Redistricting - Jimrtex, Alternate Process, Scoring System
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Author Topic: Redistricting - Jimrtex, Alternate Process, Scoring System  (Read 4210 times)
jimrtex
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« on: February 26, 2015, 01:24:53 AM »

The objectives of this scoring system are:

1. Strong incentive to respect political subdivisions.
2. Respect for major metropolitan areas.
3. Encourage crowd-sourcing.

Reasons for these objectives are as follows:

1. Strong incentive to respect political subdivisions.

A. Serves as check on gerrymandering.   Splitting public subdivisions leads to districts intricately drawn for political advantage.

B.  Respect for political subdivisions is good public policy.  Election administration is simplified.   Voters will be able to comprehend which district they live in, and be able to better focus on who their representatives are.   They will be able to join with their neighbors in electing a representative, increasing the likelihood that the representative will be responsive to their common concerns.  It will increase the likelihood that those elected will be representative of their district.

2. Respect for major metropolitan areas.

A.  Districts will be more compact.  Districts will be more likely to be entirely (or mostly) within larger metropolitan areas, reducing campaign costs.  Voters in less populous areas will not be overwhelmed by the mass of voters in the metropolitan areas.   Districts will be less likely to span across 100s of miles.  Districts that do extend outside the metropolitan areas may still have some affinity with the metropolitan city, through common media sources, shared major facilities such as airports, hospitals, sports teams, etc.

3. Encourage crowd-sourcing.

A. Makes the entire process more transparent, reducing the ability to gerrymander.  Public hearings are of limited utility, as the "public" will tend to be agents of special interests, and the public officials will be unwilling to tip their hand.  They will say they they are their to listen, but may forget what they have heard, or be unwilling or unable to apply it.
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jimrtex
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« Reply #1 on: February 28, 2015, 08:00:03 PM »

The process would be conducted in multiple phases.


Phase 1.  Divide the state in to whole county regions, each of which has a population equal to roughly an integer number of districts. 

In less densely populated areas, each region will correspond to a single congressional district, which may only need minor adjustments to meet equal-population standards.  In more-densely populated areas, particularly major metropolitan areas, regions will correspond to multiple districts.

This phase serves the objectives of respect for major metropolitan areas.  It requires use of the most important political subdivisions, the counties, to be used as building blocks for districts.  And it encourages crowd-sourcing, since creation of the regions is a much more amenable task than creation of a complete map.


Phase 2.  Refine the boundaries between the regions to bring them into Supreme Court standards for population equality.  In less densely populated areas, the regions will become the final district boundaries.   Since Phase 1 identified the size of the adjustment, and location between pairs of regions, this phase can be done independently and parallel.  Each adjustment will be done by shifting whole townships and cities between the regions.

This phase respects secondary political subdivisions, while substantially maintaining the county-based regions delineated in the first phase.  Because the second phase is done independently for each adjustment, it facilitates crowd sourcing since alternatives may be proposed for each county, without having to evaluate combinations of changes.


Phase 3.  Define congressional districts in mult-district regions.  Each region will be treated divided separately.   While there will be some county division in this phase, multiple spanning of counties will not be permitted.  Multiple spanning is when two or more districts share portions of two counties.  Alternatively, it means that only one district will cross a county boundary.

While district boundaries within metropolitan areas are less likely to conform to county boundaries, they are still respected by preventing unnecessary division of counties.  District boundaries will largely conform to secondary political subdivision boundaries.  Crowd-sourcing is supported by concentration on a single metropolitan area.
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jimrtex
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« Reply #2 on: March 01, 2015, 04:53:48 PM »
« Edited: March 02, 2015, 01:11:30 PM by jimrtex »

Definitions

Quota The idea population of a district. The quotient of the total population divided by the number of districts. For Michigan congressional districts, the quota is the state population (9,883,640) divided by the number of congressional districts (14), which is the quota of 705,974.

Normalization The population of an area may be normalized by dividing by the quota. For example, the population of Ingham County (280,895) divided by the quota is 0.395, or 39.5%. That is Ingham County has a population that is slightly less than 2/5 of the ideal district size.

Magnitude The magnitude of an area is its population divided by the quota and rounded to the nearest integer.  Thus, an area with a magnitude of four, would have the population necessary to create four congressional districts.

Deviation The difference between the population of an area, and the ideal population for the area. This is conventionally expressed as a percentage of the quota. If an area has a population greater than the ideal population, the deviation will be positive; if less than the ideal population, the deviation will be negative.

