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  Pack and cover rule revisited
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Torie
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« on: August 25, 2016, 07:28:21 am »
« edited: August 25, 2016, 09:39:23 am by Torie »

I have never done Nebraska before, and here is an example of where the rules would force the Omaha district to do something other than macro-chop Sarpy county (which is the way the lines are drawn now). These maps are just an approximation of what the next census would dictate (Douglas, Lancaster and Sarpy counties have all of the population growth in Nebraska). This will be controversial I suspect. The chop of Sarpy does not make the pareto optimal frontier.

Img


Well, I guess the Sarpy chop map can if no subdivision is chopped, and the alternative map has one chop someplace.
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muon2
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« Reply #1 on: August 25, 2016, 03:27:19 pm »

Are you saying that in 2020 it may be that neither macrochop of Douglas or Sarpy would allow for a packed CD without an extra chop into a subunit and without an offsetting erosity reduction?

Hmm.

I'll have to look at my estimates for NE.
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muon2
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« Reply #2 on: August 25, 2016, 10:39:25 pm »

Neither Sarpy nor Douglas have townships that appear in the 2015 estimates for minor civil divisions. Sarpy does have Census-defined county subdivions called "precincts", though these are not the voting precincts of DRA or the current Sarpy elections. Here's the official delineation:

Img


Though there are no 2015 estimates for these precincts, there is ACS data from 2014 that can be compared to 2010. As with the 2015 county estimates I can project these county subdivisions to 2020. It is easy to preserve these subdivisions and have none chopped, as in the following approximate (due to DRA mismatch) example.

Img


So it looks very likely that it will be possible to preserve county subdivisions in the macrochop.
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muon2
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« Reply #3 on: August 25, 2016, 10:51:30 pm »

That leaves the question of whether such a district as in the previous post can survive a Pareto challenge from a plan the keeps all counties whole at the expense of the UCC pack. The problem for my prior offering is that the macrochop runs up the erosity as it should. Since both the UCC pack and whole county plans would count as one chop, the UCC pack can't compete on erosity.

This situation presented itself in years ago in our early work on MI. We resolved the problem by factoring in population inequality along with chops, at a suggestion from train. Macrochops lend themselves better to evening out population, so the CHOP+INEQUALITY combined score replaces the CHOP score on one axis to measure the Pareto frontier. Note that in states like IA and WV where it is easy to avoid county chops, one must use INEQUALITY so that the combined score is (CHOP=0)+INEQUALITY.

I'll take a deeper look at the NE situation to see if C+I improves the outcomes much as it did in MI.
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Torie
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« Reply #4 on: August 26, 2016, 06:50:14 am »

Well that might be the best argument for elevating inequality (which I have been resisting) if the pack penalty is too weak (and one does not want to elevate it further) to keep a map on the pareto optimal frontier that is really what the public square wants when it comes to having a CD wholly within a metro area. It becomes particularly stark where you have a metro area bigger than one CD but smaller than two CD's, and represents a relative large percentage of the state. Coming up with rules that cause something that will instantly result in rejection in a given state is not good.
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muon2
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« Reply #5 on: August 28, 2016, 12:59:53 pm »

In order to look at whether adding the INEQUALITY factor to chops will help here, I want to first look at a couple of whole county examples. They will of course have a CHOP score equal to 1 due to the Omaha pack penalty. I'm using the 2015 Census estimates projected to 2020 for population. This was the INEQUALITY table that I reposted in the regional road thread earlier this year.

RangeInequality
0-10
2-101
11-1002
101-4003
401-9004
901-16005
1601-24006
2401-32007
3201-40008
4001-48009
4801-560010
5601-630011
6301-700012
7001-770013



Here's a very compact version for NE in 2020:

Img


The EROSITY is 13.

The deviations for the three CDs are
CD 1 (Lincoln) -1938
CD 2 (Omaha) -777
CD 3 (Grand Island) +2715
The range is 4654 for an INEQUALITY of 9. The combined score with CHOP is C+I=10.


Here's a much more erose plan designed to reduce the INEQUALITY.

Img


The EROSITY here is 26, much higher as expected.

The deviations are
CD 1 +130
CD 2 -182
CD 3 +52
for a range of 312 and an INEQUALITY of 3. That makes its C+I=4.

The erosity in this version is used to keep it Pareto equivalent with the compact version. My thought is that I should be able to get the same effect with the erosity from the macrochopped Sarpy when the UCC pack is obeyed.

