Iowa-style Redistricting III: The Kentucky Rule

[muon2]

Some states have a county that is too big for a CD, and therefore cannot be split into CDs with counties only using IA rules. One example is KY where Jefferson is 17,868 persons too large for a CD. A solution is to treat Jefferson as if it were only 17,868 persons and divide the state into 5 CDs instead of 6. One would still use whole counties and minimize the range from the largest to smallest CD (keeping it under 1% in any case). Afterwards one can split the large county in two to create the right number of CDs.

This could also apply to states with a county large enough for 2 CDs as in NV. I'll keep a tally of states on this OP. Combined CDs with the large county will be in parentheses. The average absolute deviation will assume the reduced number of CDs.

GA (159 counties, 14 CDs in 12): CD 1: +587/+677/+139/-82/(+140)/(+644)/+354/+573/+138/+22/+708/-3897. Range 4605, Av Dev 663.4.
IN (92 counties, 9 CDs in 8 ): +124/-60/-131/+296/(+6)/-4/+60/-288. Range 584, Av Dev 121.1.
KY (120 counties, 6 CDs in 5): -68/(+44)/-53/+118/-41. Range 186, Av Dev 64.8.
MO (115 counties, 8 CDs in 7): (-27)/-77/+134/+51/+21/+10/-113. Range 247, Av Dev 61.8.
NV (17 counties, 4 CDs in 2): -234/(+233). Range 437, Av Dev 233.5.
NC (100 counties, 13 CDs in 11): (+2826)/-1257/+1351/-716/-1877/-319/+352/(+3279)/+191/+3695/-971. Range 6974, Av Dev 1530.4.
TX (254 counties, 36 CDs in 20): (-70)/-245/-737/+701/(-459)/(+563)/-410/(-718)/+223/(-470)/+2563/(-248)/+1409/-834/(-242)/+810/-1716/-47/+48. Range 4279. Av Dev 629.8.
UT (29 counties, 4 CDs in 3): +461/(-15)/-445. Range 906, Av Dev 307.
VA (95 counties, 39 cities, 11 CDs in 10): +1056/-1016/+215/-500/+1012/-1966/+517/+498/+427/(-245). Range 3022, Av Dev 678.
WI (72 counties, 8 CDs in 7): -2794/+38/-106/(+2275)/-155/+391/+353. Range 5069, Av Dev 873.1.

[muon2]

Here's my example for KY. Based on the work in the Iowa-style states, one ought to be able to cut the range down further. CD 2 and 3 are separated in the map using the DRA precincts.



CD 1: -68
CD 2: +87
CD 3: -43 (combined with CD 2 it's +44)
CD 4: -53
CD 5: +118
CD 6: -41

[muon2]

NV is a case where Clark county can be treated as if the population were 600,994, noting that leaves two other CDs completely contained. The smallest deviation I found is CD 2 = -234, the rest +233 for a range of 467.



Though it is contiguous in a legal sense Washoe only connects to Humboldt and Pershing directly by local unpaved roads. Those aren't necessarily desirable ways to connect a district, so one can require paved state highways to go between county seats to establish contiguity. That leaves the following map with CD 2 = +2189 and the rest -2190 for a range of 4379.

[traininthedistance]

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.

[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.

[traininthedistance]

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.

Sounds good to me.  It's probably possible to reduce the deviations if you're willing to get ugly; I'd expect the size of counties in the Gary area and surrounding Indy will prevent you from actually getting anywhere close to KY or NV.

[muon2]

In UT the group of Salt Lake, Davis, Morgan, and Summit are only 15 under the ideal population for 2 CDs. Splitting the rest of the counties and dividing Salt Lake so that no cities are split gives this map.



The deviations in DRA are
CD 1: +455
CD 2: +122
CD 3: -109
CD 4: -444
However, the overall population is 7 less than the actual state population. Using the Census counts for the counties one gets
CD 1: +461
CD 2/3: -15
CD 4: -445
It looks like the offset is in Weber county.

The other downside of this map is that it relies on a connection between Box Elder and Tooele on the west side of the Great Salt Lake. I see nothing but dirt trails to make that link, so it's legal but not well connected. I don't know if there is an overall plan that can stay under 0.5% deviation and not use that link.

