Poll re 2020 Ohio CD Map

[muon2]

Thanks for clarifying that. Now I understand the choice of suburbs. I guess this highlights the issue with applying a generic formula for determining county erosity: in practice switching Euclid and Richmond Heights for Parma change little about the apparent erosity when looking at a map, but do change the number of county line connections.

For me personally, I take a dislike to districts that appear long and narrow or have concave shapes. In Torie's "You know it when you see it" view, that's what tips me off to erosity. For this reason, and the difference in cultural identity between the east and west sides of Cleveland's suburbs, I'm inclined to favor a map similar to those of Torie or Sbane that does a tri-chop of Cuyahoga County to prevent a thin suburban ring like your CD-14.

I posed a question earlier, and it's worth repeating. Is it better to create the largest BVAP district with only a chance of controlling the outcome, or should race be subordinated to compact shapes or creating more balance with partisan districts?

I think the goal should be to create the largest BVAP possible without taking the CD out of Cuyahoga County and without creating a bunch of split municipalities. I also think leaving out the small villages of Oakwood and Glenwillow from the black CD are acceptable if doing so is needed to prevent splitting Summit County to come back in. So I think the largest BVAP should be the first among several competing goals.

You raise two points that are worth thinking about. My goal is to create a set of criteria that allow a map to be drawn, with some flexibility, but not so much that political gerrymandering is an easy task. Communities of interest are a fuzzy idea that are easy to manipulate for political purposes.

First, you've pointed out the cultural differences between the east side and west side suburbs and their differences from Cleveland and the close in suburbs. Cultural differences are often synonymous with political differences and using political information is exactly what a neutral mapper wants to avoid, unless it is to test a plan for partisan fairness. Can you suggest a neutral way to identify the leanings of the communities that would tend to force the groupings you prefer? If not, then I can at best leave that as a mapping choice if other criteria are met.

Second, you've suggested maximizing the BVAP as a goal. That is a racial gerrymander and constitutes packing on the basis of race. Based on past decisions that rationale would be vulnerable to a section 2 court challenge. I suspect that the Dems would make that challenge and win since it would be to their benefit to split the black vote. I've included their counter-proposal below that has the same county erosity (there's no connection between Medina and CD 14) and less internal erosity. Can you suggest a way for the GOP to make the grouping you suggest and withstand a court challenge?

[muon2]

This is my fix for Canton. Instead of trying to park Medina somewhere whole, I let it be the subject of a chop. In Cuyahoga I'm going with my chop described above, until someone can convince me that my earlier version isn't a GOP-favoring racial gerrymander. There are only three county chops beyond what's needed and I think the districts would pass the shape test of any public panel.



Edit: Here are the erosity scores by CD:
1: 8
2: 4
3: 10
4: 22
5: 9
6: 22
7: 17
8: 2
9: 25
10: 16
11: 18
12: 8
13: 10
14: 6
15: 3
Total: 180/2 = 90
This is an improvement on the first plan I put up, so the discussion drove a better result without creating more county chops.

[muon2]

For comparison I scored Tories square boxes map from two days ago. Here's my erosity score by district.

1: 4
2: 8
3: 10
4: 22
5: 15
6: 1
7: 14
8: 10
9: 21
10: 17
11: 3
12: 12
13: 24
14: 11
15: 12

total 184/2=92

It looks like this could be improved quite a bit without major changes simply by adjusting the chops (I didn't count Portage since I found a way to make it a microchop and it would apply to yours as well.) This is important in my scheme since you have 10 chops to my 6. Using a Pareto analysis in order to justify more chops there should be a lower erosity.

[muon2]

In the meantime, here is a screen shot of the population variances. And here is a link to the county population projections for the counties in 2020. Just select Ohio from the list of states drop down to get the county numbers for Ohio. Remember if you switch out population growth counties, for population losing ones, you will need to make adjustments. Good luck.

On another issue, I see that our data sets are quite different and that can also make it hard to reconcile our maps. jimrtex and I use the census estimate data and project it forward assuming a constant growth rate equal to the rate so far this decade. Your link is using some substantially higher rates, so for example I project the state will be at 11.586 M in 2020, but the linked site projects 11.682 M which is almost 100K larger. They also don't say how they make their projections since I presume that is their proprietary info. The extra growth in their model is not distributed uniformly, either. Here's a list with both numbers for 2020 side by side in thousands.