Absolute Deviation The absolute value of a deviation.

Primary Unit The primary unit for constructing congressional districts. Typically, this will be a county.

Secondary Unit  The secondary unit for constructing congressional districts, when primary units must be divided. In states that have towns or townships, they as well as some municipalities may be used as secondary units.

Tertiary Unit  The tertiary unit for constructing congressional districts, when secondary units must be divided. These may be neighborhoods in cities.

All units will be predefined. Units must properly nested. So, for example, if a city extends across county lines, either the city must be treated as two separate secondary units, or the county boundary for purposes of drawing congressional districts must be adjusted to include the entire city. There might be a minimum size of secondary unit for which tertiary units must be defined, perhaps 10% of a quota.

Contiguous Two units are contiguous if they have have a common boundary. Point contiguity occurs when the two units only meet at a point, for example at a corner that is shared by two counties. Near point-contiguity occurs when there is an extremely short border between two units, such as sometimes occurs when adjustments are made in the Public Land Survey System to accommodate a spherical earth.

Connected Two units are connected if they are contiguous and it is reasonably easy to go between the two units. Units that are connected may be directly included in the same district. Contiguous units, that are not connected may be included in the same district, but they must also include connecting units that link the two units.

The connectivity graph will be predefined. The purpose of connectivity is to close loopholes that a literal contiguity constraint would permit, such as using point contiguity, or near-point contiguity, or a jump across a body of water to build a district.  Connectivity does not indicate that placing the units in the same district is desirable, but rather that it is possible.

Unless there is a significant barrier, such as a mountain range or body of water, that is not easily traversed on a daily basis, two units with a substantial border should be considered connected.  When there is a minimal border, consideration should be given to whether there is a direct, non-circuitous route between the units. The route may traverse other units so long as it does not pass through populous areas, or drawn in such a way as to evade populous areas.

In areas of continuous similar land use, such a agricultural areas, or urban areas, that continuity may form the connection. Within a county, most contiguous areas, other than point contiguous, or near-point contiguous areas, should be considered connected, the government and media market form a connection even if there is not an identifiable highway between the areas.

A measure of the relative length of the boundary between two units is the the shortest distance between the end points of the common boundary divided by square root of the area of the smaller unit.

If this is less than 5%, the units should be considered near-point contiguous, and not connected, unless there is strong evidence of a connection, such as a population concentration right on the border.

If it is greater than 20%, the two units should be considered connected, unless there is an extreme barrier to everyday travel between the two units.

Between these limits, consideration should be given to the directness of travel, as well as similarity of development and land use on either side of the border.


Simplified Boundary Length  The simplified boundary length is distance along a boundary using straight line segments that connect the end points of common borders between units.  Borders within the oceans, Great Lakes, and major lakes is disregarded.

The simplified boundary length is used to measure the perimeter of a district, without penalizing borders that follow a meandering river, or are somewhat irregular.

Urban County Cluster  An urban county cluster (UCC) is the portion of a Metropolitan Statistical Area (MSA), that contains the densely populated areas.  Specifically, a UCC is comprised of those counties in an MSA that have at least 25,000 persons residing in Urbanized Areas (UA), or if less than 25,000 persons, they represent 40% or more of the population.

The Census Bureau delineates a Metropolitan Statistical Area (MSA) based on a central counties or central counties containing an Urbanized Area core, and adjacent counties that have significant commuting to or from the central counties.  Often, fairly rural counties can be lassoed into an MSA. The land is more affordable, but jobs may be less plentiful.  If someone is willing to commute, they may enjoy the benefits of both a rural lifestyle and employment.  But these counties are not essential to the MSA.  On the other hand, the Census Bureau may exclude some urbanized counties from the central county, based on the grandfathering of historical definitions.  We would recognize these counties as being part of the urban footprint (or sprawl), and economically tied through employment.
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traininthedistance
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« Reply #3 on: March 01, 2015, 06:17:07 PM »

While there will be some county division in this phase, multiple spanning of counties will not be permitted.  Multiple spanning is when two or more districts share portions of two counties. 

I do worry that, while it is a good rule for 95% of our districts, absolute prohibition of double-spanning might be problematic in several cases.  Most importantly, it might be mutually incompatible with following the VRA in some areas– VA-3 and NJ-10/8 come immediately to mind; and I can imagine similar situations arising in places like South Florida and east of Los Angeles. 

