Using Urban County Clusters To Guide Redistricting

[jimrtex]

I'm still confused about the matter of the size of the chop into an urban cluster, and the issue of my map going into Walker County, to accommodate microchops elsewhere. I think that flexibility should be there, but the point needs to be clarified. Good summary Muon2 of where I think we are, on matters where there is some consensus.

Walker has nothing to do with the Birmingham UCC.  So don't let that confuse you.

Since most of the population of Walker is in the northwest region, it is counted as part of the northwest region.  This gives a population of about 1.034 of the ideal.  While 3.4% is within a 5% range, it is a largish error, and might cause your plan to be excluded because other plans might have less error while using whole county regions.

The Birmingham UCC (Jefferson and Shelby) is in a 2-district region, or alternatively Jefferson is in a 1-district region, and Shelby is in an other 1-district region.

There is no problem going outside a UCC with your chops, since the regional rules should ensure compliance with the UCC for the most part.

Think of the regional map as an off-the rack suit, which you then have to fit.  You want to require the minimum amount of customization.

Do you have the population splits for Autauga, Washington, and Tuscaloosa counties?

This is what your actual regions look like.  Your standard deviation is almost 4 times greater than that of my plan.  You require a transfer of 3 times as many persons (9 times if we discount the necessary augmentation of Jefferson.   Moreover, your entry was rejected because of the two regions with a deviation of more than 5%.

[muon2]

Defining clusters and how they should be used actually has an impact on erosity measurement. A basic tenet is that one wants there to be some parity between chop measurement and erosity to create a balance. One also want to make sure that the establishment of clusters does not force erosity into some strange corner. As I see the court at present one can't ignore population inequality entirely either since if all other measures are equal, the court is likely to insist on a plan that reduces inequality. Compactness and district design are tightly coupled to erosity as well and I find that connectivity figures into that calculation based on the tools one has to design districts.

The courts will accept slighter larger micro chops if counterbalanced by other reasonable considerations, of almost any type or nature really, and that includes less erosity. On that one, I have a very high confidence level in my legal opinion.  So unless it is a tie breaker (highly unlikely), no dice for me. Sorry.

I'm not sure we disagree here. As I understand Tennant, WV had three criteria: whole counties, preserving incumbent residences and minimizing the total population shift. The state plan had a range of 0.79% and the plaintiffs offered a number of whole county plans with substantially smaller ranges. Since the plaintiffs' plans all involved larger population shifts SCOTUS found for WV. I read that as saying inequality must be considered, but if small enough it can be subservient to other redistricting rules.

Let me apply that same logic to our rules through an example. Suppose my only criterion was minimizing chops. If I passed a plan with 3 chops and a range of 0.8% and you sued and showed a plan with 3 chops and a range of 0.4% I think you would prevail.

Now suppose there are just two criteria: chops and erosity, and I pass a plan with a score of 3 chops and 25 erosity and 0.8% range. If you sued with a plan of also 3 chops and 25 erosity but 0.4% range then again I think you win. But if you sue with a plan of 3 chops and 26 erosity with a 0.4% range then I win because you can't improve the range without making one of my criteria worse. Even a plan of 2 chops, 26 erosity and 0.4% range can't beat my plan, because it made at least one of my criteria worse.

So in short for any combination of chops and erosity a contesting plan with less inequality will beat it in court as long as it doesn't make either chops or erosity worse. This is a case of Pareto efficiency applied to the map. There are effectively three criteria: inequality, chops and erosity, and any plan that is at the Pareto frontier for those criteria will survive in court. This creates a set of optimal map choices that will be available for the decision makers.

When I am talking parity, I want to see that the metric used for the criteria creates a balance between them in such a way as to produce a meaningful Pareto frontier. Part of this balance is that the frontier has to be easily distinguishable so that the set of points don't all pack towards a single solution. Another part is to get the granularity of the measures at roughly the same scale so that one can't game the system by tweaking a fine grain measurement while being generally locked to a specific coarse measurement.

I found that the OH competition was example of scores that were not equivalent in granularity and it resulted in gaming strategies to draw the map. County fragments could obviously only jump in fixed quanta. Compactness however was measured to many decimal places and only rounded off at the final scores, so that if many maps were locked to the same county fragmentation the scoring was nothing more than measuring trivial changes in compactness. The political scores provided a different problem. A small tweak to the political split in a district could jump the resulting score by a substantial amount due to the rounding, so a competitor would try to micromanage scores right at the jump points.

The lesson I take away from this is that erosity should have roughly the same granularity as our principal other measure which is the chop count. Since chops must move in whole number increments, an ideal measure for erosity would have the same feature that it moved naturally in whole number increments. That lets a mapper more clearly see the tradeoff between chops and erosity.

[muon2]

This is what your actual regions look like.  Your standard deviation is almost 4 times greater than that of my plan.  You require a transfer of 3 times as many persons (9 times if we discount the necessary augmentation of Jefferson.   Moreover, your entry was rejected because of the two regions with a deviation of more than 5%.

The other interpretation is that there are fewer regions in that plan. In order to cover the clusters and stay within your 5% limit I see only 4 regions. One each in the SW, NW, and NE, and one 4-district region to cover the two UCCs and MCC. Fewer regions simply imply more chops or larger chops.

At this point I don't think there is an agreement on crediting smaller chop size for chops larger than a microchop. There was some discussion of this when we were working on CA plans, but there was never an agreement (other than microchops). If there is agreement to reward plans with fewer large chops, it becomes an important new rule.