.Adams County      27.7   27.9
.Allen County      101.1   102.9
.Ashland County      52.4   54.3
.Ashtabula County   96.7   98.7
.Athens County      62.8   64.7
.Auglaize County      45.4   46.3
.Belmont County      67.2   69.4
.Brown County      42.8   45.9
.Butler County      379.2   394.8
.Carroll County      27.7   27.5
.Champaign County   37.8   40.6
.Clark County      133.4   135.9
.Clermont County      205.1   209.3
.Clinton County      41.4   42.0
.Columbiana County   102.0   103.0
.Coshocton County   36.4   34.7
.Crawford County      39.8   40.1
.Cuyahoga County   1214.7   1196.0
.Darke County      51.0   51.2
.Defiance County      37.5   38.6
.Delaware County      206.8   216.6
.Erie County      74.1   74.3
.Fairfield County      152.1   159.9
.Fayette County      28.4   28.2
.Franklin County      1313.1   1313.9
.Fulton County      41.9   42.4
.Gallia County      29.9   29.7
.Geauga County      94.7   95.6
.Greene County      170.7   166.7
.Guernsey County      38.9   38.5
.Hamilton County      800.9   806.4
.Hancock County      78.8   76.2
.Hardin County      30.2   32.3
.Harrison County      15.2   14.9
.Henry County      27.5   26.7
.Highland County      41.0   40.9
.Hocking County      28.9   28.9
.Holmes County      45.4   45.6
.Huron County      58.1   58.3
.Jackson County      32.0   34.0
.Jefferson County      64.0   64.9
.Knox County      59.9   64.2
.Lake County      228.0   241.0
.Lawrence County   60.9   62.7
.Licking County      171.2   176.0
.Logan County      44.2   46.3
.Lorain County      301.9   314.6
.Lucas County      425.1   426.9
.Madison County      41.8   48.9
.Mahoning County      222.9   219.2
.Marion County      65.3   67.3
.Medina County      178.4   194.2
.Meigs County      23.0   23.8
.Mercer County      41.1   40.1
.Miami County      105.0   104.1
.Monroe County      14.2   13.5
.Montgomery County   531.5   508.6
.Morgan County      14.4   14.0
.Morrow County      35.3   35.0
.Muskingum County   85.5   84.7
.Noble County      14.4   14.8
.Ottawa County      41.0   40.6
.Paulding County      18.2   18.6
.Perry County      35.9   37.0
.Pickaway County      58.9   57.9
.Pike County      27.7   27.3
.Portage County      161.6   170.4
.Preble County      40.6   40.7
.Putnam County      33.2   33.7
.Richland County      116.7   117.3
.Ross County      75.3   77.7
.Sandusky County   59.0   58.0
.Scioto County      75.1   78.7
.Seneca County      53.6   53.3
.Shelby County      48.3   51.0
.Stark County      372.4   372.7
.Summit County      537.5   532.2
.Trumbull County      197.7   197.0
.Tuscarawas County   91.7   91.8
.Union County      54.2   58.6
.Van Wert County      28.7   26.6
.Vinton County      12.6   13.0
.Warren County      233.7   248.0
.Washington County   60.4   60.1
.Wayne County      116.0   116.6
.Williams County      37.1   34.9
.Wood County      138.0   128.2
.Wyandot County      22.6   22.3

[jimrtex]

In the meantime, here is a screen shot of the population variances. And here is a link to the county population projections for the counties in 2020. Just select Ohio from the list of states drop down to get the county numbers for Ohio. Remember if you switch out population growth counties, for population losing ones, you will need to make adjustments. Good luck.

On another issue, I see that our data sets are quite different and that can also make it hard to reconcile our maps. jimrtex and I use the census estimate data and project it forward assuming a constant growth rate equal to the rate so far this decade. Your link is using some substantially higher rates, so for example I project the state will be at 11.586 M in 2020, but the linked site projects 11.682 M which is almost 100K larger. They also don't say how they make their projections since I presume that is their proprietary info. The extra growth in their model is not distributed uniformly, either. Here's a list with both numbers for 2020 side by side in thousands.

They (Proximity One) appear to have much larger suburban ring growth.  For example, I have about 6K growth for Medina (3.5% for the decade), while they have 22K, about 13%.

[jimrtex]

This is my fix for Canton. Instead of trying to park Medina somewhere whole, I let it be the subject of a chop. In Cuyahoga I'm going with my chop described above, until someone can convince me that my earlier version isn't a GOP-favoring racial gerrymander. There are only three county chops beyond what's needed and I think the districts would pass the shape test of any public panel.



Edit: Here are the erosity scores by CD:
1: 8
2: 4
3: 10
4: 22
5: 9
6: 22
7: 17
8: 2
9: 25
10: 16
11: 18
12: 8
13: 10
14: 6
15: 3
Total: 180/2 = 90
This is an improvement on the first plan I put up, so the discussion drove a better result without creating more county chops.

Which links wouldn't you count on my map?  Just quickly glancing, I'd score yours at 192/2.



Not related:

The following Urban Areas have 50% or more of the population of multiple counties:

Cincinnati: Hamilton 96%, Clermont 74%, Butler 68%, Warren 54%
(Cincinnati UA includes Hamilton city, but not Middleton)

Cleveland: Cuyahoga 99%, Lake 93%, Medina 51%.
Lorain/Elyria is a separate UA, as is Akron.  I suspect that the growth of northeastern Portage is just enough to peel Portage from Akron, Portage is 46% in Akron UA, 18% in Cleveland UA.

Columbus: Franklin 98%, Delaware 81%.  Spillover is fairly small, and Newark and Lancaster are fairly significant towns.

Dayton: Montgomery 94%, Greene 78%.

Youngstown: Mahoning 82%, Trumbull 73%.

[muon2]

This is my fix for Canton. Instead of trying to park Medina somewhere whole, I let it be the subject of a chop. In Cuyahoga I'm going with my chop described above, until someone can convince me that my earlier version isn't a GOP-favoring racial gerrymander. There are only three county chops beyond what's needed and I think the districts would pass the shape test of any public panel.



Edit: Here are the erosity scores by CD:
1: 8
2: 4
3: 10
4: 22
5: 9
6: 22
7: 17
8: 2
9: 25
10: 16
11: 18
12: 8
13: 10
14: 6
15: 3
Total: 180/2 = 90
This is an improvement on the first plan I put up, so the discussion drove a better result without creating more county chops.

