Talk Elections

Iowa is the gold standard of redistricting with non-partisan maps that come from the legislative bureau based on a lengthy set of statutory rules. For congressional maps the districts must be of whole counties with as nearly equal population as practicable. This can be measured as the average of the absolute deviations of the districts and as the range from the smallest to largest district. There is also a compactness test which is primarily the difference between the E_W and N_S dimensions of each district added together. Unless it's way off it takes a backseat to population equality as required by federal law. The legislature does get to send a map back if they think a better plan that meets the criteria is possible, but that didn't happen this year.

The 2010-census map has 4 CDs with deviations (-41, +35, +23, -18), the absolute average is 29.25, and the range is 76.

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Given the case in WV over whole counties with minimum deviations, I thought it interesting to devote a thread to those states that can make CDs with whole counties only such that the range does not exceed 1% of the ideal district population. I'll add posts with examples that have appeared in other threads, and add some new ones. Others are welcome to add theirs and improve on the deviations of best offering, or make a case like the legislature that a slightly larger deviation better meets an important state goal.

I'll keep a tally of entered states that fit the bill here in the OP for reference.

Alabama (7 CDs, 67 counties): deviations +1750/+1523/+228/-1974/+200/-1438/-286; av dev 1057; range 3924.
Arkansas (4 CDs, 75 counties): deviations -136/+137/+138/-139; av dev 153; range 337.
Idaho (2 CDs, 44 counties): deviations +1/-1; av dev 1; range 2.
Iowa (4 CDs, 99 counties): deviations -41/+35/+23/-18; av dev 29.25; range 76.
Kansas (4 CDs, 105 counties): deviations -22/+3/+37/-17; av dev 19.75; range 59.
Louisiana (6 CDs, 64 parishes); deviations +1475/-1243/-226/+106/-909/+917; av dev 509.67; range 2718.
Mississippi (4 CDs, 82 counties); deviations +176/-152/-68/+45; av dev 110.25; range 328.
Nebraska (3 CDs, 93 counties); deviations -8/+12/-3; av dev 7.67; range 20.
New Mexico (3 CDs, 33 counties); deviations -737/+234/+503; av dev 491.33; range 1242.
Oklahoma (5 CDs, 77 counties); deviations -2/-557/-849/-1227/+2636; av dev 1054.2; range 3863.
West Virginia (3 CDs, 55 counties): deviations +113/+2/-116; average deviation 77; range 229.

Here's West Virginia as done by the Cooper 3 plan.

The average deviation is 77 and the range is 229.

I will also post Lewis' plan as perhaps the legislature feels that CD 1 is too bizarrely shaped in the Cooper plan.


This one has an average deviation of 186.33 and a range of 557.

Here was what I did for KS recently.

Mississippi:

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MS-01 - deviation +112 (60.7 McCain, 38.3 Obama)
MS-02 - deviation -365 (59.5 Obama, 39.9 McCain, 56.1% black VAP)
MS-03 - deviation +132 (59.4 McCain, 39.8 Obama)
MS-04 - deviation +122 (66.5 McCain, 32.5 Obama)

Nebraska:

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District 1: Deviation -240; 44.6% Obama.
District 2: Deviation 59; 48.6% Obama.
District 3: Deviation 182; 28.0% Obama.

Aesthetically, I'd prefer a District 2 which takes in most of Sarpy instead of going north; it would do a better job of keeping the Omaha MSA together than this plan does.

This is the best I could do at preserving CoI's, given that Louisiana has relatively few counties/parishes.

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Arkansas has a reasonable of counties so it does pretty well.

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CD 1: -136
CD 2: +167
CD 3: +138
CD 4: -169

av deviation 153
range 337 = 0.046%

Had AR done another county-based redistricting, it probably would have helped the state of WV defending a whole county approach.

What is the highest black VAP, and can a CD be drawn with over 50% as JL did in MS?

Probably not. Orleans is hedged in by Jefferson and St Tammany.

I also see that the table of deviations may be off. The plus side outweighs the minus side by 120. Louisiana's population exactly divides by six, so the pluses and minuses should cancel.

Edit: I've convinced myself that indeed 50% BVAP is not possible with whole counties in LA.

As in WV, if one wants to be a bit more irregular, the deviations can be reduced.

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CD 1: +176
CD 2: -152 (57.7% BVAP)
CD 3: -68
CD 4: +45

Only 3 districts that are over 30% black VAP:
1-> 35.9%
4-> 35.7%
6-> 34.5%

I don't think its possible to draw a black seat under an IA style map. In MS, the black population is concentrated along the delta. In LA, you'd have to find some way to connect East Baton Rouge and Orleans.

I agree that a majority BVAP district isn't possible. I think your matrix is off, perhaps due to some disconnected tiny precincts. I get the following deviations: +1475/-1243/-346/+338/-1141/+917.

Here's my take on OK. There aren't any other choices for CD-5 that keeps the district within 0.5% without using point contact (ie connecting only at the corner). Because of that the maximum deviation cannot be any less than 2,636 for CD 5. The map is helped by CD 1 which comes within 2 of the ideal population. These are the 5 deviations, with a range of 3863 (0.52%) and an average deviation of 1054.2.

