Chops and Erosity - Mid Atlantic Madness

[jimrtex]

Here is my take. We start by marking the UCCs, which should ideally match a whole number of districts, either chopping a little bit off or adding a little bit.



NYC   17.871
Albany   1.117
Rochester   1.120
Buffalo   1.472

We need to add a bit to NYC, and trim Albany and Rochester.

Buffalo is half-way, but Erie alone is 1.200 and will have to be divided, so we will define a two-district region in the west.

[jimrtex]

This is after adjusting UCC's.



NYC: We can add Sullivan, Ulster, or Columbia. Adding Sullivan gets us closest to 18 districts.

17.967 (18 districts) -0.2%

Buffalo: We first add Orleans, Genesee, and Wyoming. If we continued eastward we would be well past Rochester. We add Chautauqua and Cattaraugus. The choice of Livingston over Allegany is based on population.

1.998 (2 districts) -0.1%

Rochester: We drop Ontario. There is no county that can be added to Monroe that will make the district closer to the quota.

0.976 (1 district) -2.4%

Albany: Eliminating any of the four counties reduces the total to well below the quota. So we need to make a subtraction and an addition. Cutting Schenectady cuts in too much. Saratoga and Rensselaer are more peripheral. Rensselaer is removed because it has less population, leaving more of the UCC in  the district. Schoharie and Montgomery are added to get back up to the quota.

1.011 (1 district) +1.1%

The remainder of the state has a population equivalent to

4.048 (4 districts) +1.2%

[jimrtex]

Here is the final upstate map.



1. Buffalo
2. Niagara Frontier

1.998 (-0.1%)

3. Rochester

0.976 (-2.4%)

4. Finger Lakes - Southern Tier

1.018 (+1.8%)

5. Syracuse - Utica

0.995 (-0.5%)

6. North Country

1.011 (+1.1%)

7. Albany - Saratoga - Schenectady

1.011 (+1.1%)

8. Binghamton - Troy - Catskills

1.024 (+2.4%)

[jimrtex]

Honey, just bear in mind I did not want to macro-chop Westchester a second time, nor Rockland. Nor did I want to macro-chop Saratoga. And I paid the price, in exchange for a boatload of avoided erosity penalty points. I did basically the same thing you did, by spreadsheet, moving CD quota percentages around between CD's, and looking for macro-chop situations to either suck up or avoid.

Yeah, maybe you have found a way to avoid a chop involving the Albany CD (I have a small clean chop of Saratoga). But it looks like you got 1.1% to divide up, sluffing off 0.6% (requiring two CD's to stuff off onto), maxing out inequality, and then you have the issue of whether you will be chopping towns to get a perfect split.

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Can you seriously believe that under my plan that the people of upstate New York will not choose their representatives?

[jimrtex]

This is a roughed out version of the NYC area.



Metro North:  2.829

The area will need to go into the Bronx for about 0.157 quotas (120K persons)

The west bank of the Hudson (Rockland, Orange, Sullivan) is just above a quota (1.032). Around one of the bridges (near Newburgh, Peekskill, Nyack) about 28K persons will be added to an east bank district.

Dutchess, Putnam, the 28K from the west bank and about 345K of northern Westchester will form another district.

Around 648K from Westchester and the 120K from the Bronx will form the third district.

Bronx and Manhattan 4.138 - 0.157 = 3.981

Roughly two districts will be placed in each borough, but about 150K from extreme northern Manhattan will be added to the Bronx. I would try for a north-south split of Manhattan, and an east-west split of the Bronx.

Long Island and Staten Island have a population for 11 districts (10.999).

This can be be broken down into:

Brooklyn + Staten Island 4.148

Staten Island + about 288K from Brooklyn
3 districts in Brooklyn
114K added to Queens.

Queens and Nassau 4.909

3 districts in Queens + 114K from Brooklyn
212K added to Nassau

2 districts in Nassau + 212K from Queens
44K added to Suffolk

Suffolk 1.942

2 districts in Suffolk + 44K from Nassau

One district will cross each of the county lines:

Suffolk-Nassau
Nassau-Queens
Queens-Kings
Kings-Richmond
New York-Bronx
Bronx-Westchester
Putnam-Westchester

Orange or Rockland-Putnam or Westchester

[jimrtex]

Below is the Jimrtex map for upstate, with the details filled in. It has one less chop point as compared to mine (by avoiding a pack penalty for the NYC urban cluster), but it is at the cost of a macro-chop in Rockland, sending the erosity score through the roof (it also has to chop Orangetown), and creating a rather unfortunate looking CD that happens to be the one in which I reside.  But it does make the pareto optimal frontier.

