If every state had NC-style clusters, what would they end up like? (user search)
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  If every state had NC-style clusters, what would they end up like? (search mode)
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Author Topic: If every state had NC-style clusters, what would they end up like?  (Read 2040 times)
Kevinstat
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« on: November 26, 2021, 02:45:25 PM »

[...]
This may increase the deviation and require more county cuts. Imagine that you apportion five representatives to an area entitled to 4.85 representatives. This creates an unreasonable -3.0% deviation. But it also forces the 0.15 representatives to be placed in other districts. And what if that area is entitled to 3.15 representatives. Each district must have a population of exactly 1.0500000 quotas. You may be forcing another cut. If the area was entitled to 3.08 representatives you might have been able to divide it on a county line.
[...]

I don't want to clip your post, the whole thing does a great job summarizing the history of how the clusters come about, but the examples you give in the bolded paragraph are actually reasonable in deviation under North Carolina's current rules. As long as population does not deviate by more than ±5% off of the ideal district size, it is allowed. So a cluster entitled to 4.85 representatives getting 5 or a cluster entitled to 3.15 representatives getting 3 is actually within that acceptable range. You could even lose a tenth of an entitled delegate in the first example and it would still be fine.
[...]
I think jimrtex may have meant to write reasonable instead of unreasonable in the third sentence in the bolded paragraph. ("This creates a reasonable -3.0% deviation.")  The remainder in his example had no wiggle room, if you are committed to keeping each district within 5% of the ideal population.
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Kevinstat
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« Reply #1 on: November 26, 2021, 04:37:25 PM »
« Edited: November 26, 2021, 05:07:38 PM by Kevinstat »

For the Maine Senate, with 35 members (although under the Maine Constitution that number could also be 33 or 31), there are several NC-style clusters that would work, that don't involve relying on a northern Washington State Cascades-type boundary for contiguity. I would put Aroostook County's boundary with Piscataquis and Somerset counties in that category, as well as (at the congressional and State Senate levels but not the State House level, depending how far into a certain county the crossing district went) the Lincoln-Waldo and Hancock-Knox boundaries. Hancock-Knox, which might be the most easily identifiable "bad" connection as it involves going out to the ocean, is arguably the least egregious of these. Isle Au Haut in Knox County has its ferry connection to Stonington in Hancock County (also on an island but one with a road connection to the mainland) and at the State Senate level Isle Au Haut has alternated between Rockland- and Ellsworth/MDI/(most of the) Blue Hill peninsula-based districts. It will be moving into the latter come next year's primary and general elections. That seems fine to me but I wouldn't want anything else in Knox County being in a Hancock County-based district, or any Hancock County towns being in a Knox County based district. There's also long been an "Island" House district straddling the Knox-Hancock line, but not including Islesboro or any of Waldo County.

Okay, I got sidetracked there. Anyway, in Maine, there are a slew of NC-style clusters that would work, some being alternatives including some of the same counties so obviously you couldn't use the two together but even some of the ones without any counties in common are such that you couldn't do all of them, because it would leave the rest of the state outside of the ±5% range for the number of Senate districts that are left.

Androscoggin (2.8552 or 3×0.9517 quotas, so −4.83% for 3 districts), Cumberland (7.7861 or 8×0.9733 quotas, so −2.67% for 8 districts), Knox (1.0432 quotas, so +4.32% for 1 district), Waldo (1.0175 quotas, so +1.75% for 1 district) and Penobscot (3.9101 or 4×0.9775 quotas, so −2.25% for 4 districts) counties could all be their own cluster. But all of those could potentially be used to shore up counties or groups or counties that would otherwise be out or range or discontiguous, although the ones I've seen involving Waldo County seem rather silly (Franklin-Kennebec-Waldo-Hancock-Washington or Franklin-Kennebec-Somerset-Waldo-Hancock).