One other note is that it seems the limit on INEQUALITY in the erose plan comes down to the lowest possible deviation of the Omaha district. That makes sense since Douglas county has the largest population and the fewest possible combinations of other counties that bring it under the maximum deviation. Sarpy has a lot of very small subunits so in principle I should be able to get to even lower INEQUALITY with the macrochop.
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muon2
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« Reply #6 on: August 29, 2016, 07:26:12 am »

If I swap Butler for Thayer in the compact version I posted the erosity increases by 1 to 14, but the deviation for the Grand Island CD drops to -49, and the Lincoln CD goes to +827. Withe the Omaha CD at -777, that would make the range 1604 for an INEQUALITY of 6. The combined score with the UCC pack penalty is 7.

Now I can get rid of the pack penalty with the following plan:

Img


The deviations are
CD 1 +32
CD 2 +17
CD 3 -49
for a range of 82 and INEQUALITY of 2. The CHOP is 1, so the combined C+I = 3.

The erosity due to the macrochop of Sarpy is 17, and brings the total EROSITY to 31. That's high, but the small C+I score keeps it on the Pareto frontier.

It appears that a whole county plan that chops the Omaha UCC won't knock out the UCC pack plan if INEQUALITY is added to CHOP to make one of the Pareto variables. The only other question is whether some non-macrochop with less erosity can get the INEQUALITY low enough to knock out the UCC pack.
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Torie
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« Reply #7 on: August 29, 2016, 08:15:02 am »

A lot turns on mathematical accidents involving very few people. That gets me nervous. I like your map though.
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muon2
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« Reply #8 on: August 29, 2016, 09:07:30 am »

A lot turns on mathematical accidents involving very few people. That gets me nervous. I like your map though.

That is true. Any time one wants to preserve whole units (like counties) there will be mathematical "accidents". The WV SCOTUS case came about in part because there was the possibility of a perfect whole county CD  with no deviation from the quota.

As an illustration, there is this graph I put together.

Background: Some time ago there were some threads that tried to optimize the population equality of districts with no county splits. The result of that exercise was the following graph.

Img


Each square represents a state. New England states used towns instead of counties, and states with counties too large for a district assumed that a whole number of counties would nest inside the large county. The more counties available per district, the closer to equality one could achieve, and the relation is logarithmic in population. The green line represents the best fit to the data. Data for average deviation can be fit as well, but the result is not substantially different other than the scale factor that has the average deviation equal to about 1/4 the range.

Most of the data falls near the green line and my method wouldn't be plagued by accidents. There are exceptions, such as the yellow square near the bottom of the chart. That represents ID 2010 and the following plan.

Img


CD 1: 783,792 (quota +1)
CD 2: 783,790 (quota -1)

There just happens to be a plan of contiguous counties with a range of only 2! The good news is that the rules for connections forbids it since Lemhi county isn't connected by road to the rest of CD 1. It also gets a UCC cover penalty for Boise.

The other rules tend to limit the impact of statistical aberrations, but they are unavoidable in any scoring system. The Pareto choice at the end should further mitigate their impact by placing the aberrations in a set with some more reasonable plans.
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Torie
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« Reply #9 on: August 29, 2016, 03:16:50 pm »
« Edited: August 30, 2016, 07:41:09 am by Torie »

"The Pareto choice at the end should further mitigate their impact by placing the aberrations in a set with some more reasonable plans."

 Exactly. And one must make damn sure that it does, rather than get a suck plan, that the black box spits out, that eliminates other options that past the common sense test. Population inequality does not pass the common sense test if it involves de minimus numbers within the 0.5% pad. So its use needs a non obvious side benefit, that will usually avoid the abyss. And we seem to have found one. It would be grand if we could move from "usually" to always." Your example for Idaho would be the abyss if there were but a road from here to there. It would knock out all other maps, no?

I accept allowing a bad map through the filter. But not such a bad map knocking out all other reasonable maps, as seen through the common sense eye of the reasonable person, rather than an elegance freak.

We have a balancing test, between hewing to objectivity, and universal standards, that cannot be characterized as rigged, and avoiding offending common sense. It's not easy. But your work has gotten to a place that might be getting close. Awesome!

