Using Urban County Clusters To Guide Redistricting

[muon2]

The following maps illustrate how urban county clusters could be used in the redistricting process.

An Urban County Cluster is a group of counties from a Metropolitan Statistical Area which have 25% or more of their population in Urbanized Areas (urbanized areas are urban areas with a population of 50,000 or more).  So urban county clusters are characterized by significant levels of population concentration and significant commuting ties, which form the basis for defining metropolitan statistical areas.

There are three urban county clusters in Michigan:

Detroit: Wayne, Oakland, Macomb, Livingston, and St. Clair.   This is the entire Detroit MSA, with the exception of Lapeer, which has little population in urbanized areas, and is the most peripheral county.  Genesee, Washtenaw, and Monroe are not in the Detroit MSA, as Flint, Ann Arbor, and Monroe plus Toledo, provide an alternative focus for employment so a smaller share of their population commutes towards Detroit.

Grand Rapids: Kent and Ottawa counties.   Barry and Montcalm are also in the MSA, but do not contain portions of urbanized areas.

Lansing: Ingham, Eaton, and Clinton.  This is the entire Lansing MSA.

There are other single-county clusters, including Kalamazoo (Kalamazoo), Battle Creek (Calhoun), Muskegon (Muskegon), Ann Arbor (Washtenaw), Jackson (Jackson), Monroe (Monroe), Flint (Genesee), Saginaw (Saginaw), Bay City (Bay), Midland (Midland), and Niles-Benton Harbor (Berrien).  For redistricting purposes, these are treated no differently than other counties.

I think this makes a lot of sense as a definition. I like the restriction to counties within the MSA which avoids the whole merger question. For clarification, is the 25% rule based on some usage within the Census or is it arbitrary? I'd like to make the definition as defensible as possible. I know that the states vary on their definition of the threshold for urban vs rural. For example in PA the state average population density is used as the threshold for urban classification.

It appears that for the purposes of applying the 25% rule, the relationship of other urbanized areas within the county to the principal urbanized area is not a factor. Is there a table that clearly delineates the urbanized area population as opposed to the urban area population in the county? Again, I'd like to clearly source the definition, preferably from the Census web site.

[muon2]

Yes, I wonder how well this definition will work in other states, and where the data is.  And what and where do you look to know if more than 25% of the county is in "urbanized areas?"

The lighter shaded areas (eg Washtenaw, Genesee, and Monroe) are separate Metripolitan Statistical Areas within a Consolidated Statistical Area (CSA).  The darker area is the "main" MSA for the CSA.  The original version used CSA, but these were too extensive (Allentown MSA is part of the New York CSA),

With the latest definition, the association between Ann Arbor, Flint, and Monroe and Detroit is simply to illustrate the evolution of definition.  The single county "clusters" are treated as ordinary counties.

I think I understand, and am still looking to put a firmer basis on the 25% rule. I assume this is the excel file you are referring to on this Census page.

In the meantime, I see Lucas and Ottawa, OH in the same cluster. However, they are not in the same MSA, but Wood is 41.97% UA in the above table so it looks like it should be with Lucas instead of Ottawa.

[muon2]

So does this definition put Wood, OH with Toledo? The percentages are 41.97% UA, 28.48% UC, leaving 29.55% rural. You said it would fail before because of Bowling Green, but this new definition appears to simplify things so that one doesn't need that level of detail.

I started looking at some of the OH competition plans, since minimizing county fragments and increasing compactness were both goals. There was a 0.5% population deviation maximum for the districts. Instead of using our concept of microchops which don't count, there was a rule that allowed a chop without penalty that exactly included the part of municipality that crossed the county line. It is possible to view the top scoring plans in terms of apportionment regions, and the 1st and 2nd place plans are shown below. The plan on the left was better for compactness and the plan on the right had fewer fragments seen as more regions. It is interesting that neither plan preserves the metro areas we are identifying.

 

[muon2]

I believe my final Ohio plan did preserve all the urban clusters no? I am a bit confused about what you guys are talking about, about Wood. I get confused a lot on these matters.

I think this is the OH plan you refer to.

There are quite a few chops and splits of counties in the clusters that I see. In order to test urban cluster preservation the plan has to be reduced to a set of whole county apportionment regions. County clusters may not span different regions in a state.

Ideally there should be no population shifts between regions while providing districts within 0.5% of the quota. In practice up to one microchop may be used between any two regions to get districts within that limit. If a regular chop is needed, then those two regions are a single larger apportionment region. Chops used within a region should be kept to a minimum.

Maximizing the number of valid apportionment regions is equivalent to minimizing the number of regular chops. That chop count has to be balanced against erosity and the court will expect that for a given set of criteria (ie chop count and erosity) the population range between the most and least populous district will be minimized.

[muon2]

I believe my final Ohio plan did preserve all the urban clusters no? I am a bit confused about what you guys are talking about, about Wood. I get confused a lot on these matters.

I think this is the OH plan you refer to.

There are quite a few chops and splits of counties in the clusters that I see. In order to test urban cluster preservation the plan has to be reduced to a set of whole county apportionment regions. County clusters may not span different regions in a state.

Ideally there should be no population shifts between regions while providing districts within 0.5% of the quota. In practice up to one microchop may be used between any two regions to get districts within that limit. If a regular chop is needed, then those two regions are a single larger apportionment region. Chops used within a region should be kept to a minimum.

Maximizing the number of valid apportionment regions is equivalent to minimizing the number of regular chops. That chop count has to be balanced against erosity and the court will expect that for a given set of criteria (ie chop count and erosity) the population range between the most and least populous district will be minimized.

I think his Columbus cluster is OK.  The counties added to get to three districts don't have to be together.  The idea is to keep the 3 districts Columbus-centric.

It should pretty easy to get Lucas+Wood into a 1-district region.

Cincinnati+Dayton can probably go into a 4-district region.   4 plus 1, is just as good as 3 plus 2, and arguably better since the one is a non-metro district rather than putting a larger area under the domination of the large cities.