One measure of how well one is following the North Carolina method is the number of clusters (counties with no partial districts are their own cluster). The more clusters, the better.  I've come up with a couple "cover plans" for a 35-member Maine Senate with 8 clusters, and I thought I had one with 9 but then I realized I'd left out Piscataquis County.  I'll show what I've come up with in a later post (I'm having some computer power issues at the moment).
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Kevinstat
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« Reply #2 on: November 26, 2021, 05:18:47 PM »
« Edited: November 26, 2021, 05:37:02 PM by Kevinstat »

Some 8-cluster plans for a 35-member Maine Senate I've come up with:

Androscoggin (3 districts; 2.8552 or 3×0.9517 quotas; −4.83%)
Aroostook-Washington-Hancock-Penobscot-Piscataquis (8 districts; 8.2898 or 8×1.0362 quotas; +3.62%)
Cumberland (8 districts; 7.7861 or 8×0.9733 quotas; −2.67%)
Franklin-Somerset (2 districts; 2.0535 or 2×1.0268 quotas; +2.68%)
Kennebec-Lincoln-Sagadahoc (5 districts; 5.0245 or 5×1.0049 quotas; +0.49%)
Waldo (1 district; 1.0175 quotas; +1.75%)
Knox (1 district; 1.0432 quotas; +4.32%)
Oxford-York (7 districts; 6.9300 or 7×0.9900 quotas; −1.00%)

Androscoggin (3 districts; 2.8552 or 3×0.9517 quotas; −4.83%)
Aroostook-Washington-Hancock (4 districts; 3.9481 or 4×0.9870 quotas; −1.30%)
Cumberland-York (13 districts; 13.2318 or 13×1.0178 quotas; +1.78%)
Kennebec-Lincoln-Sagadahoc (5 districts; 5.0245 or 5×1.0049 quotas; +0.49%)
Waldo (1 district; 1.0175 quotas; +1.75%)
Knox (1 district; 1.0432 quotas; +4.32%)
Oxford-Franklin-Somerset-Piscataquis (4 districts; 3.9695 or 4×0.9924 quotas; −0.76%)
Penobscot (4 districts; 3.9101 or 4×0.9775 quotas; −2.25%)

What I thought I had for a 9-cluster plan:

Androscoggin (3 districts; 2.8552 or 3×0.9517 quotas; −4.83%)
Aroostook-Washington-Hancock (4 districts; 3.9481 or 4×0.9870 quotas; −1.30%)
Cumberland (8 districts; 7.7861 or 8×0.9733 quotas; −2.67%)
Franklin-Somerset (2 districts; 2.0535 or 2×1.0268 quotas; +2.68%)
Kennebec-Lincoln-Sagadahoc (5 districts; 5.0245 or 5×1.0049 quotas; +0.49%)
Waldo (1 district; 1.0175 quotas; +1.75%)
Knox (1 district; 1.0432 quotas; +4.32%)
Oxford-York (7 districts; 6.9300 or 7×0.9900 quotas; −1.00%)
Penobscot (4 districts; 3.9101 or 4×0.9775 quotas; −2.25%)
Piscataquis (0 districts; 0.4316 or 0×∞ quotas; +∞%)
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Kevinstat
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Posts: 1,823


« Reply #3 on: January 08, 2022, 02:53:03 PM »
« Edited: January 08, 2022, 09:48:58 PM by Kevinstat »

Some 8-cluster plans for a 35-member Maine Senate I've come up with:

Androscoggin (3 districts; 2.8552 or 3×0.9517 quotas; −4.83%)
Aroostook-Washington-Hancock-Penobscot-Piscataquis (8 districts; 8.2898 or 8×1.0362 quotas; +3.62%)
Cumberland (8 districts; 7.7861 or 8×0.9733 quotas; −2.67%)
Franklin-Somerset (2 districts; 2.0535 or 2×1.0268 quotas; +2.68%)
Kennebec-Lincoln-Sagadahoc (5 districts; 5.0245 or 5×1.0049 quotas; +0.49%)
Waldo (1 district; 1.0175 quotas; +1.75%)
Knox (1 district; 1.0432 quotas; +4.32%)
Oxford-York (7 districts; 6.9300 or 7×0.9900 quotas; −1.00%)