To which I can imagine you saying, "so much the worse for the VRA", and that's fair– holding 50% BVAP districts sacrosanct is not really necessary in those areas for electing the candidate of choice.  But if we're trying to make an action plan that has a chance of being adopted, it would be better to build in some flexibility for those situations.

And, well, there are a couple other cases where double-spanning might be appropriate.  Say, if you have a county which is discontiguous (as exist in Massachusetts and Louisiana), or functionally discontiguous by dint of having two areas which aren't accessible to each other except by leaving the county (the rural NE corner of King comes to mind).  Or, and this is admittedly a loosey-goosey "community of interest" plead but it is a universally accepted one that oughtn't be dismissed lightly, double-spanning Nassau and Suffolk to get a North Shore and South Shore district.
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jimrtex
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« Reply #4 on: March 02, 2015, 01:30:37 AM »

While there will be some county division in this phase, multiple spanning of counties will not be permitted.  Multiple spanning is when two or more districts share portions of two counties. 

I do worry that, while it is a good rule for 95% of our districts, absolute prohibition of double-spanning might be problematic in several cases.  Most importantly, it might be mutually incompatible with following the VRA in some areas– VA-3 and NJ-10/8 come immediately to mind; and I can imagine similar situations arising in places like South Florida and east of Los Angeles. 

To which I can imagine you saying, "so much the worse for the VRA", and that's fair– holding 50% BVAP districts sacrosanct is not really necessary in those areas for electing the candidate of choice.  But if we're trying to make an action plan that has a chance of being adopted, it would be better to build in some flexibility for those situations.

And, well, there are a couple other cases where double-spanning might be appropriate.  Say, if you have a county which is discontiguous (as exist in Massachusetts and Louisiana), or functionally discontiguous by dint of having two areas which aren't accessible to each other except by leaving the county (the rural NE corner of King comes to mind).  Or, and this is admittedly a loosey-goosey "community of interest" plead but it is a universally accepted one that oughtn't be dismissed lightly, double-spanning Nassau and Suffolk to get a North Shore and South Shore district.
You might be able to make a case for one district spanning the San Bernardino-Los Angeles county line, one in the Pomona-Ontario area, and another in the desert north of mountains.   I like the structuring effect of only having one district cross the Orange-Los Angeles line.  It is better than completely ignoring it.

VA-3 doesn't conform to the Gingles test.  When it was first drawn the district court said if doubted that a compact majority BVAP district could be drawn.   And that district had a 60% BVAP.  They "corrected" that district by removing Portsmouth.  It hardly makes a district more compact by removing the largest concentration of blacks, and forcing the district to jump back and forth across the James, and skip Portsmouth, but include parts of Norfolk.  In the latest litigation, Virginia claimed they were trying to reduce the number of county splits - but couldn't explain why a majority of the splits were because of VA-3.

The basic units do not have to strictly conform to counties (or parishes).  The two parts of St. Martin could be treated as separate units, or the portion of Iberville which separates them could be added to rejoin them (it is virtually unpopulated).  I would treat Grand Isle (LA) as a separate unit.

In Massachusetts, counties might not be the basic unit, or the two exclaves of Norfolk County could be placed with counties that caused them to be separated.   When Norfolk was set off from Suffolk, Hingham and Hull were in Norfolk, but ended up in Plymouth, separating Cohasset.  Roxbury and Dorchester were in Norfolk, but as Boston expanded southwestward it eventually cut off Brookline.

I think the Long Island example sounds like a political gerrymander to either help or hurt Peter King.
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traininthedistance
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« Reply #5 on: March 02, 2015, 03:29:10 PM »
« Edited: March 02, 2015, 08:47:09 PM by traininthedistance »

VA-3 doesn't conform to the Gingles test.  When it was first drawn the district court said if doubted that a compact majority BVAP district could be drawn.   And that district had a 60% BVAP.  They "corrected" that district by removing Portsmouth.  It hardly makes a district more compact by removing the largest concentration of blacks, and forcing the district to jump back and forth across the James, and skip Portsmouth, but include parts of Norfolk.  In the latest litigation, Virginia claimed they were trying to reduce the number of county splits - but couldn't explain why a majority of the splits were because of VA-3.

I think the Long Island example sounds like a political gerrymander to either help or hurt Peter King.

While the current VA-3 is indeed a monstrosity that ought not be protected, you can make something pretty compact that is black-majority, but which requires double-spanning Richmond and Henrico:



51.8% BVAP.

