxiv.org/abs/1710.08781v1 You've probably heard the basic version of how to fairly divide a piece of cake between two children. Have one of them cut it, then the other choose which piece to keep. The cutter guarantees the largest possible piece of cake by cutting the cake in half. This is the same idea, just extended: one party divides the state into districts, then the other chooses one district to "lock" and divides the remainder, then the process repeats.
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