In northeast Ohio, Summit+Portage might have to be used.

I think we agree on this, let me confirm that. The multi-county clusters in OH and their number of districts is:
Youngstown: Mahoning, Trumbull (0.623)
Akron: Summit, Portage (0.975)
Cleveland: Cuyahoga, Lorain, Lake, Medina (2.751)
Columbus: Franklin, Delaware, Licking, Fairfield (2.289)
Dayton: Montgomery, Greene, Miami (1.108)
Cincinnati: Hamilton, Butler, Warren, Clermont (2.192)
Toledo: Lucas, Wood (0.787)

In general one anticipates that each county cluster would go into a region made up of a number of districts rounded up to the next whole number. The remaining counties would be grouped into single district regions. Clusters that are proximate to one another can be placed into a single larger region. Regions can also be merged to facilitate chops designed to reduce erosity. When a single region includes two adjacent clusters, districts may split the clusters to reduce chops and erosity.

In OH, there are no small counties that can bring the Akron cluster up to the level of a one district quota, and the population can't be made up by microchops alone. Therefore Akron will have to combine with either the Cleveland or Youngstown cluster, or single counties including Stark. One possibility that occurs with a Cleveland merger is that it may may more sense to split Summit and Portage to maintain other district criteria. For example:



The Cleveland and Akron clusters can combine with Geauga and Ashtabula to form a compact region with 3.997 CDs, so no microchops with any other region are necessary. By combining Summit and Medina only a microchop using Oakwood brings it to within quota, this also provides for a much less erose CD 14 which otherwise would have to wrap around the south edge of Cuyahoga to get enough population within this region. The districts are all well within the Cleveland CSA, so the split of Summit from Portage at the district level works for me.

[muon2]

Wood is chopped anyway, so just because its rural portion was in another CD, should not add another chop should it? I thought this urban cluster thing, was to count as chops un-chopped counties which excise a portion of an urban cluster.

There's a difference between discouraging unneeded chops into metros and allowing chops of counties that avoid the urban parts. Part of the exercise is to make the process easy to use. Forcing the mapmakers to first group counties before chopping strongly limits gerrymanders, and allowing one chop for each district as in MI can create significant openings for gerrymanders. The trick is to prefer plans that force microchops or less since their small size provides superior resistance to gerrys.

[muon2]

Wood is chopped anyway, so just because its rural portion was in another CD, should not add another chop should it? I thought this urban cluster thing, was to count as chops un-chopped counties which excise a portion of an urban cluster.

There's a difference between discouraging unneeded chops into metros and allowing chops of counties that avoid the urban parts. Part of the exercise is to make the process easy to use. Forcing the mapmakers to first group counties before chopping strongly limits gerrymanders, and allowing one chop for each district as in MI can create significant openings for gerrymanders. The trick is to prefer plans that force microchops or less since their small size provides superior resistance to gerrys.

And therefore ... ?

the map would not qualify.

You don't identify regions that will preserve the county clusters. Your map is so laser-focused on rectangular shapes to achieve your vision of non-erosity that you use nearly the maximum-minimum number of chops. In principle there should be no need for more than one chop for each district beyond one. Hamilton, Clermont, Warren, Hocking, Fairfield, Franklin, Putnam, Wood, Knox, Stark, Summit, Columbiana, Cuyahoga (2). That's 14 out of a maximum-minimum count of 15. From what I see only Belmont is a microchop. Going to an extreme in minimizing erosity is just as out of balance as the test maps I draw where I preserve counties at all cost. There's utility in such exercises, but only to set limits and balance points.

[muon2]

How does my map not preserve urban clusters again (I mean, I made a deliberate effort to keep them together)? And would you mind posting the map that reduces the chops?  I mean, if it is erosity city, then depending on how we calculate the erosity score (a task still almost totally undone in my opinion), maybe whatever additional chops I have would be more than counterbalanced by the respective erosity scores.

I would say you made a deliberate effort to keep the urbanized areas together, and that is not the same as keeping the counties together. I have intentionally avoided mixing specific definitions of erosity into this thread because I think jimrtex has hit on a valuable concept in building a plan. That means understanding this definition of urban clusters and how they should apply in the context of apportionment regions.

In your plan you have two regions, a south region with 1,2,5,6,7 and 10, and a north region with the rest. Even with only two regions, you have split Miami from the region that includes the rest of the Dayton cluster. There are a huge number of possible region groupings using the rules we've started in this thread. My interest is to see if these rules provide reasonable constraints forcing maps towards specific goals.

[muon2]

As I understand the concept of the urban clusters applied to OH, one could start with a regional plan like this one. It's certainly not the only one, but it's the one I used to produce the NE OH picture I posted earlier.



Each of the seven clusters identified by jimrtex is embedded in a single region. The deviations are small enough that only microchops are needed to balance population between regions. Akron is merged with the Cleveland cluster and the Dayton and Cinci clusters are together. If one doesn't like the shape of the Youngstown region it can be combined with the Canton region using a chop in Stark to improve the shape. That's the type of tradeoff that should be permitted, one less region for less erosity.

[muon2]

As I understand the concept of the urban clusters applied to OH, one could start with a regional plan like this one. It's certainly not the only one, but it's the one I used to produce the NE OH picture I posted earlier.



Each of the seven clusters identified by jimrtex is embedded in a single region. The deviations are small enough that only microchops are needed to balance population between regions. Akron is merged with the Cleveland cluster and the Dayton and Cinci clusters are together. If one doesn't like the shape of the Youngstown region it can be combined with the Canton region using a chop in Stark to improve the shape. That's the type of tradeoff that should be permitted, one less region for less erosity.

I could take your map and separate the Akron cluster as its own region.  Though this would have greater error, it would have more regions. 