Which links wouldn't you count on my map?  Just quickly glancing, I'd score yours at 192/2.

Here's my list of contiguous but not connected counties:
Darke-Montgomery
Clinton-Clermont
Madison-Greene
Ross-Hocking
Muskingum-Noble

All of these come into play as boundaries on my map. All but Muskingum-Noble are on boundaries of your map. If I counted correctly there are 97 X's on your map and two should be discarded based on my list above. I can't tell if any should be added from the Columbus district so I'll ignore that. It looks like there are two more cut links in Guernsey. That would put the erosity at 97.

[TJ in Oregon]

You raise two points that are worth thinking about. My goal is to create a set of criteria that allow a map to be drawn, with some flexibility, but not so much that political gerrymandering is an easy task. Communities of interest are a fuzzy idea that are easy to manipulate for political purposes.

First, you've pointed out the cultural differences between the east side and west side suburbs and their differences from Cleveland and the close in suburbs. Cultural differences are often synonymous with political differences and using political information is exactly what a neutral mapper wants to avoid, unless it is to test a plan for partisan fairness. Can you suggest a neutral way to identify the leanings of the communities that would tend to force the groupings you prefer? If not, then I can at best leave that as a mapping choice if other criteria are met.

The cultural differences I refer to are mainly in ethnic origin (different immigrant groups orginally settled on either side of the city, and subtle differences in employment, housing style, religion, and, yes, sometimes politics result. The easiest marker will likely be ancestry, though it will take me some time to tabulate in a way that makes sense. In this case, income may be a poor indicator because the east side was historically the wealthier side but now has serious poverty issues in the innercity parts.

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Here, I'm slightly confused; I was under the impression that the VRA forbid cracking minorities to lessen their chance of gaining a representative who is the choice of the minority group. I'd imagine the Cleveland NAACP for one would throw a fit over the newest map you proposed. Apart from race, honestly that map does better serve the communities of interest in the Cleveland area better than the first two you drew. Clearly, as a Republican I'd prefer it not to be drawn either, but other than that, this map isn't bad.

[Torie]

Too bad the data sets are different. It really does not matter what data set is used, for this exercise, as long as we use the same one. I know my numbers are now accurate (I have a fancy spreadsheet - well I'm off by about 1,000 folks, but that should not make any difference here), and with my data set, below I think is one of two possible winning maps.  The other (which I need to re-prepare) removes the two cuts for OH-14, but adds cuts into Cuyahoga and Summit, and improves erosity. However, it then depends on how you score trichops, chops into metro areas, and chops of counties that take more than 20% of its population. I used the 0.5% population deviation allowed to not only get rid of county chops (two of them in this map), but also locality chops. This map has none (except Columbus). I also used it to straighten out lines.

I also have come up with an erosity test. You can either put a square around a CD that measure the percentage of the area in the CD not in the square, or put a square that fits entirely within a CD, and then draw straight lines connecting the farthest points outside the square (whichever approach gives you the highest score). You then take the area that is that not within the CD that is within the polygon that connects the outside points, or the area outside the CD that is within the square that contains all of the CD within it, as a percentage of the square or polygon, subtract that from 100%, and that gives you the erosity score for the CD. You then sum the percentage scores (with a perfect square CD getting a 100 score, and one that takes up half the polygon, or say 60% of the square that contains the entire CD within it,  getting a 60 score (you take the higher score), and that gives you a total erosity score for the map.

You then divide that score by the number of chops, to get your final score. County chops count as one chop, locality chops an 0.5 chop (unless say the chop involves more than say 5,000 people, and then it counts as a full chop), chopping more than 20% of the population of a county as a half chop, and maybe chopping say more than 20% of the population of a metro area as a chop potentially, along with a tri-chop counting as a double chop. (I just added the trichop thing, because I could lose a chop, by tri-chopping Summit, or for that matter moving OH-15 into Lorain avoiding Summit, which would increase the erosity of OH-15, but not enough to make it not worth getting rid of the chops for OH-14; I guess that is why there needs to be a rule counting  traveling county chops as two chops - which still might be worth it, if it avoids a metro chop, however that is defined.)

I would count as a chop a county that is part of the CD that has no state highway connecting that county with any other part of the CD. Other than that, I am not sure I think using Muon2's highway thing is a workable or wise exercise. I don't think anybody cares, and matters can turn on whether a highway is a mile this way or that. That does not make much sense to me.

Some section 5 overlay is needed as well (I see Muon2 disagrees, but ignoring that is going to kill this project in its crib - black politicians will freak out, if they think that freezes them out), but again, there is a gray zone, within which perhaps again it is not an all or nothing deal. In my map, OH-11 is 39.3% black VAP. The CD using my numbers cannot get any higher than 40%.  Oh, I don't have local projections, so I assumed the 81K population loss for Cuyahoga all come out of OH-11. If you guys have projection data for the localities, all on an organized spreadsheet, that would be helpful, but to actually use it to draw maps would take too much work I think, beyond dealing with section 5 issues, and for the Columbus CD. You guys didn't actually do that did you? Well I suppose you need it only for the chopped counties. In my map, there are 11 county chops.

Any comments on my scoring methodology? I am now fully convinced one needs to use this kind of balancing test approach to get the best maps, rather than a bright line, or lose, test, based solely on chop counts.  And how does my map score compared to the ones above, using either my scoring method, or whatever one that you prefer?