[Torie]

Do the Iowa rules have an erosity constraint?

[traininthedistance]

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

[muon2]

Do the Iowa rules have an erosity constraint?

Not directly. They have a compactness constraint which looks at both the difference between the north-south and east-west dimensions of a district and the total perimeter of the district. The perimeter measure constrains erosity, but it is specifically secondary to rules regarding population equality, contiguity, and preservation of political subdivisions. In practice, it cannot force additional splits, but it does govern the shape within a split. It can also move one to a different grouping of counties if plans are otherwise equivalent from the perspective of county integrity.

I think there's some utility in testing how well the Iowa rules work in other states, since they are so often lauded by redistricting reform groups. It's also useful to discern if there are mathematical relationships that can be extracted from the application of the rules.

As you can see, I'm also looking at the effect of the contiguity constraint in its simple form. The most equal population divisions sometimes require contiguity without the benefit of a paved road. This shows up in both NV and UT above. It also appeared in ID where a near perfect division of whole counties exists but there's no road to connect one of the counties to the rest without leaving the district. Strict Iowa rules would require the plan anyway.

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.

[Torie]

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

This is an example of what I mean about forced erosity via the application of a strict set of rules, without flex. It is an obstacle to selling the approach.

[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

This is an example of what I mean about forced erosity via the application of a strict set of rules, without flex. It is an obstacle to selling the approach.

But how do you measure it in areas dominated by rivers or mountains? In this VA map I only find CDs 6 and 10 at all unusual given the geography of the state. Compare it to the current map (2012 is hardly changed).



If you want to give weight to another factor other than fixed political boundaries, it needs to be well defined to avoid abuse. For example, you could tighten population tolerances which then forces chops and then permits other compactness measures to come into play. I'm not convinced as to how tight they should be yet. Hence an exercise like this.

[Torie]

Well if geography justifies it, like it justifies Victorville taking in Mono County, I accept that. If. I question whether a couple of CD's can be "saved" based on geography however, as you alluded to Mike.

Since this is your forte Mike, perhaps you could suggest a compactness test (make it as simple and comprehensible as possible, but enough to avoid visual "pornography," to be applied as appropriate, or ignored as appropriate, but nevertheless a test), that could be used for some flex, where appropriate.

[traininthedistance]

Missouri:



1: -293
2: -54
3: -48
4: 81
5: 1136
6: -241
7: -883
8: -181

District 1 is obviously entirely within St. Louis County, and District 3 uses the remainder to connect St. Louis City to the rest of the district; town lines are hewed to just about as well as DRA will allow.  And yes, that shape is absolutely necessary given the size of the other surrounding suburban counties.  I'm almost certain Districts 1, 2, and 3 can't be improved on, you may be able to do something horribly ugly in the Springfield area to lower the deviations outstate, but I've tried enough permutations for now.

The map's a beaut, aint it?

[traininthedistance]

Tennessee is impossible: while Shelby (Memphis) is the only county larger than a CD, you have to split at least one county in the Nashville area as well.

[traininthedistance]

The Kentucky Rule can be extended to states with more than one county which is too large for a CD.

Well, it can be extended to at least one of those states.  Presenting Georgia.



1: -174
2: -52; 46.1% black VAP (plurality black by total population, minority-majority by VAP)
3: -185
4: -82; 51.5% black VAP
5: 1302; 52.1% black VAP
6: 2105
7: 1765; 44.7% white VAP
8: -165
9: 2816
10: -1
11:  -2143
12: 198
13: -1484; 46.5% black VAP (plurality)
14: -3897

Fulton and Gwinnett are the two counties which are over a CD; they each get a district.  6 then mops up both remainders and a couple exurban counties.  Now, many folks know that DeKalb is by happy accident almost perfectly the size of a CD, but even more fortuitously, Cobb comes just close enough, with a deviation of less than 4000.  The range is 6,829, just under the 1% threshold.  All the districts surrounding Cobb and DeKalb have to deal with higher deviations, but the more rural districts– 1, 2, 3, 8, 10, and 12– are all under 200 deviation, and 10 is almost perfect.