Ideally there should be no population shifts between regions while providing districts within 0.5% of the quota. In practice up to one microchop may be used between any two regions to get districts within that limit. If a regular chop is needed, then those two regions are a single larger apportionment region. Chops used within a region should be kept to a minimum.

Maximizing the number of valid apportionment regions is equivalent to minimizing the number of regular chops. That chop count has to be balanced against erosity and the court will expect that for a given set of criteria (ie chop count and erosity) the population range between the most and least populous district will be minimized.

In OH, there are no small counties that can bring the Akron cluster up to the level of a one district quota, and the population can't be made up by microchops alone. Therefore Akron will have to combine with either the Cleveland or Youngstown cluster, or single counties including Stark. One possibility that occurs with a Cleveland merger is that it may may more sense to split Summit and Portage to maintain other district criteria. For example:



The Cleveland and Akron clusters can combine with Geauga and Ashtabula to form a compact region with 3.997 CDs, so no microchops with any other region are necessary. By combining Summit and Medina only a microchop using Oakwood brings it to within quota, this also provides for a much less erose CD 14 which otherwise would have to wrap around the south edge of Cuyahoga to get enough population within this region. The districts are all well within the Cleveland CSA, so the split of Summit from Portage at the district level works for me.

Akron is within 5%.  So I would go ahead and add Geauga and Ashtabula to bring Cleveland up to 3.022.  You have more regions, and the correction is quite localized, since the excess in Cuyahoga complements the deficit in  Moving 15,000 persons from Medina or Geauga is not grossly disrespecting counties given the density of population.

So are you saying that you would disallow the map above? How would you draw the CDs in Cuyahoga using those regions?

I have quite a difficulty with the 5% rule. In order to be a useful constraint the permitted deviation has to be based on the permitted range or deviation allowed for the type of district in the particular state. In OH a 5% deviation is fine for a legislative map since districts are permitted a 5% deviation (except for certain single county districts). In IL, 5% deviation isn't helpful since the court has ruled that legislative districts must be within 0.5%. Using a 5% standard there wouldn't help since once one shifts population in excess of the deviation, the court will inquire as to why the shift didn't get to equality. Once one requires exact equality it gets much harder to constrain the map against gerrymandering, since almost any shaped chop can be justified in the name of strict population equality.

For congressional districts it's clear to me that had WV used a 5% standard to form three regions in 2011, they would not have survived in court. They did prevail because WV provided its criteria and then since the range was under 1% the court (federal courts seem to prefer range to deviation) put the burden on the plaintiff to show that they could get a smaller range with the same criteria. Like my example above, a 5% deviation for congressional districts will force one to use exact population equality and with that most constraints are weakened as they must take a second place to strict equality. I want constraints that are on a par with population equality as shown in the WV case.

[muon2]

I am not at all persuaded that using regions, not as a device for convenience to get from A to B in order to minimize chops, or find micro-chops while drawing maps, but rather as Maginot walls,  is a wise idea at all. I have never understood that concept. Via whatever means one drew a map, you just score its chops, including urban cluster chops involving whole counties if we are going there, and the map's erosity, and come up with a score.

Computers have historically been poor at creating redistricting plans. When I've looked at their algorithms, output, and public reaction to the product it is clear that one problem is a hierarchy problem. If an algorithm takes all the data, that means going to the census block level. Optimizing a plan based on that many individual elements can be shown to be in a class of computational problems that cannot be solved in less than exponentially increasing time, what computer scientists call NP hard. Furthermore, there is such a wide variety of structures (rivers, mountains, roads, political jurisdictions) that the public recognizes as "natural" boundaries that an algorithm at that level of detail will thrash about seeking some optimal point. That same panoply of structures makes a straight up scoring system fraught with pitfalls that one can use to game the results. jimrtex alluded to the protection of whole munis in the OH competition as one such scoring consequence.

In sophisticated algorithms there is a multi-level approach to a solution. That means simplifying the problem to a relatively few elements, and then solving the problem as if they were the only elements in the problem. After that initial solution is generated, an iteration can be performed using a finer mesh of data. If necessary the process can be repeated until one reaches the most detailed and voluminous data set. Algorithms using this technique can be shown to converge to a reasonable approximation of the solution. By only using more detailed data in refining stages the computational complexity is reduced to a tractable problem.

For redistricting, counties are always on the list as a structure worth preserving. They are the fundamental unit of elections in most states, and since these are districts about elections there use is natural. Districts that preserve counties get more public approval than those that split counties. States with redistricting laws requiring reports often require county split totals as part of the report - and commercial software has that function built in. Beyond redistricting, in most states division of agency functions also adheres to counties lending their strength as a mutually agreed upon fundamental unit. The number of counties in any state is small enough that they are well within any computational constraints. For any multi-level redistricting algorithm counties are the first step.

So, if one wants a solid algorithm that can generate and score maps and doesn't run into computational issues, it will have a step that views the state as a collection of counties alone. With the assumption that there is a county-level view, the next task is to determine the rules that govern the county-level view of the plan. If one rejects the assumption, and one wants only a single step process, then one has to face the fact that the real data is not as coarse as the VTDs in DRA. That finer level of data creates exactly the challenges that cause problems with all the usual redistricting concepts from compactness measures to CoIs. I think the assumption is one worth making. 

As far as the county lines becoming walls, this is not an unreasonable concern, but one that can be addressed. This is a common issue in multi-level algorithms that fear that an early choice at the first level will trap the final solution too far from the optimum. It is also a well understood computational problem and one solution is to provide mechanisms in the process that allow for a set of choices that can be explored by later steps in the algorithm. Applied to redistricting, the need is to find rules that allow for a multiplicity of possible groupings, essentially allowing the mapper to preset where the walls should be before applying the next steps.

[muon2]

Now you seem to be abandoning the concept of erosity totally (is it just too hard to objectively measure, in which case maybe we are seeking perfection when it is the enemy of the merely good), except via the regions device perhaps (is that why you like regions so much, as the one and sole place to address the erosity issue?). Sure, maybe a computer can't do it all. So what? Do it by hand, and the most clever hand gets the highest score. I would like to see a poll about chops versus erosity. I doubt one has ever been taken. To me, if matters are erose that in the minds of the public means gerrymander, chopped counties or not.