I must say it is kind of hard to work together, because we don't seem to agree on so much. Is there any way to get our ideas more in sync, or is this a negotiation that is just destined to fail? I know not using a balancing test scoring formula where erosity is a key factor, and measured by shape rather than road connections, is  something that I cannot accept. The maps will just look a whole lot uglier, and in my view, for no good reason. I think using my approach, or some facsimile thereof, will make for more "salable" maps.

[Torie]

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Only section 5 has that approach, TJ, and unless section 5 applies to Cuyahoga, Muon2's map is legal. Section 2 of the VRA only protects minorities, if one of them hits 50% VAP or CVAP, depending on the appellate court district. But whether for prudential reasons, a state law should have a section 5 overlay of some sort, is the issue that I am raising - for the same reasons as you. It is an evidentiary matter as to whether 39%-40% or so black VAP is enough to trigger Section 5, or whether blacks are out of the hunt irrespective here. As I noted above, it is in the grey zone, and is really a function of odds, so maybe there should be some penalty for dilution in the grey zone, rather than just prohibiting it.  Section 5 also has an anti-dilution aspect, but I don't favor incorporating that prong of it. And as we all know, Section 5 may not be long for this SCOTUS world.

Putting that aside, as to other aspects of Muon2's map, which is beginning to look similar to mine (or mine to his, or both), other than the erosity issues, that split of Canton from Akron should count as a metro chop. And that nasty chop of Medina should count as a half chop. Granted, mine has Carroll and Ashland as half chops itself, but somehow that does not seems as bad for smaller counties. Maybe it should only count as a half chop if the smaller portion of the chop exceeds say 20,000- 30,000 people or something (my Ashtabula chop has 26K), in addition to being more than 20% of the county's population.

Muon's map has 8 county chops, a metro chop for Akron-Canton,  2 metro chops for Columbus  (mine between 2 CD's has one metro chop into Columbus), 1 chop for the Franklin County tri-chop, and a .5 chop for Medina. Mine has 11 county chops, 1 metro chop for Columbus, plus one potential .5 chop for Ashtabula using my formula. So Muon's map has 11 .5 chops, and mine has 12 to 12.5 chops. I guess we both also have a metro chop into Cuyahoga, so add one chop for both maps. So Muon wins with the denominator. The issue is whether my numerator for erosity is sufficiently better to come up with a better score or not. It probably does,  but it may be fairly close if Ashtabula counts as a half chop.

Oh wait a minute - Muon2 loses a chop of Carroll solely because he has different population numbers. So I have 11 chops, not 12 to to 12.5 (assuming other variances don't blow out my chop-less OH-09 and OH-05).  But then I see I forgot to count for my map a half chop for Summit, so I'm back to 11.5 chops, tying Muon2's map (assuming I don't have chops I can't avoid for OH-09 and/or OH-05 using different population numbers).  In that regard, I think using my number set is better, because it probably has more realistic projections, than just straight line extrapolations, and thus is likely to be closer to what will actually obtain in 2021, generating more interest.

Muon of course got his chop count down by using Franklin as his dumping ground to equalize populations. My formula takes the profit out of doing that, particularly if it violates the 10% rule. It's a great way to cut down the chops, but it screws the metro area that serves as the dumping ground, not only as to its unity, but also by using a high population county as a tri-chop vehicle. The same thing goes on with the great temptation to tri-chop Summit. Such an exercise should not be rewarded, simply in order to avoid chops in some far away small counties that nobody will really care about. The reason we count chops is to avoid gerrymanders, not to facilitate (and indeed encourage) the shredding of metro areas, and/or subjecting a host of rural counties to their domination.

The focus here needs not only to be to avoid gerrymanders, but also to actually have a map which makes good public policy sense (that is where compactness comes in again, along with other factors), avoiding subjective criteria that can be gamed. The black box needs to rule, and then a procedure can be used to let the contending sides pick one of the high scoring maps, and if they can't agree, let a court do it (actually better would be to pick the top five scored maps (if 5 is not deemed enough, it could be the top seven), that are deemed substantially different (because X percent of the population is moved to another CD, or the partisan effect based on what CD's are in play based on PVI analysis changes enough, and let each party veto two (or three) of them, leaving the one remaining as the adopted map).

If within a substantially similar subset of maps, both parties agree one with a lower but still high score is preferable, presumably because after negotiation both sides have agreed on that map, they can switch that one in as the choice within that subset. Thus if say there are 3 similar maps within each subset, then the two parties will have a choice of between 15 or 21 maps (depending on whether there are 5 or 7 finalist maps), from which to choose. So the parties will have some room to wheel and deal, save key incumbents, or whatever, without such back room stuff resulting in something embarrassing as the map, designed primarily for the care and feeding of incumbents, or whatever.

The above procedure will cull out maps spit out by the black box that for all the good intentions, simply in the end for subjective reasons as to which everyone agrees, are just silly, or which turn out to really favor one side, when another high scoring map is more neutral.

[jimrtex]

This is my fix for Canton. Instead of trying to park Medina somewhere whole, I let it be the subject of a chop. In Cuyahoga I'm going with my chop described above, until someone can convince me that my earlier version isn't a GOP-favoring racial gerrymander. There are only three county chops beyond what's needed and I think the districts would pass the shape test of any public panel.



