Iowa-style Redistricting III: The Kentucky Rule

[muon2]

Here's TX in the same style. Like GA counties greater than a CD are treated only in their excess population above a whole number of CDs. They are divided to keep the number of CDs serving the county at the minimum number.

The range is 4279 and the average deviation of whole counties not counting their splits is 629.8. The CD in Denton largely sets the range with a deviation of +2563.



Renumbered so groups in one county are consecutive:

CD 1-2: -70 (77.9%, 76.3% HVAP)
CD 3: -245
CD 4: -737
CD 5: +701 (49.4% HVAP)
CD 6-7: -459 (87.0%, 85.7% HVAP)
CD 9-11: +563 (61.8%, 61.7% HVAP)
CD 12: -410
CD 13-14: -718 (41.7% HVAP)
CD 15: +223
CD 16-18: -470 (17=37.4% WVAP)
CD 19: +2563
CD 20-24: -248 (20=48.4% HVAP, 21=45.0% BVAP)
CD 25: +1409
CD 26: -834
CD 27-32: -242 (30=60.3% HVAP, 31=50.9% BVAP, 32=62.4% HVAP)
CD 33: +810
CD 34: -1716
CD 35: -47
CD 36: +48

[muon2]

My Indiana map from the other thread might work.  The deviation's a little high, though it is under 1 percent at least.

If you loosen the requirements just a tiny bit- up the deviation, split counties which are larger than a CD- then you can almost do this with Indiana:



1: -3498
2: -361
3: 2185
4: -719
5: 2176
6: 1097
7: 992
8: -50
9: -1818

It may be possible to lower the deviation on CD 1 if you're willing to get really ugly, and sacrifice that beautiful CD 8.  Really, the whole map looks freakishly clean, save the jigsaw boundary between 4 and 5.

That works fine for now and perhaps someone will find a combination that reduces the deviations. I assumed that CD 5 and 7 are combined districts in my OP entry. Let me know if that's wrong.

IN doesn't have the situation of large counties next to each other in a way that can force high deviations. Based on that, it seemed like one should do much better if compactness is not a consideration. Indeed CD 6 and CD 5+7 can be made nearly exact. Overall this has a range of 584 and an average deviation of 110.



CD 1: +124
CD 2: -60
CD 3: -131
CD 4: +296
CD 5: +16
CD 6: -4
CD 7: -9
CD 8: +60
CD 9: -288

[muon2]

NC took a bit of work due to the number of populous counties, but here's version that comes in with a range under 1%. All the black-majority districts are gone, and the best is CD 4 at 34.0% BVAP. The whole county range is 6974 and the average deviation of the 11 groups is 1530.4.



CD 1&13: +2826
CD 2: -1257
CD 3: +1351
CD 4: -716
CD 5: -1877
CD 6: -319
CD 7: +352
CD 8&12: +3279
CD 9: +191
CD 10: +3695
CD 11: -971

[muon2]

Here's a first attempt at Virginia.  Fairfax+Fairfax+Arlington+Alexandria is just over the right size for two districts, and everything else is small enough to "work".  Of course, when I say "work", I include the caveat that there are two cases of using water contiguity (the 7th crosses the York, and the bridge across the James in the Hampton Roads district briefly goes through Suffolk), and the VRA is blatantly disregarded.  I'm pretty sure a better map is possible, but (especially if you want to minimize water jumps) you're not going to do better than the current 2nd's -1016.



1: 1056
2: -1016
3: 215
4: -500
5: 1012
6: -1966
7: 517
8: 498
9: 427
10: -198
11: -47

It seems that if one really wants to stick to the rules, then Fairfax county can only be split between two districts. Since it is stuck with Arlington, Alexandria and Falls Church, that area is 9484 over the population. Technically at that exceeds 1% of a district and wouldn't qualify, but if evenly split each part should be over by 0.6% to 0.7%. If no other district is more than 0.3% under population the CDs can stay within a 1% range. That forces almost every other CD to be under population but not by more than 2000. With lots of counties and independent cities it turns out that it is possible.



CD 3 really is connected to Powhatan county in the west by more than a point (there is a small common border in the James river). Needless to say that not only are rivers hopped as needed but so is the Chesapeake Bay. If MD can do strange things with MD 3 along the Bay, then why not just hop it entirely in VA.

As I drew it, I used CD 4 to be the best BVAP district I could make given the constraints. It is 45.6% BVAP and 65.7% Obama. It is quite possible that it would elect a black candidate of choice despite falling under 50% BVAP.

Here are all the deviations:
CD 1: -1887
CD 2: -1993
CD 3: +724
CD 4: -1576
CD 5: -663
CD 6: -1862
CD 7: -1118
CD 8: +4923
CD 9: -373
CD 10: -738
CD 11: +4561

[muon2]

So I have folded the results from this thread with the ones from the pure IA-style states and RI and CT using towns. The range has been reduced to a logarithm base 10 so 1 means a range of 10, 2 means a range of 100, 3 means a range of 1000 and 4 means a range of 10K. Most of the data lies on or below a line drawn in green indicating that an IA-style division should reasonable be expected to have at least that small of a range given the number of counties per district.



Points shaded purple represent states that all have a county that is between 95% and 100% of a district. All three points that are definitely above the line (OK, GA, TX) are in this group, and one might conclude that such counties make it difficult to to find a match with neighboring counties to make districts with suitably small population deviations. Some states in this category do happen to have the right sized counties.

Statistical fluctuations in the distribution of the counties play a role for all states. It has been noted in the threads that some states couldn't be modeled this way at all (eg. OR, MI, TN). Other states like NV and ID (both in yellow) do much better than expected given the number of counties available.

One conclusion one might draw is that any plan below the green line is statistically reasonable as a whole county split of the state. That leaves other factors like erosity that can be balanced against this population test. The green line itself can be approximated by a series of thresholds based on the average number of counties per district as a fraction of the district size as follows:

9 : 1.0%
10: 0.8%
11: 0.6%
12: 0.5%
13: 0.4%
14: 0.3%
15: 0.25%
16: 0.2%
17: 0.15%
18: 0.12%
19: 0.10%

For each additional 10 counties per district divide the above percentage by 10. For example 36 counties per district would expect a division with a range no more than 0.002% (0.2%/100) of the ideal district size.