I would not abandon erosity at all, and the comment about perfection as the enemy of the good is relevant here. My unscientific poll is based on hours of testimony in one state and watching some of the competitions play out in other states. It was clear to me that ugly erose districts were not desirable, but once districts were reasonable, the public cared less about the shape than about the integrity of political units within. Also, erosity based on rivers or mountains didn't bother the public, but an identically shaped line drawn through a city was of great concern. You can imagine how that creates a challenge for any scoring system. I also observed that long thin districts were generally not preferred, unless they followed the boundary of a state, in which case the public's tolerance of the narrowness increased. That also creates challenges for any metric.

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I think this is exactly what I have in mind, and the public should be able to participate by adding to that pile as well as the computer. Where I perceive our greatest disagreement is that I see a huge advantage to single districts that can be constructed from single counties like in IA and WV. The most frequent comment in IL was "why can't we do it like Iowa?" and part of that meant the type of district that was produced from whole counties. Look at the congressional map of IA-01 and its western boundary with IA-04. The public is OK with that, but I fear that it's too erose for you. In states with larger population centers the next best thing to IA is to get a reasonable number of IA-like districts that aren't too erose, then look at fair ways to chop the large urban cores.

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My goal is to have a method that permits a pile of maps to go forward, but winnows out those that shouldn't be in the mix. That means scoring is going to require careful balance between defined criteria. I think we are still at the stage of defining terms, and exploring how they interact with each other. For example I'm comfortable with the definitions of chops and microchops, but I'm not ready to sign off on how many microchops count as a chop. I'm getting more comfortable with this current definition of urban county clusters, but that's because I am with jimrtex that they are part of a system of apportionment regions (as in the OP), but like microchops I'm not ready to assign their splits a value.

I want to be able to defend the criteria and their definitions. That includes the balance between criteria as well. I can tell you with statistical certainty how to balance population inequality with county chops because I've collected the data and made the calculations. I'm still working on that level of statistics for erosity, but it won't help us if we disagree on the shape of the current IA CDs.

[muon2]

I accept Iowa, because of its county structure, its rather uniform politics, and it is easy and simple. But yes, I would prefer more compact CD's.  I still don't understand how my Ohio map chops urban clusters. And I still don't get why regions should be used. Let the computer do its maps. It doesn't need regional walls to do it. I am with you on natural boundaries, but some of that is dealt with by counting as a chop counties appended with no state highway linking them (that is nice objective rule). If a highway links, I don't care if a CD in that instance goes across a natural barrier. God invented bridges and roads over mountain passes for a reason. Where a county is itself erose, due to following natural boundaries, well every map has to contend with that, so it is a level playing field.

In the meantime, we are shadow boxing, because neither of us has a clear measure of erosity. So I need to number those damn boxes, and chat with you about that. Somehow I smell a rat in there, but we shall see.

The uniform politics in IA was not supposed to be a reason to accept the map, no? I am happy to see that we are still both on the same page when it comes to using highways for connectivity.

This thread emerged from the discussion of MI, so I used OH as an independent test of jimrtex's county clusters. It helps that I have competition data for comparison from OH. I started from counties only, and as I and jimrtex noted, more regions equates to fewer large chops, especially with the microchop definition of 0.5% for CDs. As I posted earlier, I came up with this version that has five whole county districts that can be gained by microchop or less.



By starting with this county plan I can insure that that need be no more than 8 regular chops. That come by subtracting 8 regions from 16 districts. I would expect no more than 3 chops for Cinci-Dayton, 2 chops for Columbus, and 3 chops for Cleve-Akron. Judicious grouping within the region may give me more whole county districts, but I need to first keep the county clusters intact.

Next I provide the chops and microchops within counties. Other than the city of Columbus I chop no cities, villages, or contiguous parts of townships. I found that even while keeping the Dayton region within two districts I could make one of the districts whole county with only a microchop. Similarly I could make a whole county plus microchop district by combining Summit and Medina, but that raises other questions that I posted earlier. I'll leave it for now.

Finally I took up the only shape that I think might draw some objections at a public hearing. The Youngstown CD can be made within 0.5% by shedding the two precincts of Minerva in Caroll to the Canton CD. However, the long narrow shape can be addressed by trading Belmont for a chop of Canton. I expect it would be a divided hearing with many from Stark wanting to stay intact while others argue for the overall shape of the districts.

This would be my offering from that starting point. I would rather see this plan with 7 chops and 4 microchops, than one with 14 chops and one microchop.

[muon2]

Well that map is more erose than mine, and you have a zillion urban cluster chops in Columbus, one one for Dayton, but I guess have one less for Cincy by virtue of your chop also chopping a county, which needed to be chopped anyway per your map design. I guess that gives an incentive to do your chops where an urban whole county chop would otherwise exist. I am not sure I love that incentive, but have a somewhat open mind on that one. I don't have much tolerance at all for excessive erosity tolerance, and maps that go there need to be punished, and better get their chops way, way down to next to nothing.

So tell me which districts are intolerably erose, not merely perfectable. As I said, the public has been quite clear to me that perfect is the enemy of the good in this matter.

Also, I don't follow your statement about Columbus at all. We each partition the Columbus urban county cluster (Franklin, Delaware, Licking and Fairfield) between three CDs which is the minimum that can serve that population.

For the four county Cinci cluster you use four CDs when only three are needed, but I adhere to three. We each split the Dayton cluster in two so we agree there.

Are you using a different definition of urban county cluster than jimrtex provided, or am I misreading this?