Edit: Here are the erosity scores by CD:
1: 8
2: 4
3: 10
4: 22
5: 9
6: 22
7: 17
8: 2
9: 25
10: 16
11: 18
12: 8
13: 10
14: 6
15: 3
Total: 180/2 = 90
This is an improvement on the first plan I put up, so the discussion drove a better result without creating more county chops.

Which links wouldn't you count on my map?  Just quickly glancing, I'd score yours at 192/2.

Here's my list of contiguous but not connected counties:
Darke-Montgomery
Clinton-Clermont
Madison-Greene
Ross-Hocking
Muskingum-Noble

All of these come into play as boundaries on my map. All but Muskingum-Noble are on boundaries of your map. If I counted correctly there are 97 X's on your map and two should be discarded based on my list above. I can't tell if any should be added from the Columbus district so I'll ignore that. It looks like there are two more cut links in Guernsey. That would put the erosity at 97.

How is the extension of 14 into Ashtabula scored?

I think you are gaming the scoring system by cutting off Hamilton from Butler, and to a lesser extent Cuyahoga from Lake.

The OH-1 part of Hamilton has an extremely long panhandle that does not appear to have any reason other than to reduce the link count.

The non-connection of Darke-Montgomery illustrates the probelm with using highways as links.  The North Dayton-Greenviile Pike is obviously a direct route between the two cities, but because it clips a corner of Miami, it doesn't count.  Muskingum-Noble is perhaps arguable, but the real reason is the shortness of the border.   I wonder if a simplified border length would not be a better measure.

Guernsey doesn't connect with Tuscarawas except along I-77 going north from Cambridge.  What is the Guernsey node for the blue part of the county?  Whatever it is, there isn't a very direct route from Zanesville.

[muon2]

So many thoughts that deserve a response. I'll split my posts to address them. I'll start with erosity.

I also have come up with an erosity test. You can either put a square around a CD that measure the percentage of the area in the CD not in the square, or put a square that fits entirely within a CD, and then draw straight lines connecting the farthest points outside the square (whichever approach gives you the highest score). You then take the area that is that not within the CD that is within the polygon that connects the outside points, or the area outside the CD that is within the square that contains all of the CD within it, as a percentage of the square or polygon, subtract that from 100%, and that gives you the erosity score for the CD. You then sum the percentage scores (with a perfect square CD getting a 100 score, and one that takes up half the polygon, or say 60% of the square that contains the entire CD within it,  getting a 60 score (you take the higher score), and that gives you a total erosity score for the map.

You describe at least two different variations on tests that are well known in redistricting.
I interpret them as a variation on the Reock and Ehrenberg tests. In both those tests the ideal shape is a circle rather than a square as you suggest. Reock uses the smallest circle that can be drawn outside the district and Ehrenberg uses the largest circle entirely contained in the district.

Reock was used in the Ohio Competition, and I can attest to the fact that there were some interesting ways to game the formula. I think changing from a circle to a square or other polygon, doesn't change the way the system can be gamed. The map below scored very highly, yet look at the shapes of CD 3 and 8 for example. A more detailed description of the shortcomings of these methods, with counterexamples is referenced in the paper at this link with the relevant part towards the beginning before the heavy math sets in.



In any case, as you point out its the visual shape that should matter. My experience is that the public eye can pick out bad districts easily, but become hard pressed to sort out good districts without a sophisticated mathematical tool. The public view is very important to me. As I look at our two maps I find hard to imagine an observer unfamiliar with OH rejecting either on shape alone.



If it is the case that an outside observer would pass both on shape, I think that argues for the simplest possible measure of erosity. The public can easily count connections with any mapping software. As I observed in the WA analyses a while ago, changing to contiguous counties doesn't much affect the score, it just doesn't prevent trans-mountain districts.

[muon2]

Now I'll address chops.

You then divide that score by the number of chops, to get your final score. County chops count as one chop, locality chops an 0.5 chop (unless say the chop involves more than say 5,000 people, and then it counts as a full chop), chopping more than 20% of the population of a county as a half chop, and maybe chopping say more than 20% of the population of a metro area as a chop potentially, along with a tri-chop counting as a double chop. (I just added the trichop thing, because I could lose a chop, by tri-chopping Summit, or for that matter moving OH-15 into Lorain avoiding Summit, which would increase the erosity of OH-15, but not enough to make it not worth getting rid of the chops for OH-14; I guess that is why there needs to be a rule counting  traveling county chops as two chops - which still might be worth it, if it avoids a metro chop, however that is defined.)

I would count as a chop a county that is part of the CD that has no state highway connecting that county with any other part of the CD. Other than that, I am not sure I think using Muon2's highway thing is a workable or wise exercise. I don't think anybody cares, and matters can turn on whether a highway is a mile this way or that. That does not make much sense to me.

In almost every state, and almost every hearing and panel I've attended counties reign supreme. It's the first measure of map that most go to, and it's one the public gets right away. Counties are the basic unit of elections so their importance in redistricting makes sense from that perspective, too.

Where we seem to be most in disagreement is in how to handle counties. You look at the map as a whole and then split the counties that preserve your shapes or CoIs. What you seem to resist is the idea of apportionment regions. Since you have a spreadsheet with the county pops, it's easy to group counties so that they not be close in population to one district, but instead to nearly a whole number of districts while maintaining whatever erosity measure you like. Creating the most such regions within a narrow range is equivalent to minimizing the county chops. It directly addresses the goal to balance erosity and chops.