The division of Ontario, Oswego, and Schoharie counties are not needed.

You could put Newburgh with Dutchess, Putnam, and northern Westchester.

[jimrtex]

I would think that LATFOR has the minority data from the ACS mapped to the census block group level for NYC as well as the rest of the state.

I doubt that LATFOR has done anything with ACS data.

For an area as small as a block group (around 1000 persons) you have to use 5-year data (2011-2015).

[jimrtex]

Below is the Jimrtex map for upstate, with the details filled in. It has one less chop point as compared to mine (by avoiding a pack penalty for the NYC urban cluster), but it is at the cost of a macro-chop in Rockland, sending the erosity score through the roof (it also has to chop Orangetown), and creating a rather unfortunate looking CD that happens to be the one in which I reside.  But it does make the pareto optimal frontier.

The division of Ontario, Oswego, and Schoharie counties are not needed.

You could put Newburgh with Dutchess, Putnam, and northern Westchester.

"The division of Ontario, Oswego, and Schoharie counties are not needed."

My spreadsheet says that they are.

'You could put Newburgh with Dutchess, Putnam, and northern Westchester."

You mean divide the macro-chop into two pieces, so that there is no longer a macro-chop? That generates another chop, and you are tossed off the pareto optimal frontier (if my spreadsheet numbers are right). It also generates a bridge chop, which is penalized in some fashion, and which I think should be avoided. Allowing them without substantial punishment allows games such as the one you suggest, to be played.

Read 'Tennant v Jefferson County Commission' carefully. New York has a legitimate state interest in basing congressional district boundaries on counties. Historically, until the OMOV decisions of the 1960s, only the largest counties were divided. But because Kings County must be divided does not mean that Hamilton must also be divided.

Rather than a single region covering the NYC UCC, we can subdivide it into 5 regions.

The only chopped counties are Nassau, Queens, Kings, New York, Bronx, Westchester, and Erie, all of which are entitled to more than one district. Suffolk will have two whole districts.

[jimrtex]

I have read Tennant and I don't find anything there that suggests a state can have a range substantially beyond the "minor" variation of 0.79% without something more compelling than the whole counties and minimal population shift in WV. That 0.79% refers back to a number discussed in Karcher v Daggett. As the case notes,

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Unlike WV, NY does not have a long history of completely preserving counties and they could not use that argument from Tennant (The court found that WV had never in its history chopped a county). A case could be made that preserving towns and cities while chopping some minimal set of counties would better balance those interests. I don't see the case that NY could make to have a range in excess of 1%.

That said, we are only looking at projected estimates for 2020. A larger range makes sense in that context. But it should be understood that as the estimates get closer to Census day and the accuracy of the projection increases, the range should drop accordingly.

New York does have a long history of preserving county boundaries.

In the early 19th century they used multi-member districts. By 1842 they had switched to single-member districts. New York County was divided into 4 districts. Hamilton was also divided but that appears related to its formal organization in 1847.

1850s: New York + Kings
1860s: New York + Kings
1870s: New York + Kings
1880s: New York + Kings + Erie
1890s: New York + Kings + Erie
1900s: New York + Kings + Erie
1910s: New York + Kings + Erie + Queens + Renssellaer + Monroe
1940s: +Nassau, Bronx
1960s: +Suffolk, Westchester.

New York has had some horrid districts, such as all the ones in NYC connected by stretches of water, or that district that connected Rochester and Buffalo by a narrow shoreline strip. Those cannot be considered precedental.

Do you think that Justice Neil Gorsuch's constitution has anything about making districts vary by one person?

"flexible" is the opposite of "rigid".

My plan consistently applies rules that limit division of counties to counties with more population than a single county.