[Torie]

I understand pareto optimality, and that is just a tie breaker concept. I don't see why just because chops are whole integers, the measure for erosity has to be whole integers. Maybe if you have a clear example of the gaming in Ohio, that might help. I am also not ready to sign off on creating demerit points for the size of macro chops.  But maybe if I see enough maps, and factoring that in, does not cause materially more erosity, I might see the light. It does made map making more complex, which I resist.

[muon2]

I understand pareto optimality, and that is just a tie breaker concept. I don't see why just because chops are whole integers, the measure for erosity has to be whole integers. Maybe if you have a clear example of the gaming in Ohio, that might help. I am also not ready to sign off on creating demerit points for the size of macro chops.  But maybe if I see enough maps, and factoring that in, does not cause materially more erosity, I might see the light. It does made map making more complex, which I resist.

I think we disagree on the use of Pareto optimality here. I have understood since the CA discussions that a goal of this process was to create a set of plans that could go to a decision making body. This was to address the problem you often noted where one plan was strategically designed to win yet presented other unpleasant results. So the the question is how to create a set of options.

One method is to come up with a single score that combines the impact of both chops and erosity, and use the top scoring plans to form the required set. This presents the initial difficulty of determining the relative weight of the criteria - ie how much erosity is one chop worth. Given the discussions here over the last year I think this is a point that will be very hard to get agreement on even from our little clique. Taking it on the road to other groups will expose a number of people who want to weight those factors differently. To see the second difficulty imagine that a person with a particular map agenda (such as protecting a particular incumbent) want that agenda to succeed. They would draw a map that would get a top score but embedding their little piece. Then they would produce a number of variants that were all reasonably similar to spam the map queue with top plans. This would guarantee that their agenda would be in all plans that went forward.

Another method is to keep each criteria score separate and rank the results for the separate scores. The 2009 OH competition did that where they looked at the lowest overall rank. This had the problem that a smart competitor made sure they were top in at least one category even at the expense of another category. A plan that was reasonably good across the board but not best in any category tended to lose out.

My solution to both problems is to track the criteria separately but recognize any plan on the Pareto frontier. This automatically creates a set of qualifying plans and avoids any incentive to either spam the pool or lock out balancing plans. It also avoids the debate about the relative weight of the criteria as long as they are distinct enough to identify the frontier for plans to go forward. A cut of plans at one extreme on the frontier (such as no chops but horrible erosity or perfect rectangles that make excessive chops) is also straightforward to implement.

[Torie]

What rule do you use to cut out the horrible maps?  If any map that at least beats another map on one factor makes the cut, and you have 50 maps, then what?  Give them to McNulty to pick one? 

[muon2]

What rule do you use to cut out the horrible maps?  If any map that at least beats another map on one factor makes the cut, and you have 50 maps, then what?  Give them to McNulty to pick one? 

The coarseness of the chop count will automatically limit the number of offerings. For a given chop count there is an optimal erosity that defines the frontier for those two variables. However, since I also must consider inequality as a tie breaker a coarse erosity measure further helps to limit the number of choices. Then the task becomes one of identifying for each optimal combination of chops and erosity which plan has the least inequality to move forward in the final set.

[Torie]

How do you get more than one map if for a given number of chops, you pick the map with the least erosity? I still don't understand the whole integer concept for erosity either. What you seem to want to do, is treat all maps with an erosity range (I suspect that is what this integer concept is all about) and a given chop count as equal, and then use inequality as a tie breaker. Is that right?  Just why inequality should trump erosity within a give erosity range, escapes me.

It is interesting this game we play. You use mathematical terms, which I then have to struggle to put into a legal format, using the King's English. We would do much better in communicating if you had minored in law, and I had minored in physics or something.

[jimrtex]

But what we both also agree on is that there should be local amendments to any connectivity plan and they should be established well before the process. We differ on the starting point for those amendments.

I would start by saying any contiguous counties in a UCC should be considered connected even if the connecting road clips a county (for example Montgomery to Autauga). Many of the other county clipping connections would surely be added to the list by local choice. But since most of the local decisions are likely to be based on road connection, a baseline from connections is a better starting point. In your list road connections were a key factor, and I would say more important than the length of the boundary segment.

Another advantage to using road connections as a starting point is that local decisions will only be needed to add connections, not to remove them. I don't foresee instances where there is a direct highway connection between two counties that would be excluded from the list. But there are a number that would be naturally added when using a highway-based starting point (Marengo-Greene and Marengo-Dallas are good examples.)

The definition of the state's geography should be established well in advance.

I think you may be too overly concerned about the process of doing so.  What you referred to as "amendments", I might refer to as "consultation".

As I was making my base map adding the population and county IDs, I would check the county connections, and if some looked to be within a few miles, I would make an actual measurement, look at the highways, and make a quick judgment.

The gap test is simple and can be automated.  While you suggest that the highway considerations were significant, the key was those were only seven adjacent pairs of counties that even merited further consideration.

The road connectivity test is not at all that easy to automate.  Is the route between Dallas and Marengo, between Selma and Demopolis or Selma and Linden?  And you are also raising unwarranted concerns about whether or not the road stays within the county line or not.

Measuring border miles rather than counting connections, a couple of miles does not matter.