As an extra-special bonus, this map is arguably VRA compliant!  Doing so requires that 3 be a little ugly, but it's a small price to pay when the rest of the map works out so perfectly.

[Torie]

Missouri:



1: -293
2: -54
3: -48
4: 81
5: 1136
6: -241
7: -883
8: -181

District 1 is obviously entirely within St. Louis County, and District 3 uses the remainder to connect St. Louis City to the rest of the district; town lines are hewed to just about as well as DRA will allow.  And yes, that shape is absolutely necessary given the size of the other surrounding suburban counties.  I'm almost certain Districts 1, 2, and 3 can't be improved on, you may be able to do something horribly ugly in the Springfield area to lower the deviations outstate, but I've tried enough permutations for now.

The map's a beaut, aint it?

Yes, another epic fail. Good work lad! 

[traininthedistance]

Yes, another epic fail. Good work lad! 

You just think it's an epic fail because it would send an entirely reasonable three Democrats to Congress.

[muon2]

Here's my initial plan for MO. I get the range down to 638 and the av dev to 221. I split St Louis county to create a more compact district with St Louis city that also provides an opportunity black district at 45.2% BVAP.



Deviations by district:
CD 1: -91
CD 2: +219
CD 3: -52
CD 4: -170
CD 5: +274
CD 6: +392
CD 7: -291
CD 8: -282

I can get the KC CD deviation down to -106, but I haven't worked out the rest of the plan.

[Joe Republic]

Your MO-05 looks like a penis. That is all.

[traininthedistance]

Wisconsin:



1: -2794
2: -138
3: -328
4: 1275
5: 1000
6: -1029
7: -296
8: 2312

As usual, the metro areas are the primary limiting factor in how low you can get the deviations.  Waukesha+Ozaukee+Milwaukee in 2 districts is (I'm pretty sure) the only way to attach the Milwaukee remainder to a district that doesn't split counties, which forces the high-deviation (though compact) District 1, and if you want to avoid touch-point in 5 then you have to split Milwaukee City somehow.

The other five districts are pretty and logical at least.  As usual, smaller deviations might be possible, though they'd surely produce a worse map.

[muon2]

Missouri:



1: -293
2: -54
3: -48
4: 81
5: 1136
6: -241
7: -883
8: -181

District 1 is obviously entirely within St. Louis County, and District 3 uses the remainder to connect St. Louis City to the rest of the district; town lines are hewed to just about as well as DRA will allow.  And yes, that shape is absolutely necessary given the size of the other surrounding suburban counties.  I'm almost certain Districts 1, 2, and 3 can't be improved on, you may be able to do something horribly ugly in the Springfield area to lower the deviations outstate, but I've tried enough permutations for now.

The map's a beaut, aint it?

Yes, another epic fail. Good work lad!  

If you really want to cringe, try this one. The range is down to 247 and the average deviation is only 55. There's only a minimal cut of one community in St Louis county. CD 2 has no road connection across the Missouri River.

What I seek are the other factors that can be "consistently applied" to mitigate the two factors of county integrity and minimal population deviation. Part of that requires knowing the likely range of population deviation that can be achieved in the absence of other factors. For example, how much excess boundary (ie erosity) is sufficient to permit relaxation of population deviation? I do hope the WV case answers this.



CD 1: -32
CD 2: -77
CD 3: +5
CD 4: +134
CD 5: +51
CD 6: +21
CD 7: +10
CD 8: -113

[muon2]

Wisconsin:



1: -2794
2: -138
3: -328
4: 1275
5: 1000
6: -1029
7: -296
8: 2312

As usual, the metro areas are the primary limiting factor in how low you can get the deviations.  Waukesha+Ozaukee+Milwaukee in 2 districts is (I'm pretty sure) the only way to attach the Milwaukee remainder to a district that doesn't split counties, which forces the high-deviation (though compact) District 1, and if you want to avoid touch-point in 5 then you have to split Milwaukee City somehow.

The other five districts are pretty and logical at least.  As usual, smaller deviations might be possible, though they'd surely produce a worse map.