Suffolk: 2 whole districts.
Nassau: 1 whole + 1 surplus (shared with Queens)
Queens: 3 whole + 1 surplus (shared with Nassau)
Kings: 3 whole + 1 surplus (shared with Richmond)
New York: 2 whole + 1 surplus (shared with Bronx)
Bronx: 1 whole + 2 surpluses (shared with New York, Westchester)
Westchester: 2 parts (shared with Bronx, and Dutchess/Putnam)
Erie: 1 whole + 1 surplus (shared wit 7 other counties)

The only things that are slightly irregular are the division of Westchester and Bronx, which is largely dictated by geographic constraints.

My plan has nothing to do with the fact that it is using projected population. That was simply a way to generate a different population base with a different number of districts. I could follow the same approach and generate a map for 2010, or 2016 (using the current estimates).

[jimrtex]

We've had this debate before. Fundamentally I think that as the range gets up over 1% it starts to look like the substantially equal standard which is applied to the states. The standard for CDs uses the equal as practicable standard. If words mean anything then "substantially equal" is different than "as equal as practicable", and I would expect the court to find that there is a difference. We know that substantially equal can mean up to a 10% range. If the range of a congressional plan approaches 10% and is upheld then there is no difference that I can see.

The difference in standards derives from the basis on which 'Reynolds v Sims' and 'Wesberry v Sanders' were decided. Reynolds was based on the equal protection clause of the 14th Amendment, while Wesberry was based on the court's interpretation of Article I, and a federal statute passed by Congress in 1872, that required election by districts that were "as equal as practicable" (in population). Congress repeated that language in statute for five decades before deliberately removing it.

If words indeed do have meaning, we should look at the understanding of the term when it was placed in statute:

New York congressional districts 1875-1883

[jimrtex]

I don't find the history of NY CDs compelling before the OMOV rulings of the 1960's. I'm also not seeing the case and 5 justices that would reinterpret Wesberry to match Reynolds during the upcoming cycle.

The problem is not Wesberry, The problem is Kirpatrick v Preisler, etc.

Wesberry did not define the term "as nearly as is practicable" (re-read Justice Harlan's dissent). The court apparently borrowed the term from the 1872 statute in which Congress first mandated use of single member districts. It is therefore relevant to understand what "as nearly as is practicable" meant to those (Congress and legislatures) who have actual authority under the Constitution to legislate congressional boundaries.

Explain why you believe the Muon method represents a good faith effort at population equality.

[jimrtex]

I don't find the history of NY CDs compelling before the OMOV rulings of the 1960's. I'm also not seeing the case and 5 justices that would reinterpret Wesberry to match Reynolds during the upcoming cycle.

Why is this better?



And why doesn't it beat anything that can be produced under your rules?

[jimrtex]

If the goal is to share maps that show what might be in 2020, and those maps are based on minimizing chops and erosity, then I'm saying those maps may have little to do with what will really be possible after Census data comes out. A 1% shift in the overall deviation due to differences in projection vs future reality can substantially change the groupings that minimize chops.

I disagree with that as a goal.

I think we are just manipulating our data set in a realistic way (projecting population, and reducing the number of congressional districts to  produce a different test case. We could just as easily use historical data.

[jimrtex]

I don't find the history of NY CDs compelling before the OMOV rulings of the 1960's. I'm also not seeing the case and 5 justices that would reinterpret Wesberry to match Reynolds during the upcoming cycle.

Why is this better?



And why doesn't it beat anything that can be produced under your rules?

It might depending on the specific data.

There is a natural trade off of chops for population inequality, and as more geographic units are available the lower the theoretical inequality. Analysis of the 2010 data gave rise to this graph and table from the muon rules thread.

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We looked at use of the table in the MI exercise a few years ago. Summing the CHOP and INEQUALITY scores gave a good measure of that trade off and how well optimized it was. For example, this was my upstate NY plan from last year's estimates (2015 vintage) projected to 2020. The upstate CDs (19-26) have 4 county chops, 1 UCC pack penalty, and a range of 7401 for an INEQUALITY of 13. The total with CHOP is 18 and is paired with an erosity of 44.

This might be even better politically, and it's hard to see any serious complaints from the fruited plain. It keeps chops the same and reduces erosity by 3, so it is certainly better by the basic rules. Two points of the erosity reduction is in a more compact Buffalo-Niagara Falls CD, the other point comes from a reduction of 3 from the Hudson CD with an increase of 2 from the North Country. Everything still projects within 0.5% of the quota for 2020.