Androscoggin (3 districts; 2.8552 or 3×0.9517 quotas; −4.83%)
Aroostook-Washington-Hancock (4 districts; 3.9481 or 4×0.9870 quotas; −1.30%)
Cumberland-York (13 districts; 13.2318 or 13×1.0178 quotas; +1.78%)
Kennebec-Lincoln-Sagadahoc (5 districts; 5.0245 or 5×1.0049 quotas; +0.49%)
Waldo (1 district; 1.0175 quotas; +1.75%)
Knox (1 district; 1.0432 quotas; +4.32%)
Oxford-Franklin-Somerset-Piscataquis (4 districts; 3.9695 or 4×0.9924 quotas; −0.76%)
Penobscot (4 districts; 3.9101 or 4×0.9775 quotas; −2.25%)

What I thought I had for a 9-cluster plan:

Androscoggin (3 districts; 2.8552 or 3×0.9517 quotas; −4.83%)
Aroostook-Washington-Hancock (4 districts; 3.9481 or 4×0.9870 quotas; −1.30%)
Cumberland (8 districts; 7.7861 or 8×0.9733 quotas; −2.67%)
Franklin-Somerset (2 districts; 2.0535 or 2×1.0268 quotas; +2.68%)
Kennebec-Lincoln-Sagadahoc (5 districts; 5.0245 or 5×1.0049 quotas; +0.49%)
Waldo (1 district; 1.0175 quotas; +1.75%)
Knox (1 district; 1.0432 quotas; +4.32%)
Oxford-York (7 districts; 6.9300 or 7×0.9900 quotas; −1.00%)
Penobscot (4 districts; 3.9101 or 4×0.9775 quotas; −2.25%)
Piscataquis (0 districts; 0.4316 or 0×∞ quotas; +∞%)

How many are Texas-style where you apportion a whole number of districts to large counties, and one district for any surplus or smaller counties. The goal is to avoid dividing counties with a population smaller than a quota.

My apologies for the very late reply.  I had had the need to reply in the back of my mind, but whenever I tried to come up with a scheme of clusters that would be more compliant with the Texas rules than either of my two above, I would fail and then move on to other things.  Now I've decided to work with what I already had.

While in the "scoring" of your plan for Minnesota in the second post on this page (reply #26), you treat the splits of remainders the same as splits of a small county, I am going to place an emphasis on the part of what you wrote that I put in boldface.  Since the second of my NC-style clusters above would force a split of a small county (Washington) I'll use the first cluster (the one that I haven't struck out in my above quote of that post).  It's kind of fortunate that Penobscot has just under 4 quotas rather than just over, as my plan has only two districts entirely in Penobscot County, and I'm glad I'm not giving Penobscot County two fewer whole districts than it is entitled to.  I'll follow your convention of naming clusters after the most populous county in them, but I'll also list the counties in the cluster, the population of the cluster, and the population of the districts in the cluster assuming the closest mathematically possible equality without dividing people.

First, I'll list the counties, 2020 census population and "quota" (# of 1/35ths of Maine's 2020 census population), plus how many approximate total "fractional" districts the county would have under my plan (with the district being as much of a district as the portion of its population within the county), with the number shown being the decimal fraction if all districts within the cluster had exactly the same population:

Androscoggin, pop. 111,139 (2.855 quotas; 3 districts)
Aroostook, pop. 67,105 (1.724 quotas; ≈ 1.664 districts)
Cumberland, pop. 303,069 (7.786 quotas; 8 districts)
Franklin, pop. 29,456 (0.757 quotas; ≈ 0.737 districts)
Hancock, pop. 55,478 (1.425 quotas; ≈ 1.375 districts)
Kennebec, pop. 123,642 (3.176 quotas; ≈ 3.161 districts)
Knox, pop. 40,607 (1.043 quotas; 1 district)
Lincoln, pop. 35,237 (0.905 quotas; ≈ 0.901 districts)
Oxford, pop. 57,777 (1.484 quotas; ≈ 1.499 districts)
Penobscot, pop. 152,199 (3.910 quotas; ≈ 3.773 districts)
Piscataquis, pop. 16,800 (0.432 quotas; ≈ 0.417 districts)
Sagadahoc, pop. 36,699 (0.943 quotas; ≈ 0.938 districts)
Somerset, pop. 50,477 (1.297 quotas; ≈ 1.263 districts)
Waldo, pop. 39,607 (1.018 quotas; 1 district)
Washington, pop. 31,095 (0.799 quotas; ≈ 0.771 districts)
York, pop. 211,972 (5.446 quotas; ≈ 5.501 districts)

Okay.  Let's start from the north, getting the worst out of the way first.