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[muon2]

I just followed Jimtex's map, and I see now that Union and Madison are not included in the Columbus urban cluster, so I withdraw the comment. I have marked the areas of the map that I would simply not do, and if OH-08 on your map jutted much more to the south, while having that jut to the north, that would be a fail for me, but the jut to the south is not that much, so it's OK. OH-05 does have two juts, although the one to the east is totally understandable, but the one to the west on top of it is a bridge too far - it becomes a two jut CD. If you are going to take the county to the east, you need to take the one below first, rather than go west.  I assume Canton and Akron are not in the same urban cluster, because you  split them. If they are, such a total bifurcation, as opposed to a nip,  bothers me. The worst aspect is OH-04 doing that extra rectangle to the east.




If I get up the energy, I might take your map, and make it less erose, while adding a couple of chops presumably, to see what happens, for purposes of comparison. The issue is not so much intolerably erose, but that a chop or two more is worth it, if it makes the map discernibly less erose. I would not characterize your map as "intolerably erose," but rather "uncomfortably erose."  I guess what I do is go for the least erosity, and then where possible add a bit or erosity to try to eliminate chops. I guess I must plead guilty to putting erosity first.

And I oppose the 5% variation, as opposed to the 0.5% variation. Did SCOTUS really sign off on the 5% variation in some recent case? If not, where did that come from?  Heck if it's 5%, some of my macro-chops probably go away.  The 5% will never sell anyway in most places. It's DOA.

As I noted, the 5% is acceptable only for legislative districts when there is no stricter state standards. jimrtex favors a more relaxed standard for apportionment regions, but that is ineffective at reducing regular chops. For CDs the range can be up to 1% if the state can show consistently applied principles, and there is no smaller range using those same principles. A 0.5% deviation is an easy way to insure a range within 1%.

Your observations on my map are fascinating and I now have a much better sense of your esthetic. You have a sense for a regular shape, but it isn't fixed on rectangles only. As long as things are regular its OK, but symmetry is not regular in your view. My CD 5 is quite symmetric, but is doesn't match with traditional regular forms so one of the appendages should go. Your change would actually break the symmetry.

My CD 4 is actually quite a good shape by traditional measures. It fits reasonably well in a convex polygon that connects all the outer points. It's not dissimilar to your CD 4 and better than your CD 15, since though my CD 4  has more indentations, they aren't that deep on the scale of the shape. If you consider rectangularity then it beats your CD 7 which is more rounded than rectangular. In fact discounting for the given shape of the Ohio River, my CD 6 holds a straighter line across its northern boundary than your CD 7 does so mine would be more rectangular. If we are looking at perimeter to area then your CD 12 with the erose city boundary could be worse than my CD 4. As an aside your CD 12 is the one that concerned me most when I first saw your plan, since incursions into a county to grab a large city is a hallmark of gerrymandered plans.

That lengthy exposition is simply to say that you have an artist's eye and you would like a plan that rewards art. Art is hard to quantify and I can only create mathematical models. I did take your plan and make some adjustments to make it conform with apportionment regions based on the urban county clusters. As I noted there really are a lot of ways to skin that cat and the walls are quite easy to relocate.



CDs 1,2,7 encompass the Cinci cluster and have a population of 2.988 of CD so the CDs in this cluster are each about 0.4% under the ideal and within the required deviation.

CDs 3,4 encompass the Dayton cluster and have a population of 1.995 of a CD. The city of Union which overlaps the county line is the only chop here, but it's about 6K and too big to be  a microchop. Using a microchop in SW Putnam would allow the chop in Montgomery to be replaced by a microchop.

CDs 8,9 encompass the Toledo cluster and have a population 2.003 of a CD.

CDs 5,6,10 encompass the Columbus cluster and have a population of 3.009 of a CD.

CDs 11-16 encompass the Cleveland, Akron, and Youngstown clusters and have a population of 6.004 of a CD.

The revised plan reduces the 14 chops plus one microchop in your plan to one with 11 chops. The apportionment regions provided the guide as to where I could make those reductions.

[muon2]

I just followed Jimtex's map, and I see now that Union and Madison are not included in the Columbus urban cluster, so I withdraw the comment. I have marked the areas of the map that I would simply not do, and if OH-08 on your map jutted much more to the south, while having that jut to the north, that would be a fail for me, but the jut to the south is not that much, so it's OK. OH-05 does have two juts, although the one to the east is totally understandable, but the one to the west on top of it is a bridge too far - it becomes a two jut CD. If you are going to take the county to the east, you need to take the one below first, rather than go west.  I assume Canton and Akron are not in the same urban cluster, because you  split them. If they are, such a total bifurcation, as opposed to a nip,  bothers me. The worst aspect is OH-04 doing that extra rectangle to the east.




If I get up the energy, I might take your map, and make it less erose, while adding a couple of chops presumably, to see what happens, for purposes of comparison. The issue is not so much intolerably erose, but that a chop or two more is worth it, if it makes the map discernibly less erose. I would not characterize your map as "intolerably erose," but rather "uncomfortably erose."  I guess what I do is go for the least erosity, and then where possible add a bit or erosity to try to eliminate chops. I guess I must plead guilty to putting erosity first.

And I oppose the 5% variation, as opposed to the 0.5% variation. Did SCOTUS really sign off on the 5% variation in some recent case? If not, where did that come from?  Heck if it's 5%, some of my macro-chops probably go away.  The 5% will never sell anyway in most places. It's DOA.

As I noted, the 5% is acceptable only for legislative districts when there is no stricter state standards. jimrtex favors a more relaxed standard for apportionment regions, but that is ineffective at reducing regular chops. For CDs the range can be up to 1% if the state can show consistently applied principles, and there is no smaller range using those same principles. A 0.5% deviation is an easy way to insure a range within 1%.

You're reading Tennant as narrowly as Karcher had been read.

Good faith effort can not be so narrowly defined as:

GOOD_FAITH = 0.005.

While avoiding a mini-chop which would have moved 15,000 persons.   You sliced between Portage and Summit.  You did not make a good faith effort to preserve that urban county cluster.