My latest upstate plan has a range of 880, more than 8 times as good as your plan.

What interest does the state of New York have in tying its hands with your method. As the plaintiff attacking your plan, I have met the first condition of Karcher v Doggett. What important state interests are vindicated by your method?

In Kirkpatrick v Preisler, the SCOTUS rejected shape and communication ties as justification for larger deviation. Are erosity and chops legitimate metrics for some legitimate state objectives?

A particular reason the SCOTUS rejected setting a de minimis deviation range, was that legislators might tend to use the maximum range as a target. Isn't this same problem inherent in using a single value to measure inequality?

[jimrtex]

So with the idea that the sets of numbers are independent, here's what I might draw for upstate NY using 2016 county estimates projected to 2020. CDs are all within 0.5% of the quota and chops are minimized and placed to minimize erosity. CD 18 (with Hudson) is drawn to avoid a macrochop since it would only be about 14K overpopulation with whole counties.

You are using a target deviation range of 1%, where the SCOTUS has explicitly refused to set a de minimis standard. Your plan has a deviation range about 8 times as large as my last plan. What state interest justifies this large deviation?

[jimrtex]

So with the idea that the sets of numbers are independent, here's what I might draw for upstate NY using 2016 county estimates projected to 2020. CDs are all within 0.5% of the quota and chops are minimized and placed to minimize erosity. CD 18 (with Hudson) is drawn to avoid a macrochop since it would only be about 14K overpopulation with whole counties.

You are using a target deviation range of 1%, where the SCOTUS has explicitly refused to set a de minimis standard. Your plan has a deviation range about 8 times as large as my last plan. What state interest justifies this large deviation?

I set an upper limit (not a target) of 1% range to be consistent with described minor deviations. I find a state interest in minimizing divisions of political subdivisions including counties and towns. I find a state interest in making districts compact in terms of the road connections between political subdivisions. I find a state interest in minimizing population balanced by those other interests using a consistently applied measure of that balance.

The SCOTUS has said that setting an upper limit becomes a target. What are the deviations of your districts, and what is the maximum deviation range, and what is the standard deviation of the deviations?

As early as Reynolds v Sims (quoted in Kirkpatrick v Preisler) the court rejected communication concerns as a rationale for deviation.

Did you produce your connectivity graph at the outset of the redistricting process, and available to all potential participants or was it a post hoc construction?

Side issue: won't either your 16 or 17 have to go into the Bronx?

[jimrtex]

As I noted above the chop of Saratoga County in my map is right on the edge, very close to the point where the chop can be lost, with the Albany CD taking Hamilton County instead.

Granted in some cases the precinct lines do not fit, but it should be villages that are used (the precinct lines can be corrected). Even if the entirety of the territory is not covered in villages, the odd territory remaining would need to be cut reasonably to keep the erosity score down.

I asked you before to remind me what the penalty is for a subdivision chop, and again for a bridge chop. My impression in both cases is that it results in more erosity penalty points.

A bridge chop incurs a penalty if it causes the counties to be connected only by local roads and not be regional roads. Groups of regionally connected counties are called components and a plan gets an erosity point for each component in a district in excess of 1. Note that this definition also solves the nick cut problem when counties are otherwise locally connected.

In a macrochop the rule is clear - a subdivision chop gets treated just like a county chop. For other chops we've gone back and forth. It's clear we like chops to be made of whole subunits, at least that's what we are doing in upstate NY.  If so, then chopping a subunit should be counted as any other chop. Otherwise why bother keeping subunits whole in upstate. However, you have in the past desired a "one bite" rule which allows one subunit to be chopped as part of a chop of the unit containing it. If that's applied uniformly then a simple chop of a county can include one chopped subunit.

I understand about villages, but subunits have to cover all the population of a county. They can be a hybrid of different units, such as incorporated cities and remaining school districts as we did in WA. The key point is that no population in the county can be left out of the defined subunits. If villages leave population unassigned, what is the mechanism for assigning that remmant population?

You have the same issue as between cities and unassigned territory. And villages are real. They are incorporated with real powers. They are not mere hamlet addresses, such as Stottville or Spencertown in Columbia County.