Good discussion. Thanks.
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jimrtex
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« Reply #10 on: August 29, 2016, 07:44:59 pm »

Are you saying that in 2020 it may be that neither macrochop of Douglas or Sarpy would allow for a packed CD without an extra chop into a subunit and without an offsetting erosity reduction?

Hmm.

I'll have to look at my estimates for NE.
What is the definition of the pack and cover rule?
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muon2
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« Reply #11 on: August 29, 2016, 10:25:28 pm »

Are you saying that in 2020 it may be that neither macrochop of Douglas or Sarpy would allow for a packed CD without an extra chop into a subunit and without an offsetting erosity reduction?

Hmm.

I'll have to look at my estimates for NE.
What is the definition of the pack and cover rule?


Definition: County Cluster. A connected set of counties sharing a common demographic feature. Connected means able to travel within the cluster to all counties on public roads or ferries without leaving the cluster. The size of a county cluster is the population of the cluster divided by the quota, and rounded up to the nearest whole number.

Definition: Cover. The cover of a cluster is the number of districts including all or part of any county in the cluster. The cover score for a cluster is the difference between the cover and the size of the cluster.

Definition: Pack. The pack of a cluster is the number of districts wholly contained within counties in the cluster. The pack score for a cluster is the difference between one less than the size and the pack of the cluster.

Definition: Urban County Cluster (UCC). A UCC is a county cluster where each county is within the same Census-designated Metropolitan Statistical Area (MSA), and has either an urbanized population of 25K or more, or an urbanized population of at least 40% of the total county population.

Item: A redistricting plan should avoid excess division of county clusters. The CHOP will increase by the cover score for each cluster. The CHOP will increase by the pack score for each cluster.
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jimrtex
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« Reply #12 on: August 30, 2016, 12:06:42 am »

Are you saying that in 2020 it may be that neither macrochop of Douglas or Sarpy would allow for a packed CD without an extra chop into a subunit and without an offsetting erosity reduction?

Hmm.

I'll have to look at my estimates for NE.
What is the definition of the pack and cover rule?


Definition: County Cluster. A connected set of counties sharing a common demographic feature. Connected means able to travel within the cluster to all counties on public roads or ferries without leaving the cluster. The size of a county cluster is the population of the cluster divided by the quota, and rounded up to the nearest whole number.

Definition: Cover. The cover of a cluster is the number of districts including all or part of any county in the cluster. The cover score for a cluster is the difference between the cover and the size of the cluster.

Definition: Pack. The pack of a cluster is the number of districts wholly contained within counties in the cluster. The pack score for a cluster is the difference between one less than the size and the pack of the cluster.

Definition: Urban County Cluster (UCC). A UCC is a county cluster where each county is within the same Census-designated Metropolitan Statistical Area (MSA), and has either an urbanized population of 25K or more, or an urbanized population of at least 40% of the total county population.

Item: A redistricting plan should avoid excess division of county clusters. The CHOP will increase by the cover score for each cluster. The CHOP will increase by the pack score for each cluster.
If the magnitude of a UCC is 1.4,

Why are CDs that are 100% and 40% within the UCC preferred to:

CDs that are 80% and 60% within the UCC

or CDs that are 100%, 25%, and 15%?
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muon2
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« Reply #13 on: August 30, 2016, 12:28:35 am »

Are you saying that in 2020 it may be that neither macrochop of Douglas or Sarpy would allow for a packed CD without an extra chop into a subunit and without an offsetting erosity reduction?

Hmm.

I'll have to look at my estimates for NE.
What is the definition of the pack and cover rule?


Definition: County Cluster. A connected set of counties sharing a common demographic feature. Connected means able to travel within the cluster to all counties on public roads or ferries without leaving the cluster. The size of a county cluster is the population of the cluster divided by the quota, and rounded up to the nearest whole number.

Definition: Cover. The cover of a cluster is the number of districts including all or part of any county in the cluster. The cover score for a cluster is the difference between the cover and the size of the cluster.

Definition: Pack. The pack of a cluster is the number of districts wholly contained within counties in the cluster. The pack score for a cluster is the difference between one less than the size and the pack of the cluster.

Definition: Urban County Cluster (UCC). A UCC is a county cluster where each county is within the same Census-designated Metropolitan Statistical Area (MSA), and has either an urbanized population of 25K or more, or an urbanized population of at least 40% of the total county population.