As to measuring the chops I know we went through this at length before and we were in agreement. The total count is equal to the sum of all the counties in each district summed over all the districts in the whole state. If you then subtract the number of counties in the state the difference is equal to the county chop count.

You can apply the same method to county subdivision within a split county. I think a two tier approach is best, first counting county chops, the sub-county chops. This gives the judge of the map clear and separate measures (NJ keeps separate track of them, and essentially the MI rules do too.) It also gives the mapper more flexibility to respect CoIs without being forced into an awkward map.

You raise metro chops as a formal criteria as well, and that is essentially new to our discussion (it never really arose for CA or WA.) If it does figure in a formal sense (I'm not yet sold) then it must be based on the Census definition for the state. My initial inclination is to not make it formal in chop counting, but to let it be a factor as one looks at competing maps as a balancing test.

[muon2]

Now for my thoughts on methodology.

Any comments on my scoring methodology? I am now fully convinced one needs to use this kind of balancing test approach to get the best maps, rather than a bright line, or lose, test, based solely on chop counts.  And how does my map score compared to the ones above, using either my scoring method, or whatever one that you prefer?

I must say it is kind of hard to work together, because we don't seem to agree on so much. Is there any way to get our ideas more in sync, or is this a negotiation that is just destined to fail? I know not using a balancing test scoring formula where erosity is a key factor, and measured by shape rather than road connections, is  something that I cannot accept. The maps will just look a whole lot uglier, and in my view, for no good reason. I think using my approach, or some facsimile thereof, will make for more "salable" maps.

During the CA discussions we agreed that a balancing test had to provide for substantially different maps to be considered as OK. That allowed for some choice by the map maker, which we agreed was imperative to take into account information about local preferences. To me this is the way to address concerns about metro areas. If there are multiple maps that each meet the criteria, then the commission can select one that best meets metro integrity.

There are three criteria that must be balanced - population equality, political subdivision integrity (chops), and district shape (erosity). Equality is important to keep on the list, since the WV case (Tennant) shows that you can permit a pop deviation if other criteria are strongly met. The best way to balance the criteria is to consider each separately, without combining them. Forcing them into combination requires weighting the criteria with respect to each other, and that gets into minutiae that don't necessarily improve the outcome.

Not combining the criteria also allows implementation of a system that can produce different maps that are equally good by the criteria. This then solves the problem of allowing choices to factor in local preference. The best method to balance criteria without combining them is a Pareto test. A Pareto optimal plan is one in which improving any one of the criteria makes another one worse. Comparing two maps, we can then say they are equally good if each one is better in at least one of the criteria. In some sense the Tennant court was declaring that the WV map was Pareto optimal since improving population in the challengers maps forced the displacement of more residents to new districts while keeping chops at zero (whole counties and minimum displacement being the state's goals). Our discussion about TN was an illustration of trade off between chops and erosity.

Another observation I would make about assessing systems with multiple criteria is to reduce the scoring to simple integer measures. Chops automatically have this feature. In the OH competition chops, competitiveness, and political fairness all were based on simple integers (sometimes divided so it wasn't obvious), but compactness was a mathematical entity that ha many digits of precision. That allowed one to game the system to some degree by concentrating on eking out hundredths of a point of improvement on that measure without substantially improving the plan. The coarser nature of the other measures meant that one had to make a substantial change to make a real improvement. A better plan should be substantially better, not incrementally better, to warrant consideration. The use of course measures for chops and erosity also allows one to easily justify population deviations under Tennant. If erosity is a precision measure that can be tweaked by movement of parts of counties and munis, it will be inevitable that population equality will draw mappers into a necessary hierarchy of splits like MI. I would like to keep whole county solutions in the mix, and so if there is an erosity requirement, it must be coarse.

I do think that at least one hierarchy is useful. That is the notion of apportionment regions of whole counties championed by jimrtex. A plan can first be assessed at the level of apportionment regions then again at the district level. That gives a commission the ability to see plans at the big picture level first. Your plan has four regions and can be compared to other four region plans, while mine has eight regions of whole counties. For a given number of regions, it's much easier to test for Pareto optimality. For example all four region plans would be assessed based on population and erosity and non-optimal plans would be discarded. After selecting a set of optimal regional plans, the commission can compare the plans at the district level independent of region count. The AZ commission took a two tier approach this cycle, not based on regions and erosity, but on "grid" districts and compactness. It helped them look at the big design before getting into details.

[muon2]

Now the tricky bit about the VRA.

Some section 5 overlay is needed as well (I see Muon2 disagrees, but ignoring that is going to kill this project in its crib - black politicians will freak out, if they think that freezes them out), but again, there is a gray zone, within which perhaps again it is not an all or nothing deal. In my map, OH-11 is 39.3% black VAP. The CD using my numbers cannot get any higher than 40%.  Oh, I don't have local projections, so I assumed the 81K population loss for Cuyahoga all come out of OH-11. If you guys have projection data for the localities, all on an organized spreadsheet, that would be helpful, but to actually use it to draw maps would take too much work I think, beyond dealing with section 5 issues, and for the Columbus CD. You guys didn't actually do that did you? 