Regarding unassigned territory, if most is assigned, with just a few gaps, does it matter much? Just assign a penalty point for each village that appends it that is in a different CD.

Thanks for the other explanations. I prefer the one bite rule (it should not be the same as a county chop, which is far more important, as most would agree), but there should be a preference where there is no bite at all. I know you don't like preferences, but not having one, defies common sense.

Your bridge chop rule is way too weak for me. In most cases, it will be possible to avoid severing a state road. To not penalize a bridge chop at all where such severing is avoided, I think can lead to mischief, and allows to much discretion. I dissent.

I went through a lot of examples that had bridge chops and why people put them in. I looked at my proposed rule from the purely theoretical, too. I'm actually quite confident that this rule causes no more mischief than the basic chop rule. I'm open to a case that causes such mischief that it could be rethought. Show me the basis for your dissent.

Since you prefer the one bite rule, but not at the level of counties, does that mean you only want it for sub-subdivisions? If so, and NYC is divided up into the neighborhoods we discussed, then those are only first level subdivisions and the one bit rule wouldn't apply. Yet predefined neighborhoods in Chicago (77 community areas tied to the Census) would be second level and one-bite would apply. Am I getting any of this right?

I'm completely blank on your suggestion for unassigned territory. Every census block must be assigned to a subdivision before maps are drawn other wise the scoring becomes arbitrary and algorithms fail. If Nassau's villages are incorporated like cities can the the remaining area be fragments of the unincorporated town? I'm thinking of the pieces of townships left in Hamilton county OH between Cincinnati. It doesn't help that some of the places in a town in Nassau are actually villages (eg Atlantic Beach) and others are Census Designated Places (eg East Atlantic Beach) and they are all sub-subdivisions of the county as opposed to OH where they are just county subdivisions.

Edit: Upon investigation I learned a little more about places in Nassau. There are five county subdivisions. Glen Cove and Long Beach are cities. Hempstead town is totally filled by villages and CDPs, so there is no issue with remnant population. North Hempstead and Oyster Bay towns do have remnant 2010 populations of 571 and 405 respectively. I know these are small, but they still have to be definitively assigned either to a place or as their own fragments prior to mapping.

Edit 2: I checked Suffolk as well. There are 12 county subdivisions, but only two towns that have any 2010 population not in a village or CDP: Brookhaven town has 18 and Huntington town has 30. Of course the algorithms still need them assigned to some sub-subunit despite their small size.

Villages in New York are not independent of towns, and may cross town and even county boundaries.

Cities in New York are not incorporated in the sense found elsewhere, but are chartered by the state legislature, and are treated as town equivalents for purposes of subdivision of counties.

Nonetheless, it is reasonable to base 3rd-level divisions in Nassau, Suffolk, Westchester, and Rockland on villages, at least for congressional district sized units. For county legislatures, towns may be ignored.

[jimrtex]

These are 5 county-level maps.

Jimrtex 19.0% cumulative deviation (this treats the two westernmost districts as one district, and disregards the Long Island and Staten Island districts). Interior perimeters 949 miles, and stranded persons: 87,747 persons (11.4%) to be shifted to bring the map into perfect equality.



Torie: 21.6%, 999 miles, 82,748 persons (10.8%)



Torie (modified by switching Cortland and Hamilton): 13.6%, 1077 miles, and 100,724 persons (13.1%) (though district deviations are decreased, an regional bias is introduced which requires some double shifts to eliminate).



Muon2: 14.0%, 1049 miles, 56,259 persons (7.3%)



Muon2 (modified by switching Seneca) 8.8%, 1058 miles, 35,874 persons (4.7%)



*****

Even if the boundaries are later fudged to comply with presumptive SCOTUS dictates, isn't this as much simpler and transparent way to evaluate maps.

[jimrtex]

Should the percentages add up to 0? Ie, the percentage are measured as a fraction of a quota, which is how we measured multi-district regions in the past.

It looks like these percentages are measured as a fraction of whole number of districts. At one point we thought that it might make sense to constrain the size of multi-district regions by something like the square root of the number of districts times the deviation. The idea being that it gets hard to follow subunits and maintain reasonable deviations when the multi-district region has itself a large deviation.