And range criteria is the wrong one to apply.  If you'd like, I'll show the MALC proposal for Texas House seats that cranked every Republican/Anglo seat up to 4.99%.  If the redistricting application displayed another digit, they would have gone to 4.999%.  Good faith is attempting to hit the bulls eye, and scoring 10 if you are within or even touching the ring.  Bad faith is to carry the red arrows down to the target, and insert them so that they are touching the ring.

I posed this map of NE OH precisely to understand how well one must preserve a cluster beyond the first step of its inclusion wholly within one region. I noted that there were two factors that should be weighed against preservation of the cluster within the region. One was the ability to have a nearly whole county district. The other factor was the reduction of erosity that was provided by the split. Without that split CD 14 needs a wrap around to Parma and Strongsville which is far less compact than the map I drew. You are suggesting that the weight of those two factors cannot outweigh the chop of the cluster.

That implies that the chop of the cluster within a region is not merely a scoring factor but is a rule in and of itself. Perhaps something of this form:

An urban county cluster within a region cannot be represented by more districts than the nearest whole number of districts in excess of the number that would be apportioned to the cluster alone.

With that rule Summit and Portage would always be wholly together plus about 18K from one of the neighboring counties. Without that rule one has to consider what set of factors is enough to balance the chopped cluster.

[muon2]

As I noted, the 5% is acceptable only for legislative districts when there is no stricter state standards. jimrtex favors a more relaxed standard for apportionment regions, but that is ineffective at reducing regular chops. For CDs the range can be up to 1% if the state can show consistently applied principles, and there is no smaller range using those same principles. A 0.5% deviation is an easy way to insure a range within 1%.

You're reading Tennant as narrowly as Karcher had been read.

Good faith effort can not be so narrowly defined as:

GOOD_FAITH = 0.005.

While avoiding a mini-chop which would have moved 15,000 persons.   You sliced between Portage and Summit.  You did not make a good faith effort to preserve that urban county cluster.

And range criteria is the wrong one to apply.  If you'd like, I'll show the MALC proposal for Texas House seats that cranked every Republican/Anglo seat up to 4.99%.  If the redistricting application displayed another digit, they would have gone to 4.999%.  Good faith is attempting to hit the bulls eye, and scoring 10 if you are within or even touching the ring.  Bad faith is to carry the red arrows down to the target, and insert them so that they are touching the ring.

I don't find any comfort in Tennant that a 5% variation would be permitted in congressional districts. The opinion said that a range of 0.79% was considered a minor deviation under Karcher and is still minor today, despite the ability of computers to create plans with less deviation. Since it is a minor deviation the state needed to show that the deviation was necessary to meet legitimate state objectives, not merely a good faith effort to meet those objectives. A 5% deviation for congressional districts has not been seen as minor to SCOTUS in the past, and there is nothing in the opinion to suggest that would change. I also reiterate that SCOTUS has consistently used population range, not percent deviation, to measure inequality between the largest and smallest district as they did in Tennant and Karcher.

[muon2]

"An urban county cluster within a region cannot be represented by more districts than the nearest whole number of districts in excess of the number that would be apportioned to the cluster alone."

At first blush, the above seems like a good rule.

What city did my OH-12 grab?  Your OH-05 (Toledo) isn't bad, just a tad elongated. The second prong as you say is mitigated by symmetry. What I dislike about your OH-04 and OH-06 are those choke points. I don't do choke points if at all avoidable. I would prefer doing a chop first. Oh, my OH-07 even though not as rectangular as yours, is as good as yours or a tad better, because the bulge up is symmetrical and subtle and akin to a circular shape. There is nothing wrong with that. There are no juts - it's all nicely smooth and flowing. Your version however is certainly acceptable.

It's not that OH-12 grabs a city, it's that Canton and environs were added. Excising a city/urban area out of a county is a pretty common gerrymandering trick. That's why it would raise a red flag with me. In any case under the rule I proposed, your CD-14 is disallowed since Summit and Portage would have to be whole in a single district.

I absolutely understand your sense of what constitutes a choke point. I would describe it as a county that links two separate groups of two interconnected counties. It would be described in graph theory as containing a butterfly graph (think of a bowtie shape made of five counties) with the central node of the butterfly serving as an articulation point (when removed the district becomes discontiguous). Conventional geometric measures of compactness don't deal with this type of structure, but as you see other branches of mathematics do.

I only raised the example of your OH-7 to show the impact of conventional compactness measures. A nice rounded shape like yours works very well for some measures, but those same measures may do poorly with a compact rectangular L-shape, and vice versa. I think both of our Ohio river CDs should be acceptable as part of a plan.

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I didn't apply my proposed rule in Summit, but I did in Dayton. The rule would allow the Dayton CD to come down into Warren, but you couldn't also have a split of Clermont such that four CDs served the Cinci cluster. That's what makes these rules tricky. This proposal would take a level-one regional rule and force it to have more consequences at the level-two district process. I'm OK with that, but one might rather have a more flexible rule that allows the clusters more splits at the district level. Of course that has the potential consequence of allowing the Lansing split (perhaps with a chop penalty) that fired up a lot of this current discussion of how to factor metro areas into redistricting.

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You're welcome.

[muon2]

Some CD had to take the balance of Stark after the Akron CD going down to take the city of Canton and stuff in between had its fill of population. The idea was to keep Akron and Canton together, with a nice compact result as well. But all of that assumed that Akron/Canton was a metro area of some sort, and who knew Summit and Portage were?  Summit grabbed the wrong county! So of course, with the new urban cluster definition, in that respect my map is blown out in NE Ohio. You change the rules, and you play the game differently. Akron goes to Kent State, and not to Canton. Who knew?

Here's one way to adjust your revised plan to conform with the rules. It actually improves things by splitting the Youngstown cluster into its own region and thereby reduces chops by one. There are other ways to swing the chops if you prefer.