I'm not even sure how to respond to your thoughts on Long Island, except to cite Emerson's quip about how "a foolish consistency is the hobgoblin of little minds".  I mean, have you seen the current NY-2?  Do you have any sense of the history and geography of Long Island?  Does anyone think that the current district (which is, BTW, an R+1 PVI district surrounded by R+2, EVEN, and D+3 districts) was drawn for the purposes of being a gerrymander?  

I mean, I respect that this might be a corner case where optimal lines end up being sacrificed for the good of better redistricting everywhere else.  But it's a sacrifice all the same.
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jimrtex
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« Reply #6 on: March 03, 2015, 09:16:19 AM »

I think the Long Island example sounds like a political gerrymander to either help or hurt Peter King.
I'm not even sure how to respond to your thoughts on Long Island, except to cite Emerson's quip about how "a foolish consistency is the hobgoblin of little minds".  I mean, have you seen the current NY-2?  Do you have any sense of the history and geography of Long Island?  Does anyone think that the current district (which is, BTW, an R+1 PVI district surrounded by R+2, EVEN, and D+3 districts) was drawn for the purposes of being a gerrymander?  

I mean, I respect that this might be a corner case where optimal lines end up being sacrificed for the good of better redistricting everywhere else.  But it's a sacrifice all the same.
Who drew the current New York districts, and why did they do so?

Suffolk is entitled to 2.08 districts.  HMM how about one on the South  Shore and one on the north.  You pick where the other 0.08.

Nassau is entitled to 1.87 districts.  Add in the 0.08 from Suffolk, and take 0.05 from Queens, and you have two districts.  One North Shore and one South Shore.


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jimrtex
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« Reply #7 on: March 09, 2015, 04:55:00 AM »
« Edited: March 09, 2015, 05:30:49 PM by jimrtex »

I'm taking too long to explain the details of the process, so I'm going to jump ahead to scoring.

Since I had already scored Train A2, I'll go ahead and display.  I have placed his name in parentheses to indicate it is not his plan, but based on his plan.   This will be better for comparing Muon2's system with mine.

Regions in my maps are numbered as follows:

1: Region containing UP.
2: Northernmost region not containing Grand Rapids or Lansing.  May include Midland-Bay-Saginaw.
3: Region containing Grand Rapids (magnitude 2).
4: Region containing Lansing.
5: Region containing Flint.
6: Southwest-most remaining district.
7: Southeast-most remaining district.
8: Region containing Detroit (magnitude 6).

In converting district plans to regional plans, I assigned counties to regions based on the district with the largest share of the population.

For (Train A2) this meant assigning Saginaw to Region 2, and consequently a very large shift.



In determining whether regions had to be corrected, I required that the populations for an ara be within 0.5% x sqrt(magnitude).   For regions 6 and 7, their total population of 1.994 is within the limit of 0.5% x sqrt(2) from the ideal population.  The correction made between these two regions is that necessary to make their population equal, not the minimum to bring both regions within 0.5% of the ideal.  This is consistent with an objective of as equal as practicable.  Once we breach a county line, we are obligated to get as close as possible, within a secondary constraint of chopping only one county, and adhering to township and municipality boundaries.

The actual adjustment may be made anwhere along the boundary between regions.  A small adjustment of this size can be made from St.Joseph, Calhoun, or Jackson counties, without materially altering the overall plan.  In a better world, we would not have to make any adjustment.

If we were to fully equalize regions 2, 5, 6, 7, and 8, the total shift is only slightly greater, but there is a 4th shift needed between region 8 (Detroit) and 7 (Southwest).  This shift would be quite small, about 0.6% or around 4000 persons.

A modified version would shift Bay and Sanilac counties to reduce the interregional population difference.



The shifted population is about 1/4 as much reflecting the elimination of the large Saginaw chop, while increasing erosity by 10%.

I had originally envisaged this type of an adjustment as an automatic process, but this might not be the best idea.

The algorithm was:

For each pair of neighboring regions that have connecting counties, process the pairs in order of decreasing population difference (ie do the pair of regions with the largest difference first):

1) Determine if there are one or more counties on the more populous side of the boundary, that if shifted would reduce the difference, would not split a UCC, and would not break the connectivity of the donor region.  Counties with a population less than the current difference qualify.
2) If any such counties exist, choose the one that reduces the difference the most.  The best county to shift is the one with a population closest to half the difference.
3) If a shift is made, restart at the beginning.
4) If no more shifts may be made, quit.

