[maxpalmer]

I'm one of the authors. Thanks for reading our paper. Happy to answer any questions.

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/

[vitus]

Hm. This doesn't seem like it does much if there's a sufficiently high concentration of cracked districts, relative to packed districts.

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.

[maxpalmer]

Suppose you're defining as Party B, and you draw 8 majority-B districts (2:3) and 2 majority-A districts. Then, when Party A is combining, they would pair each of the majority-A districts with a majority-B district with a smaller margin, resulting in 2 A districts and 3 B districts. This is an improvement compared to if B drew 5 districts unilaterally, where it could draw 4 majority-B districts.

[vitus]

Yes, it is an improvement in this specific scenario, since there's limited granularity in how we can draw the districts.

If instead we had 9 population nodes we could assign to each Define district, then we might be able to draw nine 4:5 districts in favor of B, and a single 9:0 district in favor of A. In that case, A cannot recover any of the unfairness that B introduced.

[stephencanon]

Biggest potential weakness seems like the ability for the merging party to strategically collapse districts such that two legislators from the opposing party are made to reside in the same district, creating a new district with no incumbent. Not all legislatures require that representatives live in the district, and there would be real trade-offs to doing so, but it would be a pretty powerful hammer to wield against up-and-coming opposition candidates.

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.

[maxpalmer]

You're right that this method doesn't protect incumbents. However, protecting incumbency and avoiding open-seat elections isn't necessarily a bad thing, and could increase electoral competition in some places. Some states don't allow incumbency to be taken into account when redistricting already.

[consumer451]

I really appreciate your work. It appears to address one of the biggest issues of our time.

Please do not get discouraged by anyone or anything. We need more of this.

[mfrieswyk]

Would it scale to beyond 2 parties?

[maxpalmer]

Potentially in some form, but we haven't investigated it. The utility functions for each party would be very different. Instead of trying to maximize the seats that they win, parties would also need to think about the coalitions that could form if no party won a majority of the seats.