[muon2]

Some CD had to take the balance of Stark after the Akron CD going down to take the city of Canton and stuff in between had its fill of population. The idea was to keep Akron and Canton together, with a nice compact result as well. But all of that assumed that Akron/Canton was a metro area of some sort, and who knew Summit and Portage were?  Summit grabbed the wrong county! So of course, with the new urban cluster definition, in that respect my map is blown out in NE Ohio. You change the rules, and you play the game differently. Akron goes to Kent State, and not to Canton. Who knew?

As to Dayton, what you are just saying is that there can be but one chop into the Cincy cluster, so take your best shot. Fine. I understand that. If you chop Clermont, you can't chop Warren too. The problem however is that the Cincy and Dayton clusters are just wrong. That is because of the whole county, rather than split county syndrome. If one cluster takes part of a county, and another cluster the part on the other end, then the county should be chopped for purposes of defining the perimeters of an urban cluster, rather than just awarding the whole county to the cluster that has a higher percentage of the county population within it, or whatever the rule is. So the issue is whether to made an exception for this one rifle shot issue - correcting for perimeter drift effected for the winner of the split county which has how most population therein game.

I am trying to think of another county in the US that has this issue. I am sure that there are; I just can't put my finger on any at the moment. It's rare to have two separate substantial cities merge towards one another in a neutral county in-between them. It would apply to Dallas and Ft Worth perhaps, except that there is no neutral county between them.

I suspect a similar situation arises with St Cloud, MN. Sherburne county is in the Mpls cluster, but has significant overlap from St Cloud.

Rather than deal with cases, I'm still inclined to either take the rule or creating a scoring penalty for the extra chop. Each option has consequences and will either exclude plans one might want or permit plans that one might wish to reject. Are any of the impacted plans important enough to sway the decision?

[muon2]

Yes, good example. The case is rare enough, that I suppose for those two examples, one could choose to have a unique pre-agreed upon exception, or not. The loser of the neutral county competition might prefer such an exception potentially.

I am not sure what you meant, or whether you meant a distinction, between take the rule or have a scoring penalty? If you take the rule, you just cannot have an extra chop at all?

Yes that's what I mean. A mapping rule is something that cannot be avoided. A scoring rule creates a cost for the extra chop, but permits flexibility. The downside of flexibility is that plans like my MI plan that splits Lansing may get through for commission review and might even bump out a more appealing plan. Also every flexible rule can potentially open the door to those who want to game the system. A hard rule cuts plans like that off at the start, but will also cut out some plans like the 4-split of the Cincy cluster or the separation of Summit from Portage.

[muon2]

Man you have bought into this urban cluster thing lock, stock and barrel haven't you? A veritable epiphany, with Jimtex your mentor. I can't say that I disagree with the hard rule however, but can't really sign off until enough examples are explored. Did I ever tell you that I loved the common law? It is all those examples, that allow lesser minds like myself to really get it around an idea, and have adequate perspicacity to fathom all of its significant consequences. I in short need mental crutches.  So be patient with those of us relatively mentally handicapped "challenged." As I say in so many economic contexts, time horizons matter!

So perhaps we should look at MN since it is has adjacent clusters with an overlapping urbanized area. That may tell us if there are problems with the rule. The clusters are
Minneapolis (Anoka, Carver, Dakota, Hennepin, Ramsey, Scott, Sherburne, Washington, Wright) - 4.620
St Cloud (Benton, Stearns) - 0.285
Mankato (Blue Earth, Nicollet) - 0.146

With a hard rule the Mpls cluster counties cannot be covered by more than 5 CDs. St Cloud can be added to that since the total is still within 5, or it can go in its own CD separate from Mpls. Perhaps you want to pull up one of your old maps to revisit as I will mine?

[muon2]

As I noted, the 5% is acceptable only for legislative districts when there is no stricter state standards. jimrtex favors a more relaxed standard for apportionment regions, but that is ineffective at reducing regular chops. For CDs the range can be up to 1% if the state can show consistently applied principles, and there is no smaller range using those same principles. A 0.5% deviation is an easy way to insure a range within 1%.

You're reading Tennant as narrowly as Karcher had been read.

Good faith effort can not be so narrowly defined as:

GOOD_FAITH = 0.005.

While avoiding a mini-chop which would have moved 15,000 persons.   You sliced between Portage and Summit.  You did not make a good faith effort to preserve that urban county cluster.

And range criteria is the wrong one to apply.  If you'd like, I'll show the MALC proposal for Texas House seats that cranked every Republican/Anglo seat up to 4.99%.  If the redistricting application displayed another digit, they would have gone to 4.999%.  Good faith is attempting to hit the bulls eye, and scoring 10 if you are within or even touching the ring.  Bad faith is to carry the red arrows down to the target, and insert them so that they are touching the ring.

I don't find any comfort in Tennant that a 5% variation would be permitted in congressional districts. The opinion said that a range of 0.79% was considered a minor deviation under Karcher and is still minor today, despite the ability of computers to create plans with less deviation. Since it is a minor deviation the state needed to show that the deviation was necessary to meet legitimate state objectives, not merely a good faith effort to meet those objectives. A 5% deviation for congressional districts has not been seen as minor to SCOTUS in the past, and there is nothing in the opinion to suggest that would change. I also reiterate that SCOTUS has consistently used population range, not percent deviation, to measure inequality between the largest and smallest district as they did in Tennant and Karcher.

If it was possible to create a map with whole counties, and it was necessary to have a district with a greater deviation than 0.5%, it might well be be approved by the SCOTUS.

What has happened in Kirkpatrick v Preisler and Karcher v Daggett, is that the Missouri and New Jersey legislatures did not make a good faith effort to achieve equality.

In Kirkpatrick, the legislature claimed that they were making adjustments for non-resident population, and future growth.  But these were transparent guises.  When a plan was eventually drawn, it had the same deviation as that drawn by the legislature.