In this instance, the difference between Region 2 (Mid-Northern) and Region 5 (Flint) was the greatest, and shifting of Bay to Region 5 reduced the difference.  The increase in Region 5 made the difference between Region 5 (Flint) and Region 8 (Detroit) the greatest, and Sanilac was shifted.  An additional shift of Oscoda was identified, but then dropped, because it would have increased the necessary correction between regions, and also forced the excess of the Detroit region to be delivered even further north.

So I think the automated "improvement" should be dropped:

(1) It is not what Train wanted.
(2) Someone else could suggest the plan, without the automatic change.
(3) It won't find solutions that involve multiple swaps (such as Train's A3).
(4) It might make matters worse.  For example, if Bay could not be shifted, then it is likely that there would have been shifts made to regions 3 (Grand Rapids) and 4 (Flint).   But this simply spreads the excess around.
(5) The large chop of Saginaw will cause the plan to score poorly, which is a check in and of itself.

The one remaining concern is that to be comparable, plans must have the same number of regions.   Otherwise, I could propose a region consisting of the entire state.  It requires zero inter-regional shifts, and it has zero length internal boundaries.  It is perfect, infinitely better than Iowa.  It of course totally hides the intra-regional adjustments that would be needed.

The simple solution is to require the most number of regions.  Plans with fewer regions would be rejected.   But this opens up the possibility of someone proposing a region consisting of the Grand Rapids UCC.   One possible solution would be to set a limit on the amount of deviation is permitted for a region.  The 22.7% deviation for a minimal Grand Rapids region might be too large.

Alternatively, creation of a 9th region might not be permitted to increase the necessary shift by "too much".  Starting from our perfect 1-region plan, we know we can create 8 regions while only increasing the total shift amount by around 5%.  But creating a 9th region is going to quintuple that amount.

If (when) Michigan loses its 14th CD, the Grand Rapids UCC is going to be around 110% of the quota, and keeping it all within a single CD less a small chop might be a preferred solution.

Another possibility would be permit a UCC to be covered by multiple regions, so long as the magnitude of those regions is not more than necessary.  I suspect it is fairly easy to split the Grand Rapids UCC into two regions on the Kent-Ottawa county line.  Is it desirable to force such a split?  And if not, how would two plans be scored if Plan A placed the two counties in different regions, and Plan B placed the whole UCC in a magnitude 2 region?

Also if we permitted placing the Grand Rapids UCC in two regions, would that require splitting the Detroit UCC in two regions: Wayne-Macomb-St.Clair (4.001) and Oakland-Livington (1.959), even though the borders between Oakland and Macomb and Wayne are arguably the county borders we should be least concerned about breaching.



Thought exercise.  Imagine that a plan proposed regions consisting of (1) Detrout UCC; (2) Grand Rapids UCC; (3) Lansing UCC; (4) Washtenaw County; (5) Monroe County; (6) Jackson County; (7) Hillsdale County; and (Cool the rest of the state.   Then apply the automatic algorithm proposed above.  Initially Region 8 would have a magnitude of around 5, and would have a deviation of about 400%, so counties would transferred from it, as it withdrew northward.  Two districts would follow through the Ionia-Barry gap.

Alternatively, the seeds could be (4) Washtenaw County; (5) Kalamazoo Count; (6) Genesee County; and (7) Saginaw County.
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jimrtex
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« Reply #8 on: March 09, 2015, 06:37:02 PM »

This map is based on Train's A3.



Compared to the plan based on Train A2, there is a small improvement in erosity.  Since I am using distance, rather than a count of county boundaries, there is no difference in whether the boundary is south of Missaukee and Roscommon, or to the north.  The reduction in the boundary is due to the the elimination of the Benzie-Leelanau arm.

Qualitatively this map is better since it reduces the chopping of the Traverse City area.

The shift amount increases negligibly.  While Region 1 (UP and northern LP) is a tad closer to the quota, there is more population to be dispersed southward from Region 2.

This is the equivalent version, with Bay and Sanilac swapped.  In this case, the total shift is negligibly improved, since the swap of 4 counties reduces the deficit of Region 2.

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« Reply #9 on: March 09, 2015, 09:00:51 PM »

This is based on Train B.  Unlike my earlier attempt, I have not shifted any counties.  Since it eliminates the impled Saginaw mactochop, the shift amount is about 1/2 as much, with some increase in erosity due to looping in Isabella.