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Only section 5 has that approach, TJ, and unless section 5 applies to Cuyahoga, Muon2's map is legal. Section 2 of the VRA only protects minorities, if one of them hits 50% VAP or CVAP, depending on the appellate court district. But whether for prudential reasons, a state law should have a section 5 overlay of some sort, is the issue that I am raising - for the same reasons as you. It is an evidentiary matter as to whether 39%-40% or so black VAP is enough to trigger Section 5, or whether blacks are out of the hunt irrespective here. As I noted above, it is in the grey zone, and is really a function of odds, so maybe there should be some penalty for dilution in the grey zone, rather than just prohibiting it.  Section 5 also has an anti-dilution aspect, but I don't favor incorporating that prong of it. And as we all know, Section 5 may not be long for this SCOTUS world.

Let's posit that section 5 is indeed on its way out. That leaves section 2, and Gingles won't apply in OH in 2020. What remains is the direction in Bartlett v Strickland. The holding permits but does not require the creation of crossover districts where some fraction of the white majority will vote with the minority to elect the minority candidate of choice. A state may create crossover, as well as coalition and influence districts to provide opportunities for minorities. A stated preference for such districts when other criteria are met is one way to address the situation. One has to be careful, because a non-retrogression clause could look like a racial gerrymander and throw any process into the courts.

[muon2]

This is my fix for Canton. Instead of trying to park Medina somewhere whole, I let it be the subject of a chop. In Cuyahoga I'm going with my chop described above, until someone can convince me that my earlier version isn't a GOP-favoring racial gerrymander. There are only three county chops beyond what's needed and I think the districts would pass the shape test of any public panel.



Edit: Here are the erosity scores by CD:
1: 8
2: 4
3: 10
4: 22
5: 9
6: 22
7: 17
8: 2
9: 25
10: 16
11: 18
12: 8
13: 10
14: 6
15: 3
Total: 180/2 = 90
This is an improvement on the first plan I put up, so the discussion drove a better result without creating more county chops.

Which links wouldn't you count on my map?  Just quickly glancing, I'd score yours at 192/2.

Here's my list of contiguous but not connected counties:
Darke-Montgomery
Clinton-Clermont
Madison-Greene
Ross-Hocking
Muskingum-Noble

All of these come into play as boundaries on my map. All but Muskingum-Noble are on boundaries of your map. If I counted correctly there are 97 X's on your map and two should be discarded based on my list above. I can't tell if any should be added from the Columbus district so I'll ignore that. It looks like there are two more cut links in Guernsey. That would put the erosity at 97.

How is the extension of 14 into Ashtabula scored?

That is a microchop of two whole townships with less than 0.5% of the population. In previous threads there was discussion about microchops not counting as a chop, so it doesn't count towards erosity either. A case could be made to count it globally, and certainly the erosity within the chopped county matters.

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The factors that I used in the Hamilton and Cuyahoga chops was to maintain wholly connected chops and to reduce internal erosity. Sharonville overlaps the border between Hamilton and Butler, so to keep it together and not double chop I needed to extend along the northern border of Hamilton. I do agree that my counting for chops can lead to gaming the system, noting that your chop of Warren is less erose by my measure than mine is. I think a rule about minimizing erosity within the county, using local roads to determine connections would reduce the possibility of such antics.

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When we looked at WA, I concluded that counting any contiguous county did not effectively change the ranking of plans compared to using highway-defined connections. If highway-defined connections are used for contiguity, then it's simpler to have one map of connections, rather than one for contiguity and one for erosity.

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I used Byesville for the node. OH 146, 313, 660 and 209 provide a path from Zanesville. I agree that there is no connection from Tuscarawas, as I had mistaken a numbered county road for a state road.

[jimrtex]

Now for my thoughts on methodology.

...

Another observation I would make about assessing systems with multiple criteria is to reduce the scoring to simple integer measures. Chops automatically have this feature. In the OH competition chops, competitiveness, and political fairness all were based on simple integers (sometimes divided so it wasn't obvious), but compactness was a mathematical entity that ha many digits of precision. That allowed one to game the system to some degree by concentrating on eking out hundredths of a point of improvement on that measure without substantially improving the plan. The coarser nature of the other measures meant that one had to make a substantial change to make a real improvement.  A better plan should be substantially better, not incrementally better, to warrant consideration. The use of course measures for chops and erosity also allows one to easily justify population deviations under Tennant. If erosity is a precision measure that can be tweaked by movement of parts of counties and munis, it will be inevitable that population equality will draw mappers into a necessary hierarchy of splits like MI. I would like to keep whole county solutions in the mix, and so if there is an erosity requirement, it must be coarse.

The competitiveness and fairness measures used in Ohio encouraged ratcheting and titration.  If a district was switched from a D-R difference from 5.01% to 4.99% it would score higher though there was marginal improvement of competitiveness.

The effect on fairness of moving a 60-40 precinct is much greater than swapping it with a 55-45 precinct along a district boundary.  This leads to variations in district population intended to produce political results.  Even if "fairness" and "competitiveness" are seen as positive goals it should not be used as justification for population variance.

The problem with non-integer values is when they are converted to rankings, such as to measure best plans.  If they were use to measure relative quality, as is a plan good enough, then there is not the problem of tiny changes giving an exaggerated effect.

I do think that at least one hierarchy is useful. That is the notion of apportionment regions of whole counties championed by jimrtex. A plan can first be assessed at the level of apportionment regions then again at the district level. That gives a commission the ability to see plans at the big picture level first. Your plan has four regions and can be compared to other four region plans, while mine has eight regions of whole counties. For a given number of regions, it's much easier to test for Pareto optimality. For example all four region plans would be assessed based on population and erosity and non-optimal plans would be discarded. After selecting a set of optimal regional plans, the commission can compare the plans at the district level independent of region count. The AZ commission took a two tier approach this cycle, not based on regions and erosity, but on "grid" districts and compactness. It helped them look at the big design before getting into details.