Penobscot cluster (Aroostook, Hancock, Penobscot, Piscataquis & Washington), pop. 322,677 (8.290 quotas); 8 districts with avg. pop. 40,334.625 (+3.62%):
1 district: ≈ 60.1% of Aroostook
1 district: ≈ 30.9% of Aroostook (≈ 26,770.375 people; ≈ 66.4% of the district) (1 large county split) & 8.9% of Penobscot (≈ 13,564.25 people; ≈ 33.6% of the district) (1 large county split)
1 district: ≈ 15.5% of Penobscot (≈ 23,534.625 people; ≈ 58.3% of the district) (1 small county split, since that's a split of the Penobscot surplus) & Piscataquis (16,800 people; ≈ 41.7% of the district)
2 districts: each ≈ 26.5% of Penobscot
1 district: ≈ 10.6% of Hancock (≈ 5,903.75 people; ≈ 14.6% of the district) (1 large county split) & ≈ 22.6% of Penobscot (≈ 34,430.875 people; ≈ 85.4% of the district) (1 small county split, since that's another split of the Penobscot surplus)
1 district: ≈ 72.7% of Hancock
1 district: ≈ 16.7% of Hancock (≈ 9,239.625 people; ≈ 22.9% of the district) (1 small county split, since that's a split of the Hancock surplus) & Washington (31,095 people; ≈ 77.1% of the district)

Somerset cluster (Franklin & Somerset), pop. 79,933 (2.054 quotas); 2 districts with avg. pop. 39,966.5 (+2.68%):
1 district: ≈ 79.2% of Somerset
1 district: Franklin (29,456 people; ≈ 73.7% of the district) and ≈ 20.8% of Somerset (≈ 10,510.5 people; ≈ 26.3% of the district) (1 large county split)

Waldo cluster (Waldo), pop. 39,607 (1.018 quotas); 1 district with pop. 39,607 (+1.75%):
1 district: Waldo

Knox cluster (Knox), pop. 40,607 (1.043 quotas); 1 district with pop. 40,607 (+4.32%):
1 district: Knox

Kennebec cluster (Kennebec, Lincoln & Sagadahoc), pop. 195,578 (5.025 quotas); 5 districts with avg. pop. 39,115.6 (+0.49%):
1 district: ≈ 3.1% of Kennebec (≈ 3,878.6 people; ≈ 9.9% of the district) (1 large county split) & Lincoln (35,237 people; ≈ 90.1% of the district)
1 district: ≈ 1.9% of Kennebec (≈ 2,416.6 people; ≈ 6.2% of the district) (1 small county split, since that's a split of the Kennebec surplus) & Sagadahoc (36,699 people; ≈ 93.8% of the district)
3 districts: each ≈ 31.6% of Kennebec

Androscoggin cluster (Androscoggin), pop. 111,139 (2.855 quotas); 3 districts with avg pop. 37,046.33 (−4.83%):
3 districts: each ≈ 33.3% of Androscoggin

Cumberland cluster (Cumberland), pop. 303,069 (7.786); 8 districts with avg. pop. 37,883.625 (−2.68%):
8 districts: each ≈ 12.5% of Cumberland

York cluster (Oxford & York), pop. 269,749 (6.930); 7 districts with avg. pop. 38,535.57 (−1.00%):
1 district: ≈ 66.7% of Oxford
1 district: ≈ 33.3% of Oxford (≈ 19,241.43 people; ≈ 49.9% of the district) (1 large county split) and ≈ 9.1% of York (≈ 19,294.14 people; ≈ 50.1% of the district) (1 large county split)
5 districts: each ≈ 18.2% of York

Overall:
4 small county splits (all splits of remainders; no actually "small county" (one with less than 1/35th of Maine's population) is split)
7 large county splits (if I've calculated those correctly)

[Edited several times in the afternoon and evening of the day I posted this, at first as I posted it before I was done to a avoid the risk of losing all my work, and then because I saw an error or something I saw fit to add.]
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