A regional analysis such as this helps highlight where larger shifts are being required.  In this case, the largest excess is in Region 2 (Saginaw) and the largest deficit is Region 8 (Detroit).  Since they are not adjacent, there must be larger chop between Region 2 and Region 5 (Flint) to get enough population to Detroit.

This map swaps Newaygo and Mecosta for Isabella, which moves the surplus from Region 2 (Saginaw) to Region 4 (Lansing), which permits a direct transfer to Region 8 (Detroit).



Region 2 is just outside the 0.5% deviation limit (0.54%).  The system could be gamed a bit by equalizing between Region 1 and Region 2.   I instead equalized between Region 2 and Region 3 (Grand Rapids) which brings the two regions quite close to the quota.

The boundary length is reduced a small amount, due to southward notch to Region 2 caused by Newaygo, and the shift is reduced by about 1/3.
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« Reply #10 on: March 10, 2015, 07:17:36 AM »

This is based on Train's 2015D.  (2015C scores the same as 2015B, since it only makes changes internal to the Detroit UCC.



The use of Bay as a bridge, can be resolved by swapping Otsego and Gladwin.  This will require a small adjustment to Region 2 (Traverse City), but will also reduce the boundary length some.
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« Reply #11 on: March 10, 2015, 04:24:08 PM »

This is based on Tories 2015A.  It leaves the shifts where he placed them.



A reasonable definition of a chop into a UCC (for Muon's scoring system) might be based on the extra district(s) beyond the minimum needed for coverage of the UCC.  In Torie's map, the chop of Clinton is slightly less than 50% of the population.  But what if it were more?  Is the chop based on the smaller part of the county?   Basing it on population share of the UCC would even permit a gargantuation chop that included all of Clinton and Eaton.   In my representation, the Grand Rapids region would simply be grossly underpopulated, and Lansing region would include the entire UCC and be overpopulated.  The requirement for a chop would be shown, but the details not identified.

This is based on Torie 2015A, with the switch of Missaukee to Region 3 (Grand Rapids).  It is not intended as an alternate map, but as part of a commentary on scoring systems.  I have included a double set of parentheses to insulate Torie from direct responsibility.

The shift permits the reduction of the shift from Clinton or Eaton (or Calhoun) into Region 3 (Grand Rapids) which I believe is qualitatively better.  It eliminates the Saginaw chop, which is qualitatively better.  It splits the shift into Region 8 (Detroit) into two parts, which I would consider qualitatively neutral.  There is no change in the shift from Region 4 (Lansing) to Region 7 (Southeast).

It scores better under my system, and there is no increase in erosity.


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« Reply #12 on: March 10, 2015, 10:22:40 PM »
« Edited: March 10, 2015, 11:58:22 PM by jimrtex »

This is based on Torie B.  I left out the inexplicable chop of Osceola.  If Muon's scoring system incentivizes a chop where, none is necessary, it should be regarded as a perverse incentive.



This map rearranges the shifts, and reduces the overall inequality.   The double parentheses indicate that Torie is not responsible for the change.

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« Reply #13 on: March 11, 2015, 01:55:46 AM »

This is based on Torie 2015 C.



And this is my alternative, with the shifts adjusted.  The use of double parentheses indicates that Torie is not responsible for this alternative.

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« Reply #14 on: March 11, 2015, 11:35:36 PM »

This is based on Torie 2015E.  (2015D scores the same as 2015E).



This is 2015E with the shifts adjust.  The double parentheses indicates that Torie is not responsible for it.

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« Reply #15 on: March 12, 2015, 12:40:18 AM »

This is a chart of the adjustment and boundary length.



Red squares are Train's plans.
Green squares are Train's plans with my modifications.
Blue squares are Tories plans.
Orange squares are Tories plans with my modifications.
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jimrtex
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« Reply #16 on: March 12, 2015, 04:23:45 AM »

This is the first of several plans that I did in 2013.

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« Reply #17 on: March 12, 2015, 01:22:41 PM »

Another plan from 2013.  This improves equality at the expense of erosity.

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« Reply #18 on: March 13, 2015, 08:19:08 PM »

A small improvement in equality and erosity.

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jimrtex
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« Reply #19 on: March 13, 2015, 10:01:13 PM »

More equal, less erose.

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jimrtex
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« Reply #20 on: March 14, 2015, 03:41:55 AM »

Slightly less erose, but more inequality due to the double shift.

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jimrtex
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« Reply #21 on: March 14, 2015, 06:15:58 AM »

This was created by Muon2 in 2013.