Item: A redistricting plan should avoid excess division of county clusters. The CHOP will increase by the cover score for each cluster. The CHOP will increase by the pack score for each cluster.
If the magnitude of a UCC is 1.4,

Why are CDs that are 100% and 40% within the UCC preferred to:

CDs that are 80% and 60% within the UCC

or CDs that are 100%, 25%, and 15%?

The full answer is to read the thread from 2013 (I think) when we were all drawing plans for MI. That's where the UCC rules were fleshed out.

The short answer is that a UCC is a community of interest. It should be neither diluted nor have its power dilute other areas outside the UCC. The cover rule initially arose to address the chops to the Lansing area which diluted it and to Detroit so it didn't sway too much of the surrounding area by sending out fingers. The pack rule served some of the same purpose with the Detroit UCC, creating a preference to keep its influence in its UCC to the extent possible.

As Torie noted earlier in the thread UCC's with a population between 1 and 2 CDs seem to provide the greatest challenges. We spent a lot of time discussing Grand Rapids in that MI thread, precisely because of its size.
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jimrtex
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« Reply #14 on: August 30, 2016, 12:41:44 am »

Are you saying that in 2020 it may be that neither macrochop of Douglas or Sarpy would allow for a packed CD without an extra chop into a subunit and without an offsetting erosity reduction?

Hmm.

I'll have to look at my estimates for NE.
What is the definition of the pack and cover rule?


Definition: County Cluster. A connected set of counties sharing a common demographic feature. Connected means able to travel within the cluster to all counties on public roads or ferries without leaving the cluster. The size of a county cluster is the population of the cluster divided by the quota, and rounded up to the nearest whole number.

Definition: Cover. The cover of a cluster is the number of districts including all or part of any county in the cluster. The cover score for a cluster is the difference between the cover and the size of the cluster.

Definition: Pack. The pack of a cluster is the number of districts wholly contained within counties in the cluster. The pack score for a cluster is the difference between one less than the size and the pack of the cluster.

Definition: Urban County Cluster (UCC). A UCC is a county cluster where each county is within the same Census-designated Metropolitan Statistical Area (MSA), and has either an urbanized population of 25K or more, or an urbanized population of at least 40% of the total county population.

Item: A redistricting plan should avoid excess division of county clusters. The CHOP will increase by the cover score for each cluster. The CHOP will increase by the pack score for each cluster.
If the magnitude of a UCC is 1.4,

Why are CDs that are 100% and 40% within the UCC preferred to:

CDs that are 80% and 60% within the UCC

or CDs that are 100%, 25%, and 15%?

The full answer is to read the thread from 2013 (I think) when we were all drawing plans for MI. That's where the UCC rules were fleshed out.

The short answer is that a UCC is a community of interest. It should be neither diluted nor have its power dilute other areas outside the UCC. The cover rule initially arose to address the chops to the Lansing area which diluted it and to Detroit so it didn't sway too much of the surrounding area by sending out fingers. The pack rule served some of the same purpose with the Detroit UCC, creating a preference to keep its influence in its UCC to the extent possible.

As Torie noted earlier in the thread UCC's with a population between 1 and 2 CDs seem to provide the greatest challenges. We spent a lot of time discussing Grand Rapids in that MI thread, precisely because of its size.
Are we trying to extrapolate from larger UCCs such as Detroit where it is trivial to have CD's within the UCC, and smaller UCC's such as Lansing where it relatively trivial to have the whole UCC within a CD. Also since the Detroit UCC is so close to a whole number, it may have influenced our thinking. If its magnitude was 5.5 or 6.5 would the rule been the same.

Should the same rule apply to a UCC with a magnitude of 1.8 and one with a magnitude of 1.2?
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muon2
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« Reply #15 on: August 30, 2016, 06:40:05 am »

Some of the initial discussion of the UCC rules considered mandating certain numbers of pack and cover districts. Because of the wide variation of situations for UCCs the rules became point modifiers. I pictured the cover rule as an extension of the county chop rule to entities made up of multiple counties.
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jimrtex
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« Reply #16 on: August 31, 2016, 04:40:52 am »

Some of the initial discussion of the UCC rules considered mandating certain numbers of pack and cover districts. Because of the wide variation of situations for UCCs the rules became point modifiers. I pictured the cover rule as an extension of the county chop rule to entities made up of multiple counties.

What if it were a pack OR cover rule?

Have you considered a cover: of ceil(pop/quota + x) where x is some value greater than zero?
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