It doesn't matter at the abstraction of proportional representation, but it potentially matters quite a bit when you get into the nitty-gritty of actual elections.
It doesn't matter at the abstraction of proportional representation, but it potentially matters quite a bit when you get into the nitty-gritty of actual elections.
Seems like a pretty trivial way to break the algorithm. But I probably misunderstood something.
> "Valid districts are contiguous and have equal population. Strict constraints on compactness, geographic splits, or other restrictions are not necessary, but such limitations could be included. However, valid districts may not include “donuts,” where one district entirely encircles another."
If so, where I can I find more?
Note that this paper contains no optimality proofs.
There's a lot of mathy-looking stuff, but then instead of a proof we get "yeah we took this one particular Markov-chain algorithm and had it play against itself and it failed to generate a gerrymander".
If deployed in real life, an immense amount of power -- and therefore money -- will be at stake: certainly more than enough money to hire persons with intelligence equal to or greater than the creator of "the ShotBurst Algorithm" as consultants.
If an optimality proof is not possible, the only alternative is to test using real humans and (very substantial) real rewards.
[1]: https://static.cambridge.org/content/id/urn%3Acambridge.org%...
If you're interested, here is a (still in-progress) simulator I wrote where you can try out Define-Combine on a simple grid. https://mpalmer.shinyapps.io/DefineCombine/
I gerrymandered during the define phase using classic packing / cracking strategies, such that I had 8 majority-B districts (2:3) and 2 majority-A districts (4:1 and 5:0), and unsurprisingly, the only districts I was able to combine that were majority-A were those that included the packed districts.
If the overall split was, say, 27:23 instead of 25:25 such that we could define 9 majority-B districts in the define phase, then I would only have been able to define a single majority-A district in the combine phase.
(And yes, all of these gerrymandered districts would be considered safe B seats, as one would expect with a 20% margin)
There are also potentially issues if the packed districts are geographically clustered -- we see this a lot in states with a single predominant urban center (e.g. Kansas, Minnesota, Kentucky). In those cases, you might be forced to combine multiple packed districts due to pathological maps. For instance, consider a map where a Democratic bastion is districted into concentric rings -- that satisfies the contiguity requirement, yet only the outermost district abuts any Democratic-minority districts.