Let's keep clear what we are trying to curb.  We don't want someone drawing a Pierce-Kittitas district.  But  if we say we don't allow point connectivity, someone will use Lawrence-Cullman.  So we have to expand it further.  While we don't want a Whatcom-Okanogan district, if the folks in Bellingham and Onak get it wrong, it really isn't harmful to the process.

[jimrtex]

Blazer District:

Since Jefferson is close to the population for a district, and since adding no connected county would make it closer, it was made a region of its own.  Whatever is needed to make up the population difference, would be an interregional shift of a portion of a county.

It is possible to create a 2-district region centered on Jefferson (Jefferson plus the 6 adjacent  counties and Cullman is real close to 2.  This might permit either a donut plan, or a split between east and west.  But it appears to also require a rather torturous definition of the surrounding areas.  Placing Jefferson and Shelby within a single two-district region is really the same as simply attaching Jefferson to another region, before splitting it off.

Gamecock District:

A district was created working down from DeKalb, and needed Shelby to get to the correct population (or isolating Shelby if I had continued further south.  The original plan included Cleburne, which would have given a slight over-age to the region, to make up for the deficit in Jefferson.

Based on the usage of UCCs and regions I would say these two form one region at the initial stage. That conforms with the idea that a UCC is entirely embedded in one region. The fact that Gamecock is within 0.5% of the district quota becomes a plus when counting district-level chops, but shouldn't allow it to sit as a separate region.

I understand that you suggested a rule that a whole county region that sits within a UCC can be a separate region, but I'm not sure we have all bought into that. It biases plans towards making such a split if one was available, since that would increase the region count. I'm not sure we all want that bias. I would want to give weight to placing the chop within the UCC if that makes a more compact region centered on the UCC.

Smaller UCCs definitely should be contained within a region.

With larger UCCs, the concern was that you could split outward, Anoka to Superior, Wright to Grand Forks, Carver to Sioux Falls, and Dakota to La Crosse, and reach equality levels that would be impossible if the metro area were kept whole.  But the intent was not to prevent use of internal groupings such as Ramsey-Washington.

Large conglomerations of people make it hard to use whole counties.   But it doesn't make it impossible.  Where they naturally occur, there use should be encouraged.

If the two regions were merged, I would move Cleburne back, and my standard deviation would drop from 1.69% to 1.44% of the quota.  My boundary length would decrease, my population shift would decrease by  about 37%.   But this would be because I am hiding an intra-regional cut.

You do have a point if I had centered a 2-district region on Birmingham (this is possible using Jefferson, its 6 neighbors, including Bibb, and Cullman.   I think that Madison ends up in the wrong place for the two surrounding districts, but disregarding that, that might be an accurate portrayal.

[jimrtex]

I also absent finding a snake hidden away, tend to be comfortable with his connectivity approach, but only for the purpose as counting as another chop appending two whole counties together that have no state highway between them. Adding an exception for a highway that gets there via another county is an unnecessary complication.

It is unclear who "his" refers to.

The objective is to make districts from whole counties.

Imagine an outline map of the state, and you click on a county and it adds it to a district.  You click merrily away, and being a clever lawyer realize that the counties don't have to be touching each other.   The naive program didn't stop you.

To those who created the program it was "obvious" that the counties had to be connected, but had never formally stated that.

So they produce a new program that requires the counties to be touching.   But you are no less clever than before, and discover that Lawrence and Cullman actually do touch, and utilize that in your entry.

The organizers never "thought" of that.

So we are really just defining what touching means.  You think you know what "state highway" means or via another county, because you drive a car, but they really aren't that well defined.  And words like square root scare you.

[traininthedistance]

The objective is to make districts from whole counties.

I strongly disagree with this.  The objective is to make fair, sensible districts, and using counties as a proxy for that is better thought of as merely a means to an end, rather than the end itself.  There are cases where other factors can and should override (such as, but not necessarily limited to, VRA concerns of course).

[jimrtex]

At this point I don't think there is an agreement on crediting smaller chop size for chops larger than a microchop. There was some discussion of this when we were working on CA plans, but there was never an agreement (other than microchops). If there is agreement to reward plans with fewer large chops, it becomes an important new rule.

Our objective is to create districts from whole counties.

We can't do that in most states.   A court would laugh at us if we said our standard was to use whole counties, except when we don't.   Look what happened in Pennsylvania (Bandemer) when they didn't use a consistent standard.

So we have to provide for the use of whole counties, with minimal changes, measured in a standard way, while also supporting other important state goals such as compactness, communities of interest, and citizen participation in the redistricting process, to a reasonable extent.

Splitting counties is bad for a number of reasons:
(1) It supports gerrymandering;
(2) It increases complexity of election administration;
(3) It increases campaign and representation costs;
(4) It may be used for political purposes, protecting a residence, or a political party;
(5) It makes it harder for residents of the county to be represented, or to be elected as the representative.  In effect, vote dilution.

It therefore should be minimized, so that the fewest persons are affected, consistent with our other criteria.

I have not used chop count at all.  If there are N whole-county regions, then N-1 shifts are necessary to provide full equality.  Shifts which are not necessary to bring a region within a deviation of less than 0.5% need not be used.   Shifts which merely bring a region within a 0.5% range are not permitted.   Our objective is equality.

[jimrtex]

The objective is to make districts from whole counties.

