# Do parties whose support is geographically concentrated have an advantage in “cake cutting” redistricting?

In the question about preventing political gerrymandering, I brought up a new method for preventing Gerrymandering using game theory. This involves one party, let's call them red, drawing district lines, and then the second party, let's call them blue, locking one of the districts. Then the blue party would draw new lines and the red party would lock one of those districts. This study demonstrated that this method doesn't convey an advantage to the party that goes first.

However, in the comments, a user suggested that this redistricting method might not be as "fair" as it originally looks.

I'm not sure that it's symmetrically unfair. Democrats, who want to crack their urban districts, would seem to have an advantage over Republicans who want to pack those districts...

It's an advantage for drawing the lines to crack rather than pack. Because it is possible to draw all districts cracked, where it is not possible to draw all districts packed in your favor. I.e. Democrats have an inherent advantage under this system due to how they clump and how this system works...

It's in the quoted matter: "In fact, we establish mathematically that this protocol can prevent one party from packing a targeted group of voters into a district." Note how it says that it prevents packing, which is what Republicans want to do. But it doesn't prevent cracking, which is what Democrats want to do.

I'm intrigued by this explanation, however I'm having trouble intuitively understand why geographically clustered parties would have an advantage, and I can't draw a simple example showing how this would be the case. Do parties whose support is geographically concentrated have an advantage over parties whose support is spread wider in this kind of "I cut you choose" redistricting?

• Will depend on your definition of fair. Yes, the commenter is misrepresenting the paper, but that doesn't matter. Both sides are quick to point to states where an almost 50-50 vote gives a large discrepancy with the elected officials, ignoring the fact that redistricting itself had a purpose even before the blatant current abuse in introducing a geographical dependency of representation. – DonFusili Jul 8 '19 at 15:34
• Anyway, for people wanting to construct an answer, the comment is basically touched on in remark 2.7 and section 5 of the original paper. It can be spun either way, so there should be at least 2 answers. – DonFusili Jul 8 '19 at 15:42
• @DonFusili I'm explicitly not looking for fair, just at advantage in seats won. – lazarusL Jul 8 '19 at 15:55
• The problem with Gerrymandering is not that we lack an algorithm for fair redistricting. Virtually every country in the world manages without the patently unfair map that the US has. The problem is that partisan governments are allowed to redistrict at will with no checks. – DJClayworth Jul 8 '19 at 19:09
• @lazarusL They are, but if you actually read the paper, they only show asymptotic non-partisan results with a huge amounts of extra conditions for real-world applications. The match checks out for arbitrary, clearly defined loyal districts of equal size, if that's your question. But the caveats given boil down to "We believe it's better than the nonsense we use right now, but haven't investigated a number of influences", which will just allow responses to be spun either way. – DonFusili Jul 9 '19 at 7:05