The percentages on the map are deviation per district.

My New York-Bronx-Westchester-etc. region, has a a population of 5.936 quotas for 6 districts, or 0.989 per district. The map shows a deviation of -1.1% per district.

But in calculating the total deviation I used the combined deviation of -6.4%. What we are trying to calculate is the number of persons that have to be moved into or out of regions to bring them into total equality. For this purpose, I treated the Buffalo and Niagara Frontier regions as a single region having a deficit -0.2%. I also excluded the Long Island and Staten Island regions since they are the same for all the maps, and have a total magnitude extremely close to 11 quotas.

This percentage assumes that we can move people in and out without shifting boundaries. But we have to move people between adjacent districts. If districts with a surplus were adjacent to districts with a deficit, we can simply move people from the surplus regions to the deficit regions. The number of people moved can be as small as half the total deviation. That is, to equalize a region with a 3% surplus  with a region with a 3% deficit, we only need to shift population equivalent to 3% of a quota. Moving 3% reduces both the surplus and deficit by 3%.

But we might have to move people from a region with a surplus into a region with a deficit, and then on to another region with a bias. This can indicate a regional bias. This be seen most clearly with Torie's plan and the version that I modified by shifting Cortland. This reduces the total deviation, but increases the number of persons that have to be moved.

His plan was designed to reduce the amount of correction needed to approach equality, while the modified plan provides better equality among whole county regions.

To calculate the number of people that need to be shifted to achieve total equality, begin with a network where each node represents a region, and the links represent adjacent regions (here adjacency takes into account non-traversable boundaries such that the regions on either side are not considered to be adjacent).

We find a subnet that has exactly N-1 links, where N is the number of nodes, and there are no loops and would require the minimum number of persons shifted to reach full equality.

The amount shown does not include the shift between the Buffalo and Niagara Frontier region, but it does include a small shift from the Southern Tier-Finger Lakes region to the Niagara Region. It also does not include the shifts among the Long Island and State Island regions, or the tiny amount from Manhattan to the south. It does include a consequent adjustment in the upstate region.

*** Note I recalculated the total deviation using my spreadsheet. I also expressed the total shift amount as a percentage of a quota. And I halved the perimeter. I had measured the perimeter of each region and then summed them. This in effect doubles the length.

[jimrtex]

Here's hwo I would analyze the maps. I'm only going to consider the upstate CDs, and I'll treat the two Buffalo CDs as a single whole county region of size 2 and ignore internal chops. The number of chops are based on the fewest county divisions needed to bring populations to the level of minor variations cited in Tennant. Regional erosity uses this map of regional connections and counts the number of cut links. I ignore the ability of well-designed chops to reduce erosity.

These are 5 county-level maps.

Jimrtex 19.2% cumulative deviation (this treats the two westernmost districts as one district, and disregards the Long Island and Staten Island districts). Interior perimeters 1898 miles, and stranded persons: 87,747 persons to be shifted to bring the map into perfect equality.

Chops 5, Erosity 40

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Chops 5, Erosity 44

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Chops 6, Erosity 45

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Chops 3, Erosity 44

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Chops 3, Erosity 45

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Perimeter measurements are fine to a point, but they have known shortcomings. They overcount perimeters due to natural geography like rivers and mountains. For example Herkimer has a long perimeter up north that encloses little population and has no impact on erosity. Perimeters also undercount effects in urban areas since they aren't scalable to districts that pack in a city.

I used the straight-line distance measured from intersection to intersection. While there is some additional erosity caused by Herkimer in your and Torie's map it does not account for all the differences.  My Albany and Syracuse districts are more compact, as is the Finger Lakes-Southern Tier district because it is more square.

It is very hard to count erosity, and the rules for treating counties as being connected is close to capricious. New York in the past has had districts connecting Schoharie and Greene; Madison and Oswego; Hamilton and St. Lawrence; Herkimer and Lewis; Herkimer and St.Lawrence; and Allegany and Livingston.

Even including a connection between Seneca and Yates across Seneca Lake should be acceptable at the scale of congressional districts. The route from Waterloo to Penn Yan avoids the center of Ontario County.

Does the erosity measure scale within cities, and does it matter if it does or not? If a better division of Queen can be devised, should it matter to the upstate districts?