I strongly disagree with this.  The objective is to make fair, sensible districts, and using counties as a proxy for that is better thought of as merely a means to an end, rather than the end itself.  There are cases where other factors can and should override (such as, but not necessarily limited to, VRA concerns of course).

If there is not a strong objective of whole counties, then the districts are neither fair nor sensible. 

[jimrtex]

What rule do you use to cut out the horrible maps?  If any map that at least beats another map on one factor makes the cut, and you have 50 maps, then what?  Give them to McNulty to pick one? 

Once you have reduced the number of plans, you present them to a panel of ordinary citizens.  They would be selected on a statewide basis, large enough to be statistically reliable.

They would rate each plan based on how they like the district they would be placed in under each plan.  The best plan would be selected based on Condorcet methods.

There would be a second check to see if the citizens in each district agreed with the statewide consensus, with a possible additional passes for areas of the state that disagreed.

[jimrtex]

Edit: Correction to map only.




Oklahoma

OKLAHOMA CITY, OK 1132/1184 (4/5): Oklahoma County (Oklahoma City, OK 670)  719  670  93% SUA;  Cleveland County (Oklahoma City, OK 107; Norman, OK 104)  256  211  82% SUA;  Canadian County (Oklahoma City, OK 74)  116  74  64% SUA;  Grady County ()  52  0  0% NSUA;  Logan County (Oklahoma City, OK 10)  42  10  25% SUA.

TULSA, OK 746/921 (3/6): Tulsa County (Tulsa, OK 569)  603  569  94% SUA;  Rogers County (Tulsa, OK 18)  87  18  21% NSUA;  Wagoner County (Tulsa, OK 38)  73  38  52% SUA;  Creek County (Tulsa, OK 25)  70  25  36% SUA;  Osage County (Tulsa, OK 6)  47  6  13% NSUA;  Okmulgee County ()  40  0  0% NSUA.

LAWTON, OK 124/124 (1/1): Comanche County (Lawton, OK 94)  124  94  76% SUA.

FORT SMITH, AR-OK 0/0 (0/0): None.


South Carolina

GREENVILLE-ANDERSON-MAULDIN, SC 758/824 (3/4): Greenville County (Greenville, SC 278; Mauldin--Simpsonville, SC 116)  451  394  87% SUA;  Anderson County (Anderson, SC 76; Greenville, SC 32)  187  107  57% SUA;  Pickens County (Greenville, SC 77)  119  77  64% SUA;  Laurens County (Mauldin--Simpsonville, SC 2)  67  2  3% NSUA.

COLUMBIA, SC 647/709 (2/3): Richland County (Columbia, SC 350)  385  350  91% SUA;  Lexington County (Columbia, SC 188)  262  188  71% SUA;  Kershaw County (Columbia, SC 13)  62  13  20% NSUA.

CHARLESTON-NORTH CHARLESTON, SC 665/665 (3/3): Charleston County (Charleston--North Charleston, SC 312)  350  312  89% SUA;  Berkeley County (Charleston--North Charleston, SC 126)  178  126  71% SUA;  Dorchester County (Charleston--North Charleston, SC 110)  137  110  81% SUA.

CHARLOTTE-CONCORD-GASTONIA, NC-SC 226/303 (1/2): York County (Rock Hill, SC 105; Charlotte, NC--SC 55; Gastonia, NC--SC 0)  226  160  71% SUA;  Lancaster County (Charlotte, NC--SC 14)  77  14  19% NSUA.

SPARTANBURG, SC 284/313 (1/2): Spartanburg County (Spartanburg, SC 181; Greenville, SC 15; Mauldin--Simpsonville, SC 2)  284  197  69% SUA;  Union County ()  29  0  0% NSUA.

MYRTLE BEACH-CONWAY-NORTH MYRTLE BEACH, SC-NC 269/269 (1/1): Horry County (Myrtle Beach--Socastee, SC--NC 187)  269  187  70% SUA.

FLORENCE, SC 137/206 (1/2): Florence County (Florence, SC 76)  137  76  55% SUA;  Darlington County (Florence, SC 14)  69  14  20% NSUA.

AUGUSTA-RICHMOND COUNTY, GA-SC 160/160 (1/1): Aiken County (Augusta-Richmond County, GA--SC 101)  160  101  63% SUA.

HILTON HEAD ISLAND-BLUFFTON-BEAUFORT, SC 162/162 (1/1): Beaufort County (Hilton Head Island, SC 69)  162  69  43% SUA.

SUMTER, SC 107/107 (1/1): Sumter County (Sumter, SC 73)  107  73  68% SUA.


Tennessee

NASHVILLE-DAVIDSON--MURFREESBORO--FRANKLIN, TN 1347/1544 (5/8): Davidson County (Nashville-Davidson, TN 605)  627  605  97% SUA;  Rutherford County (Murfreesboro, TN 133; Nashville-Davidson, TN 85)  263  218  83% SUA;  Williamson County (Nashville-Davidson, TN 119)  183  119  65% SUA;  Sumner County (Nashville-Davidson, TN 105)  161  105  65% SUA;  Wilson County (Nashville-Davidson, TN 42)  114  42  37% SUA;  Maury County ()  81  0  0% NSUA;  Robertson County (Nashville-Davidson, TN 13)  66  13  20% NSUA;  Dickson County ()  50  0  0% NSUA.

MEMPHIS, TN-MS-AR 928/989 (1/2): Shelby County (Memphis, TN--MS--AR 891)  928  891  96% SUA;  Tipton County ()  61  0  0% NSUA.