At the time of Karcher, 12 congressional plans had greater deviation than New Jersey, and 4 were of comparable magnitude.  But the New Jersey sloppily drew a partisan gerrymander, and tried to justify it on VRA grounds.

Where the Supreme Court has used the word "justify", the legislatures have tended to use "rationalization".

The SCOTUS has stated that there is no de minimis standard.  That means that it is impossible to determine whether larger ranges might be acceptable based on actual cases.

If I am going to justify a somewhat larger deviation,  I am going to have to show that my goal was to use whole counties, and that I had made a good faith effort in other portions of the state, where it was possible to achieve equality.   I can not demonstrate that with range.  I can with standard deviation.

I don't see any real evidence that the SCOTUS has expressed a preference for range over better and more appropriate measures of equality among multiple districts - it was just simpler for them to express their opinion.  In Karcher, they did make a comparison between two other districts.  They have also used average deviation - which is not a good idea either, since one can transfer from one overpopulated district to another even more overpopulated district with no penalty for the increased inequality.  Standard deviation penalizes collective disparity.

White v Regester has the actual house district populations in Texas.  They form a very nice normal distribution.   District populations since then have had worse and worse since then, approaching a uniform distribution.  

But the plan had an asymmetry in range.  It was possible to create one district with two counties that had a deviation of 5.8%, and there were no alternatives in compliance with the Texas Constitution.  At the same time there was a single county with a deviation of -4.7%.  Rather than violating the Texas Constitution by cutting a county.  They kept the 5.8% district, and violated the Texas Constitution by adding part of another county to the county that was naturally within the 5% limit, in a less egregious violation of the Texas Constitution, such that the overall range was 9.9%.  A good faith effort to achieve equality could have accepted the deviations of two districts at 5.8% and -4.7%.   Or the cut should have been applied to the 5.8% district (once a cut was made, it would have been possible to get much closer to 0.0% for that district.

And then they compounded their mistake by creating a multi-county district with a deviation of +5.7%, in an area where it was quite possible to have a district with near zero deviation.  That is, using total range permitted them to create another district with a larger deviation when it was absolutely not required.

Since then, range has been used to create or propose plans with greater overall inequality.  It is the wrong standard to use for measuring inequality.  There is no reason to dumb this down for the SCOTUS.

Note, I am not attempting to justify a 2.5% deviation for a Summit-Portage district.  I am permitting a larger deviation at this stage as part of a comprehensive method, devised in advance, as opposed to a post hoc rationalization of a legislature-drawn plan, that would:

(1) Be gerrymander resistant;
(2) Would largely adhere to political boundaries;
(3) Recognize larger metropolitan areas as significant communities of interest;
(4) Be reasonably compact; and
(5) Permit significant and real public participation.

Note that geographic compactness, may be simply one way to express conceptual integrity or concreteness.  Why are compact districts desirable?  It doesn't have anything to do with rubber bands.  It is because they are more likely to place neighbors with similar interests together.  An urban concentration is conceptually compact, as is a less urban area, even if it somewhat wraps around urban regions.

I can easily accept a statistical measure for district inequality, but the issue the court has considered most important is the disparity between the largest and smallest districts. The relative size from the largest to smallest district was the issue in Reynolds v. Sims, not the average or standard deviation. The fact that there is a disparity in the value of a person's vote drives the decisions related to one man one vote, and the greatest disparity occurs when viewing the extreme cases among districts.

Consider the following hypothetical set of 20 districts with an ideal population of 100,000 persons in each. Two plans are submitted that comply with all state objectives. In plan A there are 10 districts with a population of 99,900 and 10 with a population of 100,100; giving a range of 200 (0.2%) and a standard deviation of 100 (0.100%). In plan B there are 19 districts with a population of 99,980 and one with a population of 100,380; giving a range of 400 (0.4%) and a standard deviation of 87.2 (0.087%). Plan B has the smaller standard deviation, but I find it unlikely that the court would ignore the fact that plan B has twice the maximum disparity present in plan A. So though I prefer standard deviation as a statistical measure, I think the law of one man one vote requires a range measure.

Other than the question of population deviation I think your principles are on target.

[muon2]

We agree that one of the goals is significant and real public participation. I'd love to see statistical education get to the point where the standard deviation is as obvious to the public as the mean, but that day is far away. Standard deviation is just not a measure that is set up for public participation.

There's a reason that the legislatures and courts tend to use maximum deviation, average deviation or range, and that's because these are values they understand. Even if the Congress were to enact a standard for population inequality, and that standard were upheld by SCOTUS, I would be surprised if the choice is standard deviation.

It's true that the more accessible measures I mention allow for more obvious games to be played with district populations. A skilled mathematician can tilt the field with standard deviation, too. The point is that population inequality should be measured to show that after considering other criteria such as chops and erosity the plan has the least inequality. I'll rely on those other criteria to control gerrymandering. Thereafter I'd like the simplest measure to show the plan has addressed inequality. The courts have used range in many decisions, and it's simple to understand. Mathematically I found that it correlates slightly better than average deviation to the number of geographic units available to make a map.

[muon2]

Returning to the issue of adjacent clusters I looked at MN.

Plan A puts the St Cloud cluster in with Mpls. In doing so I only need to add Rice to bring the Twin Cities region to within 0.16% of 5 CDs. The region range is 0.33% (st dev 0.12%). Within the TC there are the minimum 4 chops (2 Hennepin, Ramsey, Dakota) and CD 6 was kept more compact by going south into Hennepin rather than stretching east to the WI line.




Plan B keeps the St Cloud cluster separate from Mpls. The erosity is lower than in plan A but the region range inequality rises to 0.98% (st dev 0.42%). It also raises a question about subregions of a cluster. The Dakota county CD 2 could exist as a region unto itself, but requires counties outside the cluster yet within the CSA. Keeping it to counties within the CSA might be a desirable extension from the pure cluster subregion.




Both these seem like plausible plans using the hard rule, so I don't see a problem here.