CD 1 (-2)
CD 2 (-557)
CD 3 (-849)
CD 4 (-1227)
CD 5 (+2636)

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With only 67 counties, one wouldn't necessarily expect to make 7 CDs fit for AL within the 0.5% limit. They do, but with a couple of caveats. Like LA, no BVAP majority district is formed so it wouldn't pass the VRA. CD-7 is a black plurality district with 46.0% BVAP, and CD-6 is 39.1% BVAP. CD-6 also has the unpleasant feature that though Jefferson and Bibb are adjacent counties, there is no road that connects them.

The average deviation is 1057 and the range is 3924 (0.57%)

CD 1 (+1750)
CD 2 (+1523)
CD 3 (+228)
CD 4 (-1974)
CD 5 (+200)
CD 6 (-1438)
CD 7 (-286)

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New Mexico:

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Oregon, Colorado, and Utah can not be done.

I guess I could also use this map here:

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My guess is that a bureau like IA uses would insist on greater equality between districts. Keeping your CD 2, the counties can be shifted between CD 1 and 3 to keep all under 100. This has an average deviation of 39 and a range of 93 (0.015%).

CD 1: -34
CD 2: +59
CD 3: -24

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If compactness is not a factor, but only population deviation there's an amazingly precise plan that can be drawn. The range is only 20 (0.003%), and the average deviation is 7.67.

CD 1: -8
CD 2: +12
CD 3: -3

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Idaho, though it's a bit ugly:

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Most of the other states not mentioned can't be done. SC might be possible, but you might need to stretch the acceptable limit a bit.

It's ugly, but also you can't get to the eastern counties from the rest by roads within the district. With a slightly higher deviation of 146, I can stay connected by road and keep Boise metro together.

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Edit: I got a deviation of -134/+134 when I drew your map. You may have misplaced precinct.

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:

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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.

As I noted above, it looks like there is a missing precinct in the ID plan from realisticidealist. I double-checked by adding the county pops on the census website. Anyway, I thought I would try to recover ri's basic idea, by shifting a couple of counties. What I found is a plan of whole counties with a deviation of exactly 1! CD 1 has one too many people, and CD 2 has one too few. It still lacks a road to Lemhi county, but that's the price to pay.

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I like how you are thinking, and it anticipates the regional approach I have used in states like CA and NY. I was planning to do a separate thread for that type of state, I can start it using your IN if you like.

Maine is technically possible, just squeaking in under the 1% threshold:

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Deviations 5889 and 5890.

Obviously in New England it makes more sense to do things by town line than county line; counties aren't that important and you can be much more precise.  Maine is the only New England state where this is even theoretically possible, though.

I'd argue that keeping whole municipalities together at the expense of a couple more county splits is also the right policy in PA, NY, and NJ.  Counties do still have some power here in the Mid-Atlantic, but these three states have no unincorporated areas, or even any survey townships; municipalities hold most of the power.  And many of the counties are large enough that frequent splitting is unavoidable anyway.

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Tried South Carolina, pretty sure it's impossible mainly due to Greenville and Spartanburg.

We found 11 states that had a range of 1% or less using whole counties. I suspected that there could be a relationship between the number of counties per CD and the range. With the list from the thread, I did a regression analysis to a power law fit on the data. A power law graph is also known as a log-log plot uses the logarithm of the data values to find a linear fit.

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ID and OK appear as outliers since ID had an unusually perfect plan and OK was stuck by the counties around Oklahoma City. The remaining points fall on a straight line with 96% correlation. The best fit can be approximated by a power-law relation of the form R = (32E+6)/C^4. Translated this says the range is approximately equal to 32 million divided by the average number of counties per district raised to the fourth power.

Here's how it works out for those 11 states, showing the counties per CD and estimated range with the actual range found by our maps in parentheses.

AL 9.6; 3813 (3924)
AR 18.8; 259 (337)
ID 22.0; 137 (2)
IA 24.8; 85 (76)
KS 26.3; 67 (59)
LA 10.7; 2472 (2718)
MS 20.5; 181 (328)
NE 31.0; 35 (20)
NM 11.0; 2186 (1358)
OK 15.4; 569 (3863)
WV 18.3; 283 (229)
 
From this one can also estimate how many counties one should need to expect whole county redistricting to have a range of less than 1%. That limit is about 8.3 counties per district. With fewer counties, the model would predict a range in excess of 7000 or about 1% of an ideal district. The above ME example is a case in point, since it has only 8 counties per CD and has a range just over 1%.

Doh, I was thinking "range" was just the highest deviation for some reason.  That'll teach me to read better.

Can you do Washington(Preserving the acceptable mountain and ferry crossings)? I want to see how bad of a gerrymander 2010 is.

WA can't be done directly with whole counties since there are counties larger than a district. Once I complete the data analysis from those that can, I will suggest a way to extend that to states like WA.

It would be interesting to use the 2011 estimates to see whether maps would radically change from year to year.   And perhaps draw N+1 and N-1 districts.

I think the more interesting question is how rapidly a whole-county district map drawn with best precision become indistinguishable in terms of deviations from a more compact version that started with more generous population tolerances.

I got the green district less spread-out, at least:

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-737/+234/+503.

Interesting and the range is smaller, too. Since the purple district gets more spread out, I wonder if compactness is better or worse.

That's actually quite similar to the 1980's map, for what it's worth.

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I don't know what standards New Mexico used to redistrict in the 1980's, but there's definitely a precedent for a district stretching from the southwest across the southeast to the northeast.

Interesting thread.
What would this look like on 2020s numbers?