KNOXVILLE, TN 679/774 (4/6): Knox County (Knoxville, TN 385)  432  385  89% SUA;  Blount County (Knoxville, TN 83)  123  83  67% SUA;  Anderson County (Knoxville, TN 43)  75  43  58% SUA;  Roane County (Knoxville, TN 3)  54  3  6% NSUA;  Loudon County (Knoxville, TN 29)  49  29  59% SUA;  Campbell County ()  41  0  0% NSUA.

CHATTANOOGA, TN-GA 336/336 (1/1): Hamilton County (Chattanooga, TN--GA 303)  336  303  90% SUA.

KINGSPORT-BRISTOL-BRISTOL, TN-VA 214/214 (2/2): Sullivan County (Kingsport, TN--VA 76; Bristol--Bristol, TN--VA 36; Johnson City, TN 4)  157  117  74% SUA;  Hawkins County (Kingsport, TN--VA 18)  57  18  31% SUA.

JOHNSON CITY, TN 180/180 (2/2): Washington County (Johnson City, TN 82; Kingsport, TN--VA 8)  123  90  74% SUA;  Carter County (Johnson City, TN 34)  57  34  59% SUA.

CLARKSVILLE, TN-KY 172/172 (1/1): Montgomery County (Clarksville, TN--KY 138)  172  138  80% SUA.

JACKSON, TN 98/98 (1/1): Madison County (Jackson, TN 72)  98  72  73% SUA.

CLEVELAND, TN 99/99 (1/1): Bradley County (Cleveland, TN 66)  99  66  67% SUA.

MORRISTOWN, TN 63/114 (1/2): Hamblen County (Morristown, TN 49)  63  49  78% SUA;  Jefferson County (Morristown, TN 10)  51  10  20% NSUA.


Texas

DALLAS-FORT WORTH-ARLINGTON, TX 6001/6359 (7/11): Dallas County (Dallas--Fort Worth--Arlington, TX 2313; Denton--Lewisville, TX 39)  2368  2352  99% SUA;  Tarrant County (Dallas--Fort Worth--Arlington, TX 1785; Denton--Lewisville, TX 0)  1809  1785  99% SUA;  Collin County (Dallas--Fort Worth--Arlington, TX 560; McKinney, TX 170)  782  730  93% SUA;  Denton County (Denton--Lewisville, TX 327; Dallas--Fort Worth--Arlington, TX 260)  663  587  89% SUA;  Johnson County (Dallas--Fort Worth--Arlington, TX 44)  151  44  29% SUA;  Ellis County (Dallas--Fort Worth--Arlington, TX 84)  150  84  56% SUA;  Parker County (Dallas--Fort Worth--Arlington, TX 7)  117  7  6% NSUA;  Kaufman County (Dallas--Fort Worth--Arlington, TX 3)  103  3  2% NSUA;  Hunt County ()  86  0  0% NSUA;  Rockwall County (Dallas--Fort Worth--Arlington, TX 66)  78  66  84% SUA;  Hood County ()  51  0  0% NSUA.

HOUSTON-THE WOODLANDS-SUGAR LAND, TX 5773/5849 (6/7): Harris County (Houston, TX 4043)  4092  4043  99% SUA;  Fort Bend County (Houston, TX 547)  585  547  93% SUA;  Montgomery County (Conroe--The Woodlands, TX 240; Houston, TX 66)  456  305  67% SUA;  Brazoria County (Houston, TX 152; Lake Jackson--Angleton, TX 75; Texas City, TX 0)  313  227  72% SUA;  Galveston County (Houston, TX 123; Texas City, TX 106)  291  229  79% SUA;  Liberty County ()  76  0  0% NSUA;  Chambers County (Houston, TX 13)  35  13  36% SUA.

SAN ANTONIO-NEW BRAUNFELS, TX 1955/2033 (3/5): Bexar County (San Antonio, TX 1634)  1715  1634  95% SUA;  Guadalupe County (San Antonio, TX 70; San Marcos, TX 3)  132  73  55% SUA;  Comal County (San Antonio, TX 53)  108  53  49% SUA;  Atascosa County ()  45  0  0% NSUA;  Kendall County (San Antonio, TX 1)  33  1  4% NSUA.

AUSTIN-ROUND ROCK, TX 1604/1716 (3/5): Travis County (Austin, TX 954)  1024  954  93% SUA;  Williamson County (Austin, TX 356)  423  356  84% SUA;  Hays County (Austin, TX 53; San Marcos, TX 46)  157  99  63% SUA;  Bastrop County ()  74  0  0% NSUA;  Caldwell County (San Marcos, TX 4; Austin, TX 0)  38  4  11% NSUA.

EL PASO, TX 801/801 (1/1): El Paso County (El Paso, TX--NM 772)  801  772  96% SUA.

MCALLEN-EDINBURG-MISSION, TX 775/775 (1/1): Hidalgo County (McAllen, TX 729; Harlingen, TX 1)  775  729  94% SUA.

CORPUS CHRISTI, TX 405/428 (2/3): Nueces County (Corpus Christi, TX 303)  340  303  89% SUA;  San Patricio County (Corpus Christi, TX 17)  65  17  26% SUA;  Aransas County ()  23  0  0% NSUA.

BROWNSVILLE-HARLINGEN, TX 406/406 (1/1): Cameron County (Brownsville, TX 218; Harlingen, TX 135)  406  353  87% SUA.

