Using Urban County Clusters To Guide Redistricting

[jimrtex]

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.

What I envision happening is that some agency (eg secretary of state, legislative council, state statistical agency) would prepare the data.   They could also include some simple interactive tool for drawing maps.  There would be some data standard so that people can use their own software to submit maps.

In particular, they would produce a file of border lengths and connectivity.

In Ohio, I would not permit a direct connection between Clermont and Clinton, nor Mercer and Shelby (Auglaize and Darke are not contiguous).  I would include the length of these border connections in determining the length of the border.

Stark-Holmes, Ross-Jackson, Montgomery-Clark do meet my suggested standard of border gap greater than 10% of the square root of the area of the smaller county.

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.   I suspect a similar split would be possible in the southwest.   And how close is Franklin+Licking or Frankilin+Delaware to 2.00?  In the case of Franklin+Licking, I would also require the other region to include both Delaware and Fairfield.

[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.

[Torie]

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.

[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.

[Torie]

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.

Presumably a computer could come up with the maps with the fewest chops in order, and then with that array of 20-50 maps or whatever, one could start picking out the maps with the lowest erosity, balancing that against the chop count.  I see no need for preset and rather artificial walls, based on what is close to a whole CD integer in population, or whatever.

Is there any agreement that one counts macro chops (with spitting off a whole urban cluster county also a chop), and microchops, to get a chop score. Or have we agreed on essentially nothing so far, about how regions are used if at all, chop counts, erosity, you name it?  Is one of us part of the progressive caucus, and the other a tea party member as it were?  What we have not done, ever, is actually list, systematically, on just what points there is agreement, and where not, and why. The discussion is disorganized, and seems not to progress.

[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.

[Torie]

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.

[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.

[Torie]

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.

[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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[jimrtex]

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.

This is the initial step, to establish the number of regions.  It is like pulling a suit off the rack and checking for the basic fit.  Other suits may fit better, and require less customization.

After the number of regions is established, there would be additional rounds of submissions.  Plans that had substantially greater deviation or greater erosity would be excluded.

You should read Tennant again.  West Virginia largely made up its rules on fly, and rationalized them on the basis of past practice.

The 3 stated interests of West Virginia were:

(1) Not pairing incumbents.   This is totally a made up interest, and of dubious legitimacy,
(2) Not splitting counties.  A reasonable criteria, though justified in part based on the state constitution's requirement to not split counties to form senate districts (which is flatly unconstitutional given the number of senate districts.
(3) Not making too many changes.  Possibly reasonable, but not if the districts were flawed in the first place.

You are probably correct about the 5% vs 0.5%, but that is because of sticker shock on the part of the SCOTUS.

Ohio has a specific standard in its constitution, and constrains how house districts are formed.  Illinois has no standard in its constitution, and no rules other than compactness,

There are better more practicable ways of measuring equality.  Use of range permits greater inequality, and grossly disregards the totality of a plan.  It can not be used to determine whether there is “a good-faith effort to achieve absolute equality.”

[Torie]

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.

[jimrtex]

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.

Iowa has 99 counties and 4 congressional districts, or roughly 25 per district.  Further the counties have relatively modest populations.  None grossly huge, none very small.  The current map has districts of 39, 24, 20, and 16 counties, for a standard deviation of 8.7 counties.

Now imagine you have an state like Iowa where counties line up in neat rows, and pretty neat columns.   You have a n x 2 area where the boundary between districts should go.   The border roughly goes between two columns, n counties high.   If we permit the boundary to advance one county to the west, remain the same, or retract one county to the east, in each row, how many variations are there?

Answer: 3ⁿ.

If n is 4, that is 81.  If n is 5 it is 243.   With some variation between the counties, we get an almost continuous distribution of population.  And even the more toothier combinations aren't that horrible looking when they are made out of bricks.

If n is 3 or 2, then the number of combinations shrinks.  And if some of the counties are large, the distribution of population becomes decidedly chunkier.

It is this exponential explosion of options when the district are made up of a large number of counties that makes Iowa easy.  Iowa is a degenerate case.  And the problem is trying to extrapolate from Iowa.  It is better to have a general method when applied to Iowa drops out a nice map.

Thought exercise.  Divide Iowa on an east-west line that is approximately equal in population.  Shift the fewest numbers of counties at the east or west end that produces better equality.  So our north-south boundary is a line with at most a single jog.   Then divide the north and south halves on separate north-south boundaries.

Since Iowa is roughly 11 counties wide by 9 counties high, this gives 20 county pairs along the boundaries.  If we adjusted those boundaries one county to the east or west or north or south, we would be able to make 3²⁰ or 3.48 billion variations.  We could get quite nice districts, and eliminate the infamous Minnesota Finger.  There are some constraints near the junction of the districts, so that we can't shift a county both east and south, for example, but the number is still close to one million.

[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.

[jimrtex]

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.

[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.

[Torie]

"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.

Overall, I think your revisions to my map are superior (congratulations, and btw, if you want to revise one of my maps, just ask for the data file so you don't have to start from scratch). I particularly like the square/rectangular shapes in the NE that are more perfected than mine. I am not sure about the OH-02 vis a vis OH-03 dance. That corner of Warren in OH-03 per my plan makes it more compact, and OH-06 more square (with my design, not yours), and the fact of the matter is that that portion of Warren is really in the Dayton metro area, not Cincy (which is why I felt comfortable drawing it). I take it that despite the density metric dictating that it is in the Dayton metro area, it is deemed to be in the Cincy urban cluster. Is it worth making an exception for this type of situation?

Thank you for the "artist eye" comment. I guess I fit at least gay stereotype after all.

[jimrtex]

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.

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.

While eliminating a shift of 18,000 persons across county lines, you have swapped 330,000 persons between the core part of the two metropolitan areas.  While there is certainly a connection between Medina and Akron, and Portage and Cleveland, the connections, as measured by census data is much stronger the other way:

Population in Urbanized Area:

Medina: Cleveland UA 88K, Akron UA 24K
Portage: Akron UA 73K, Cleveland UA 28K

Commuting to Main County of MSA:

Medina: Cuyahoga 29K, Summit 10K
Portage: Summit 19K, Cuyahoga 13K

The supposed increase in erosity is because of the odd shape of Cleveland, and the VRA.

[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.

[Torie]

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.

[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.

[Torie]

No, those chops are fine, and the Youngstown CD is more of a rectangle to boot. Did I ever tell you that I liked rectangles?

I appended my post above to chat about Dayton ad nauseum. You might peruse that.

[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?

[Torie]

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?