I agree with your assessment of SE WI, and it's nice that CDs 1,4, and 5 together only have a deviation of -519. I would separate Ozaukee and Waukesha and split Milwaukee county differently if I follow a comment about bridging fragments from dpmapper in the recent CA discussion.

It looks like you may have a misplaced precinct between CD 2 and CD 3. I get deviations of +38 and -533 respectively for those.

I've also made a shift in CDs 6, 7, and 8 to test your hypothesis about smaller deiations with a worse map. The result is below. It appears to make CD 6 more compact and CD 8 is also still fairly compact, but CD 7 seems more erose.

If I use a simple test suggested by a comment from jimrtex, I can look at the number of counties that are contiguous to counties in other CDs in that state. Your plan has 51 with a population range of 5106. My modification increases the border counties to 52 and reduces the range to 4623. This is perhaps the type of trade off Torie is looking for.



CD 1: -2794
CD 2: +38
CD 3: -533
CD 4: +1374
CD 5: +901
CD 6: +1829
CD 7: -671
CD 8: -142

Footnote: By really contorting the CDs other than CDs 1, 2, 4, and 5 the range can be made to depend entirely on the difference between CD 1 and larger of CD 4 and 5. Still splitting only Milwaukee, I found a range of 3934. The other CDs had deviations of -106/-155/+391/+353. However, this doesn't improve the range considering 4 and 5 together.

[traininthedistance]

CD 1: -2794
CD 2: +38
CD 3: -533
CD 4: +1374
CD 5: +901
CD 6: +1829
CD 7: -671
CD 8: -142

Footnote: By really contorting the CDs other than CDs 1, 2, 4, and 5 the range can be made to depend entirely on the difference between CD 1 and larger of CD 4 and 5. Still splitting only Milwaukee, I found a range of 3934. The other CDs had deviations of -106/-155/+391/+353. However, this doesn't improve the range considering 4 and 5 together.

It's a tiny bit more erose, but still entirely reasonable.  Your map is a definite improvement here.

[muon2]

The Kentucky Rule can be extended to states with more than one county which is too large for a CD.

Well, it can be extended to at least one of those states.  Presenting Georgia.



1: -174
2: -52; 46.1% black VAP (plurality black by total population, minority-majority by VAP)
3: -185
4: -82; 51.5% black VAP
5: 1302; 52.1% black VAP
6: 2105
7: 1765; 44.7% white VAP
8: -165
9: 2816
10: -1
11:  -2143
12: 198
13: -1484; 46.5% black VAP (plurality)
14: -3897

Fulton and Gwinnett are the two counties which are over a CD; they each get a district.  6 then mops up both remainders and a couple exurban counties.  Now, many folks know that DeKalb is by happy accident almost perfectly the size of a CD, but even more fortuitously, Cobb comes just close enough, with a deviation of less than 4000.  The range is 6,829, just under the 1% threshold.  All the districts surrounding Cobb and DeKalb have to deal with higher deviations, but the more rural districts– 1, 2, 3, 8, 10, and 12– are all under 200 deviation, and 10 is almost perfect.

As an extra-special bonus, this map is arguably VRA compliant!  Doing so requires that 3 be a little ugly, but it's a small price to pay when the rest of the map works out so perfectly.

I like CD 10 and the VRA effort, but the total deviation for the combined 5, 6 and 7 is over 5K and would make too large of a range with 14 if Fulton and Gwinnett were reduced by subtracting exactly one CD each. DeKalb is a near perfect size for a CD, but Cobb's deviation of -3897 sets a minimum range that would occur if all the other CDs (or combinations) were about +400.

I set about to see how close to that I could get. I got it to 4605 or about 300 more than the ideal. Doing this I ignored the VRA and only got two CDs that would elect a candidate of choice. BTW, I also tried this for MI, but like TN could not avoid a county split.



CD 1: +587
CD 2: +677
CD 3: +139
CD 4: -82
CD 5: +575
CD 6: -435
CD 7: +587
CD 8: +354
CD 9: +57
CD 10: +573
CD 11: +138
CD 12: +22
CD 13: +708
CD 14 -3897