KILLEEN-TEMPLE, TX 386/386 (2/2): Bell County (Killeen, TX 172; Temple, TX 90)  310  262  85% SUA;  Coryell County (Killeen, TX 45)  75  45  60% SUA.

BEAUMONT-PORT ARTHUR, TX 389/389 (3/3): Jefferson County (Port Arthur, TX 117; Beaumont, TX 114)  252  231  92% SUA;  Orange County (Port Arthur, TX 36; Beaumont, TX 17)  82  53  65% SUA;  Hardin County (Beaumont, TX 17)  55  17  31% SUA.

LUBBOCK, TX 279/279 (1/1): Lubbock County (Lubbock, TX 237)  279  237  85% SUA.

WACO, TX 235/235 (1/1): McLennan County (Waco, TX 172)  235  172  73% SUA.

AMARILLO, TX 242/242 (2/2): Potter County (Amarillo, TX 110)  121  110  91% SUA;  Randall County (Amarillo, TX 86)  121  86  72% SUA.

LAREDO, TX 250/250 (1/1): Webb County (Laredo, TX 236)  250  236  94% SUA.

COLLEGE STATION-BRYAN, TX 195/195 (1/1): Brazos County (College Station--Bryan, TX 171)  195  171  88% SUA.

LONGVIEW, TX 122/175 (1/2): Gregg County (Longview, TX 93)  122  93  76% SUA;  Rusk County (Longview, TX 0)  53  0  0% NSUA.

TYLER, TX 210/210 (1/1): Smith County (Tyler, TX 130)  210  130  62% SUA.

ABILENE, TX 132/132 (1/1): Taylor County (Abilene, TX 110)  132  110  84% SUA.

WICHITA FALLS, TX 132/132 (1/1): Wichita County (Wichita Falls, TX 98)  132  98  75% SUA.

MIDLAND, TX 137/137 (1/1): Midland County (Midland, TX 118; Odessa, TX 2)  137  120  88% SUA.

ODESSA, TX 137/137 (1/1): Ector County (Odessa, TX 124)  137  124  91% SUA.

SHERMAN-DENISON, TX 121/121 (1/1): Grayson County (Sherman, TX 62)  121  62  51% SUA.

SAN ANGELO, TX 110/110 (1/1): Tom Green County (San Angelo, TX 93)  110  93  84% SUA.

VICTORIA, TX 87/87 (1/1): Victoria County (Victoria, TX 64)  87  64  73% SUA.

TEXARKANA, TX-AR 93/93 (1/1): Bowie County (Texarkana--Texarkana, TX--AR 52)  93  52  56% SUA.

[jimrtex]

So of 268 metropolitan counties, 153 (57%) are clearly in, 100 (37%) are clearly out, and 15 (6%) are edge cases.

Continuing with OK, SC, TN, and TX.

Oklahoma City, OK/Logan County 10K, 25%.   Logan County is north of Oklahoma City on I-35, and barely (25.05%) qualifies.  Guthrie helps hold down the population some.  The 25% of the population in the urbanized area lives in 0.7% of the county area, which illustrates a bit of the problem of characterizing counties.  Most of the land is farm land, but 40% more persons work in Oklahoma County, than do in Logan County.

Tulsa, OK/Creek County, 25K, 36%.  Creek would qualify under a 25%, 40% test.  The urbanized area has absorbed Sapulpa, but the county spreads out and with I-44 access it is easy to commute a long way.

Nashville, TN/Wilson County, 42K, 37%.   Lebanon Urban Cluster is separate from the Nashville urbanized area, and holds the percentage down.  Wilson would qualify under a 25K test.

Kingsport-Bristol-Bristol, TN-VA/Hawkins County, 18K, 31%.

Dallas-Fort Worth, TX/Johnson County, 44K, 29%.  Cleburne Urban Cluster has 35K and holds the urbanized area percentage down.  It is likely that either it will join with the DFW urbanized area, or become an urbanized area in its own right (see McKinney).

Houston, TX/Chambers County, 13K, 36%.  Chambers doesn't have a lot of developable land, so a little bit of spillover goes a long way.

Corpus Christi, TX/San Patricio County, 17K, 26%.  Ingleside-Aransas Pass Urban Cluster as well as several others account for much of the rest of the population.  The county is 80% urban, so the distinction of urbanized area is critical here.

Beaumont-Port Arthur, TX/Hardin County, 17K, 31%.

Summary:

437 metropolitan counties in 11 southeastern states.
133 lack an urban core.

Of the 304 remaining, 232 would pass a 50K/50% threshold, 49 would fail a 25K/25% threshold, and 23 are in between.

[muon2]

My view is that both chops and erosity are important criteria to design a fair map. In measuring those criteria I have two guiding principles. First I want the criteria to robustly capture the essence of how chops and erosity are perceived as creating gerrymandered maps. Second I want the criteria to be simple, KISS as Torie would suggest. As part of the second principle I want the criteria to be easy enough that they can be operated without redistricting software more sophisticated than DRA or even Google Maps, since that's the best way to get the most public participation.

So to this mathematician, here's my view of AL:

Any map can be transformed into a simple planar graph like the one above. For a state each county is a node (or vertex) with links (or edges) between them. For this map the links exist when there is a state highway that links the two counties without going through an intervening county. The only exception is for contiguous counties in the smae UCC which are presumed to be linked. Here that means Montgomery and Autauga are linked despite the highway cutting through a bit of Elmore. Before asking to add other county crossers, I would suggest asking whether one would really want to create a district that hung together solely based on that connection.