Region5 (Flint) is just outside the 0.5% limit (0.51%).  But the adjustment is calculated such that the regions with changes have their populations equalized.
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jimrtex
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« Reply #22 on: March 16, 2015, 08:00:08 AM »

This is another Muon2 map from 2013.



Region 1 (UP and Northern LP) and Region 5 (Flint) are just outside the 0.5% tolerances.
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muon2
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« Reply #23 on: March 16, 2015, 08:43:47 AM »

This is another Muon2 map from 2013.



Region 1 (UP and Northern LP) and Region 5 (Flint) are just outside the 0.5% tolerances.

I'm not sure I follow how you get these shifts. If populations are equalized between regions with shifts, then shouldn't the Detroit are shift out slightly more than 1.8% to the other two regions (2.0%) leaving all three slightly over population?

Are the choices of shifts set by algorithm or by the plan submitter. When this was drawn I imagined that the user submitted the shifts. Now it seems that there is an algorithm applied to get the shifts.

That leads to an important question in this process. If there is an algorithm to get the shifts, then the shifts must be taken one at a time (assuming a coded binary operation). If it is an iterative minimization process then there must be a metric to measure whether a shift is used or not. Either way the order of the shifts matters.

For example, a natural choice is to start with region with the greatest deviation and the neighbor with the greatest deviation in the other direction. In this case it would be Detroit to Bay, but Bay can't accommodate all of Detroit's excess, so how much should it shift? If it shifts just what Bay needs (since its the smaller deviation), then does 0.95% go from Detroit to Ann Arbor which would equalize those populations after the first shift? At that point, does the excess from Flint go to Lansing because it has the greatest deviation in the other direction? If the process starts from the direction of the smallest disallowed deviation, then it would seem that 0.1% would shift from Grand Rapids to the UP region. In any simple algorithm based on adjacency I find it hard to get the 0.5% from Flint to jump across to UP - more likely is a 0.2% shift from Flint to Bay and a 0.4% shift from Bay to UP.

Can you describe your algorithm for shifts in discrete steps?
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jimrtex
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« Reply #24 on: March 16, 2015, 12:52:10 PM »
« Edited: March 16, 2015, 09:29:16 PM by jimrtex »

This is another Muon2 map from 2013.



Region 1 (UP and Northern LP) and Region 5 (Flint) are just outside the 0.5% tolerances.

I'm not sure I follow how you get these shifts. If populations are equalized between regions with shifts, then shouldn't the Detroit are shift out slightly more than 1.8% to the other two regions (2.0%) leaving all three slightly over population?

Are the choices of shifts set by algorithm or by the plan submitter. When this was drawn I imagined that the user submitted the shifts. Now it seems that there is an algorithm applied to get the shifts.

That leads to an important question in this process. If there is an algorithm to get the shifts, then the shifts must be taken one at a time (assuming a coded binary operation). If it is an iterative minimization process then there must be a metric to measure whether a shift is used or not. Either way the order of the shifts matters.

For example, a natural choice is to start with region with the greatest deviation and the neighbor with the greatest deviation in the other direction. In this case it would be Detroit to Bay, but Bay can't accommodate all of Detroit's excess, so how much should it shift? If it shifts just what Bay needs (since its the smaller deviation), then does 0.95% go from Detroit to Ann Arbor which would equalize those populations after the first shift? At that point, does the excess from Flint go to Lansing because it has the greatest deviation in the other direction? If the process starts from the direction of the smallest disallowed deviation, then it would seem that 0.1% would shift from Grand Rapids to the UP region. In any simple algorithm based on adjacency I find it hard to get the 0.5% from Flint to jump across to UP - more likely is a 0.2% shift from Flint to Bay and a 0.4% shift from Bay to UP.

Can you describe your algorithm for shifts in discrete steps?
Step 1.  Draw a graph, with the vertices representing regions, and the edges representing connected regions.  For regions to be connected, there must be connected counties on either side of the boundary between the regions.

Step 2.  Identify regions that are close enough to a multiple of the quota such that no adjustment is necessary.   The rule is:

     deviation <= 0.5% x quota x sqrt(magnitude)

On your plan the following qualify: Region 3 (Grand Rapids), Region 4 (Lansing), and Region 6 (Kalamazoo).  Region 1 (UP/Northern LP) and Region 5 (Flint) are just barely outside the range. Note that when they are being corrected, getting them barely within tolerance will not be done. If an adjustment is necessary it will be towards full equality.  Region 8 (Detroit) is also outside of range, since the deviation of 2.2% is greater than the maximum of 1.2%.  Even though we could create 6 districts in the region that were within individual tolerance, it would represent a systematic spatial bias to have all the districts overpopulated.