[jimrtex]

I think you are gaming the scoring system by cutting off Hamilton from Butler, and to a lesser extent Cuyahoga from Lake.

The OH-1 part of Hamilton has an extremely long panhandle that does not appear to have any reason other than to reduce the link count.

The factors that I used in the Hamilton and Cuyahoga chops was to maintain wholly connected chops and to reduce internal erosity. Sharonville overlaps the border between Hamilton and Butler, so to keep it together and not double chop I needed to extend along the northern border of Hamilton. I do agree that my counting for chops can lead to gaming the system, noting that your chop of Warren is less erose by my measure than mine is. I think a rule about minimizing erosity within the county, using local roads to determine connections would reduce the possibility of such antics.

The extension of Sharonville is from Hamilton into Butler, and cuts a subdivision, properties, and probably houses.  If integrity of cities is considered important, it would be better to adjust the county boundaries to match the city boundaries for redistricting purposes.  So in this case all of Sharonville would be treated as if it were in Hamilton County.

The non-connection of Darke-Montgomery illustrates the probelm with using highways as links.  The North Dayton-Greenviile Pike is obviously a direct route between the two cities, but because it clips a corner of Miami, it doesn't count.  Muskingum-Noble is perhaps arguable, but the real reason is the shortness of the border.   I wonder if a simplified border length would not be a better measure.

When we looked at WA, I concluded that counting any contiguous county did not effectively change the ranking of plans compared to using highway-defined connections. If highway-defined connections are used for contiguity, then it's simpler to have one map of connections, rather than one for contiguity and one for erosity.

Though it could  change the relative quality of the plans.

Guernsey doesn't connect with Tuscarawas except along I-77 going north from Cambridge.  What is the Guernsey node for the blue part of the county?  Whatever it is, there isn't a very direct route from Zanesville.

I used Byesville for the node. OH 146, 313, 660 and 209 provide a path from Zanesville. I agree that there is no connection from Tuscarawas, as I had mistaken a numbered county road for a state road.

Byesville is part of the Cambridge Urban Cluster, and two miles south of the I-70, I-77 interchange.  Your route is 51 minutes versus 30 minutes on the direct route.

[muon2]

I think you are gaming the scoring system by cutting off Hamilton from Butler, and to a lesser extent Cuyahoga from Lake.

The OH-1 part of Hamilton has an extremely long panhandle that does not appear to have any reason other than to reduce the link count.

The factors that I used in the Hamilton and Cuyahoga chops was to maintain wholly connected chops and to reduce internal erosity. Sharonville overlaps the border between Hamilton and Butler, so to keep it together and not double chop I needed to extend along the northern border of Hamilton. I do agree that my counting for chops can lead to gaming the system, noting that your chop of Warren is less erose by my measure than mine is. I think a rule about minimizing erosity within the county, using local roads to determine connections would reduce the possibility of such antics.

The extension of Sharonville is from Hamilton into Butler, and cuts a subdivision, properties, and probably houses.  If integrity of cities is considered important, it would be better to adjust the county boundaries to match the city boundaries for redistricting purposes.  So in this case all of Sharonville would be treated as if it were in Hamilton County.

The non-connection of Darke-Montgomery illustrates the probelm with using highways as links.  The North Dayton-Greenviile Pike is obviously a direct route between the two cities, but because it clips a corner of Miami, it doesn't count.  Muskingum-Noble is perhaps arguable, but the real reason is the shortness of the border.   I wonder if a simplified border length would not be a better measure.

When we looked at WA, I concluded that counting any contiguous county did not effectively change the ranking of plans compared to using highway-defined connections. If highway-defined connections are used for contiguity, then it's simpler to have one map of connections, rather than one for contiguity and one for erosity.

Though it could  change the relative quality of the plans.

Guernsey doesn't connect with Tuscarawas except along I-77 going north from Cambridge.  What is the Guernsey node for the blue part of the county?  Whatever it is, there isn't a very direct route from Zanesville.

I used Byesville for the node. OH 146, 313, 660 and 209 provide a path from Zanesville. I agree that there is no connection from Tuscarawas, as I had mistaken a numbered county road for a state road.

Byesville is part of the Cambridge Urban Cluster, and two miles south of the I-70, I-77 interchange.  Your route is 51 minutes versus 30 minutes on the direct route.

An alternative to highway counting is to consider erosity in county chops by a different measure. One would count highway connectivity only for the whole county apportionment step. Within a county there would be a defined set of county subdivisions. They are pretty clear in states like OH that align state-defined subdivisions with census subdivisions. They aren't so clear in western states, though there are units that the census uses on its map.

Let me assume there is agreed subdivision that covers the whole county. Connections between subdivisions would be established by contiguous boundaries that include a public road so that one could go between subdivisions without crossing into any other subdivision. Internal erosity is then measured the same way as for the apportionment regions by counting the number of severed connections.

This approach would keep a level of separation between the two levels of the map. Each level would separately be subject to a Pareto test to optimize the map. This makes it hard to rank two maps that start from different numbers of apportionment regions, but would act to block the type of system gaming that you raise.

Thoughts?