We've mostly agreed how to measure chops, but erosity has been a thorn in our side. I suggest that part of that is from making perfect the enemy of the good. My observation is that the primary goal is to penalize districts with long narrow peninsulas, more so when the cut into a district making a cove in the other district. Connections are actually quite good as a means to measure the occurrence of peninsula and coves in a plan.

Division of a planar graph is a well studied field, and when a planar graph is divided one measure is the cut set. That's the set of links that get severed to create the division. It is simple and more erose districts have to sever more links. So I'm using the cut set for a plan as the measure of erosity.

The limitation of the cut set on its face is when there is a chop. To take a simple approach I will treat a chopped county as if it formed a new node for each chop. The chops in the county are presumed to be connected if there is any local road connection. The links that went to the chopped county go to the separate chops based on the chops connections to the adjacent counties.

Let me use two AL plans as illustrations.
Here's my Mobile chop plan. There are two chops (Mobile and Jefferson) plus one microchop (Tuscaloosa). It also includes one chop of the Montgomery MCC and the necessary chop of the Black Belt MCC. I follow the plan with a simple overlay on the graph version of the state. The microchop doesn't count towards the chop count but it does towards erosity. With those three chops added to the cut set the erosity is 53.




Now let me analyze Torie's plan. It has four chops (Walker, Tuscaloosa, Autauga and Washington), and also has the UCC and MCC chop shared by my plan. When I overlay it on the graph it has an erosity of 50 including the addition of the 4 chops to the cut set.




So using the concept of Pareto optimality both these plans are equivalent since one has a lower chop count and the other has lower erosity. However, two of Torie's chops are barely larger than a microchop. If it were possible to reduce those to the size of microchops, perhaps by stretching the Tuscaloosa chop a bit more, then it would exclude my Mobile plan. It would then have the same number of chops, but lower erosity.

[traininthedistance]

The objective is to make districts from whole counties.

I strongly disagree with this.  The objective is to make fair, sensible districts, and using counties as a proxy for that is better thought of as merely a means to an end, rather than the end itself.  There are cases where other factors can and should override (such as, but not necessarily limited to, VRA concerns of course).

If there is not a strong objective of whole counties, then the districts are neither fair nor sensible. 

If whole counties are the only objective, then the districts are neither fair or sensible. 

[jimrtex]

My view is that both chops and erosity are important criteria to design a fair map. In measuring those criteria I have two guiding principles. First I want the criteria to robustly capture the essence of how chops and erosity are perceived as creating gerrymandered maps. Second I want the criteria to be simple, KISS as Torie would suggest. As part of the second principle I want the criteria to be easy enough that they can be operated without redistricting software more sophisticated than DRA or even Google Maps, since that's the best way to get the most public participation.

I don't think that there can be true public participation without access to state supported tools.  

So to this mathematician, here's my view of AL:


Any map can be transformed into a simple planar graph like the one above. For a state each county is a node (or vertex) with links (or edges) between them.

I think most mathematicians would transform a county map into a simple planar graph using a node for each county, and an edge for each pair of adjacent counties, and wonder why your graph does not form a triangular mesh.

Each edge might have various attributes associated with it, such as the coordinates of actual boundary (or direct derivatives such as the end points, or the distance between those two endpoints), whether there is a state highway that ("please explicitly fill in the blank"), as well as whether the two counties may be directly linked into a congressional district.

This format would permit transformation of the graph back into a map.   I don't think that your graph has that property, does it?

For this map the links exist when there is a state highway that links the two counties without going through an intervening county. The only exception is for contiguous counties in the smae UCC which are presumed to be linked. Here that means Montgomery and Autauga are linked despite the highway cutting through a bit of Elmore. Before asking to add other county crossers, I would suggest asking whether one would really want to create a district that hung together solely based on that connection.

"links the two counties" is ambiguous.   "state highway" is ambiguous.  While it might be possible to define districts using linear features, where the population is migrated to the nearest highway, arterial, or collector street, it is much more practical to use areal features like counties.  Further to maintain logical consistency, you should separate parts of counties that are not directly linked by state highway.  While I did that for Grand Isle, I don't think that is a morass that you want to enter into in general.

Further, you open the process to ridicule when the bypass around Hurtsboro snips one census block off Macon County.

I don't see how the following two are materially distinguishable, yet I don't know what my score is on the second map.

We've mostly agreed how to measure chops, but erosity has been a thorn in our side.

Any definition that disregards the magnitude of the chops is wrong.  Dividing a county has a dilutive effect on the representation of the voters in that county.  

I suggest that part of that is from making perfect the enemy of the good. My observation is that the primary goal is to penalize districts with long narrow peninsulas, more so when the cut into a district making a cove in the other district. Connections are actually quite good as a means to measure the occurrence of peninsula and coves in a plan.

Border length is as effective.

[jimrtex]

The objective is to make districts from whole counties.

I strongly disagree with this.  The objective is to make fair, sensible districts, and using counties as a proxy for that is better thought of as merely a means to an end, rather than the end itself.  There are cases where other factors can and should override (such as, but not necessarily limited to, VRA concerns of course).

If there is not a strong objective of whole counties, then the districts are neither fair nor sensible. 