While these regions need not be adjusted, they _may_ be adjusted.  Ordinarily this will have a lower score, but not always.

Step 3.  Identify areas that may be adjusted.   The deviation for an area must satisfy

     deviation <= 0.5% x quota x sqrt(magnitude)

In your plan, an area comprised of Region 1 (UP/Northern LP) and Region 3 (Grand Rapids) would not be permitted under this rule.  I had miscalculated, and this area would be OK, and might be an improvement.  Region 6 (Kalamazoo) and Region 7 (Ann Arbor) would also be OK.

In general, you want an area to consist of regions of surplus adjacent to regions with a deficit. More areas with fewer regions will generally be better.

An area of Region 2 (Mid-North LP), Region 5 (Flint), and Region 8 (Detroit) has too large of a deviation.

In my analysis, I used one area of Regions 1, 2, 5, 7 and 8.  It is likely that regions 2, 7 and 8 must be together to draw off the surplus from Detroit.   It is conceivable that two areas consisting of:

Region 1 (UP/Northern LP) and Region 3 (Grand Rapids); and
Region 2 (Mid-Northern LP), Region 5 (Flint), Region 7 (Ann Arbor), and Region 8 (Detroit);

would score slightly better.

Step 4.  Calculate the adjustments necessary to bring each area into full equality.



Column G is the population of each region; Column H is the Region number; Column I is the population of each region expressed in quotas; Column J is the number of counties; Column L is a repetition of Column I.

M12 (1.000) is the target population for the single area: =SUM(L1, L2, L5, L7, L8)/10   Note, the actual target is 1.00029.

If there were more than one area, there would be a target for each in Row 12.

Our trimmed graph has the following edges: 1,2; 2,5; 2,8; and 7,8,  It is easiest to work backwards from the exposed vertices (those that have only a single edge linking them to the rest of the area).  

In Column M we calculate the shift between Region 8 (Detroit) to Region 7 (Ann Arbor).  The difference between the target in M12 and the current value for Region 7 is 0.008 (M9).  Converted to an actual number it is 5,822 persons (M11).  M10 is not a formula, but a comment.

Column N is the shift between Region 5 (Flint) and Region 2 (Mid-Northern LP).  Since the exposed vertex has a surplus, the flow is its population minus the target.  We of course want the shifts to all be positive.

Column O is the shift between Region 2 and Region 1 (UP/Northern LP).  Note the O2 contains the cumulative adjustment from the shift into Region 2 from Region 5, and out of Region 2 into Region 1.

Region 2 is now exposed, and we can calculate the shift from Region 8 (Detroit) into Region 2.  The difference between the shift of 0.012 and (1.000 - 0.989) is due to rounding in the displayed values.

We can visualize the process as cylindrical tanks filled with a liquid with pipes between them.  The tank for Region 8 has 6 times the cross-section are as the other tanks.   The volume in each tank is the initial value in Column L.  We open the valves and measure the flow until the tanks reach an equal level that is the target.  Initially, there will be a back flow from Tank 1 into Tank 2, but this will reverse.  We are measuring net flow.

Column S is the final population per district for each region.  For Region 8 (Detroit) it is the population divided by 6; and for Region 3 (Grand Rapids) it is the population divided by 2.

S9 has the total shift =SUM(M9:P9) expressed as a percentage of the quota.   S11 has the total population shifted.  Note, the values in M11:P11 are display-rounded.   That is why the displayed values don't add up to 21,182.

The shifts are not ordered.  They will take place simultaneously.  But they can easily be calculated stepwise. 

I am of two minds about whether the shifts should be automatically or not.  It is easy to draw a graph, and typically pretty straightforward to find an efficient set of shifts.  Once you understand the process it is relatively easy to calculate the shift amounts with a spreadsheet.  And doing the analysis will probably lead to better plans.  But that is me.

When I initially scoring the plans by Train and Torie I was usually making adjustments.   But it is clear that they were optimizing for a different rule set.   They are pretty good at adapting to your rule set.

I did leave out one step, which would be to calculate the minimum shift necessary to equalize all regions to (a multiple of) the quota.  If all the regions are within the threshold of 0.5%, then we want to seek equality, as in Iowa (maybe).   In Nebraska, this might force a split of Douglas and Sarpy, with relatively limited choices as the Omaha district heads north. 
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