If whole counties are the only objective, then the districts are neither fair or sensible. 

If NO county cuts were made to this map:



It would be both fair and sensible.

[muon2]

I don't think that there can be true public participation without access to state supported tools.

And I find it equally difficult for participation when the state has a monopoly on the tools, particularly if the tools are designed for expert use (as happened in IL in 2011). I liked your suggestion of a tool where users could point and click on whole geographic areas at a time. To be useful it would need to include the ability to turn on a layer and do the same for county subdivisions.

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I think most mathematicians would transform a county map into a simple planar graph using a node for each county, and an edge for each pair of adjacent counties, and wonder why your graph does not form a triangular mesh.
[/quote]
Interesting planar graphs are often those that don't form triangular meshes. Pruning graphs to remove weak links is every bit a part of graph theory. I've taken the graph based on contiguity and pruned it.

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Graphs can have the properties you describe, but need not. I looked at some of those and found they introduced complexity that really didn't change the outcome.

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"links the two counties" is ambiguous.   "state highway" is ambiguous.  While it might be possible to define districts using linear features, where the population is migrated to the nearest highway, arterial, or collector street, it is much more practical to use areal features like counties.  Further to maintain logical consistency, you should separate parts of counties that are not directly linked by state highway.  While I did that for Grand Isle, I don't think that is a morass that you want to enter into in general.

Further, you open the process to ridicule when the bypass around Hurtsboro snips one census block off Macon County.
[/quote]
I will accept the charge of ambiguity. I've posted in the past at greater lengths about highway connectivity and since this post was already quite long I did not go into detail on my views on that point.

I have two comments about the Hurtsboro bypass. First is that a district that only hung together by way of that connection was likely to be erose. In fact I'm not sure any of the offerings relied on that connection so this seems like a point of form over function. Second, you have suggested local modifications to your boundary percent rule and I agree that local modifications can be in order. We both establish baselines, and as long as there is a mechanism for local adjustment I see no reason for ridicule of one baseline compared to the other.

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The score on the map seems pretty easy to compute to me. Since you show no chops, you only need to add up the set of cut links. The yellow line cuts 16, the red line 3, the blue line 2, the green line 5, the purple line 22 and the orange line cuts 3 links. That adds up to 51 total erosity. It's a task that's not much harder than counting chops in a plan.

I don't disagree that we are essentially measuring the same thing. That becomes especially true since you get rid of the problem of wiggly natural boundaries by measuring straight lines to county corners. It becomes a question of computational preference. This probably falls into the same category of my preference to measuring inequality by range instead of your preference to use standard deviation.

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Any definition that disregards the magnitude of the chops is wrong.  Dividing a county has a dilutive effect on the representation of the voters in that county.  

I suggest that part of that is from making perfect the enemy of the good. My observation is that the primary goal is to penalize districts with long narrow peninsulas, more so when the cut into a district making a cove in the other district. Connections are actually quite good as a means to measure the occurrence of peninsula and coves in a plan.

Border length is as effective.

[/quote]
See my comments above.

[traininthedistance]

The objective is to make districts from whole counties.

I strongly disagree with this.  The objective is to make fair, sensible districts, and using counties as a proxy for that is better thought of as merely a means to an end, rather than the end itself.  There are cases where other factors can and should override (such as, but not necessarily limited to, VRA concerns of course).

If there is not a strong objective of whole counties, then the districts are neither fair nor sensible.  

If whole counties are the only objective, then the districts are neither fair or sensible.  

If NO county cuts were made to this map:



It would be both fair and sensible.

No it wouldn't, because it would flount the VRA and obviously fail the Gingles test.  You may think that the state would defend it in court, but if they do so they are wrong, and I will eat all of my hats if the court doesn't concur.

[Torie]

Can you do a gratuitous micro-chop in order to reduce a macro-chop at the other end of a CD into a micro-chop?  That seems wrong to me. And if it is wrong, I don't see how one can reduce chop size without moving whole counties around. Am I missing something?

I take it Muon2 is relying entirely on road chops to test erosity.  That may be a good proxy, or not, in most instances, but whether it is or not, depends on the amount of erosity it allows, which again gets back to how to measure erosity. Why not go for the real thing, rather than the proxy?

[muon2]

Can you do a gratuitous micro-chop in order to reduce a macro-chop at the other end of a CD into a micro-chop?  That seems wrong to me. And if it is wrong, I don't see how one can reduce chop size without moving whole counties around. Am I missing something?

We were doing that in some of the MI examples and everyone seemed ok with it. Essentially it a way of recognizing that the chop is small yet slightly larger than a microchop, and there are convenient nearby districts that can accommodate the shift.

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It's about simple but effective rules. We don't do CoI because it gets complicated, but instead we proxy it with whole counties, munis and UCCs. There are a lot of well known deficiencies with a direct border sum, though jimrtex avoids some of those. Even IA uses two measures rather than rely solely on border length and they have their remarkably uniform counties.

If I add back all possible contiguous links to my graph and assign each a weight equal to the length between the counties on that segment described by the link, then the sum of the weights would be identical to the total border length. Instead I assign a binary 1 or 0 to each of those links based on their connectivity and add up the binary sum, and the graph just shows those links whose value is 1. It correlates well with the actual length, it solves the connectivity definition at the same time, and it can be determined by any of us using DRA much as we do chops.

Why don't we test it and see if it fails in a way that some more mathematical technique would not?