Using urban county clusters in MI

[muon2]

Let me start with the chop analysis of this plan. I'm not considering MI law, only our current operating set of rules.

To make districts no city or township is split except for Detroit. Microchops less than 0.5% of a CD are used to balance population, and only Ottawa outside of the three large counties has a chop larger than a microchop. The range is 3292 and the average deviation is 463. The district chop count is 8. The VRA districts 13 and 14 are 51.5% and 54.0% BVAP.

As the post notes there is 1 chop in Ottawa, 1 chop in Macomb, 3 chops in Oakland, and 3 chops in Wayne for a total of 8. The microchops don't count in this analysis. The Grand Rapids and Lansing UCCs have no extra chops, but the Detroit UCC has 7 CDs so there is a penalty of 1 chop for that. The new total becomes 9 chops. BTW, Wayne is just a fraction of a percent under 40% BVAP so it isn't an MCC, but if it was I would have one too many chops there as well.

After complaints about my incursion to pick up the Grosse Pointes, I revised the Detroit ares to look like the following.

CD 11 is nicely compact along southern Oakland and has a deviation of +167. (DRA says +180 but I'll trust my spreadsheet addition of the actual 2010 census figures.)

CD 9 now has a deviation +579. (DRA says -1027, but it clearly has a bug that links a precinct in New Baltimore with a disconnected one in Lenox Twp, again I'll trust the census.)

CD 10 has a reduced erosity and a corrected deviation of -1717 and its the only one that exceeds 1000 in the state.

I've also rearranged the VRA CDs to get more compact shapes. They have 51.5% and 54.8% BVAP for 13 and 14.

The overall inequality has dropped my range to 2476 with an average deviation of 427. The chop count is down to 7, and the erosity is reduced from my previous plan.

The number of Wayne chops drops from 3 to 2, so the basic chop count drops to 7 and with the UCC penalty in Detroit it goes to 8 chops.

[muon2]

By contrast, here is the Lansing split plan I offered.

To compare maps it's a useful exercise to push the county chops as low as possible. The theoretical chop minimum is equal to the number of districts that can be completely nested in a county. That is equal to 4 for MI. I couldn't get it to 4, but I could get it down to 5 with use of microchops. The range pushes out to 6599 and all CDs are with 0.5%. I would note that I could get rid of all the microchops but the one from CD 7 into Ingham by adding a chop that puts Holly twp in Oakland into CD 5. There is also one chop into Westland in Wayne, but it could be eliminated and a microchop of Rockwood used instead (I saw it after I printed the map).

One other issue that arises in the exercise is the minimum BVAP for the VRA. The SCOTUS standard for 50% only applies to the question of whether there is sufficient population to require that there is a district that can elect a candidate of the minority's choice. It doesn't apply to the district itself, and Dems in IL were successful in arguing that percentages in the upper 40% range where the white population was overwhelmingly Dem was sufficient to elect a candidate of choice for blacks. It didn't go to SCOTUS but it did pass the lower courts. The OH competition after consultation with the NAACP came to the same conclusion and allowed a CD of as low as 47% BVAP in Cuyahoga. I'm going to use their argument here and the CDs have 50.2% and 49.2% BVAP and I feel confident that statistical analysis of voting would conclude that blacks could elect candidates of choice in both CDs.

The count here is 1 each for Ingham, Macomb and Oakland, and 2 for Wayne. There is a penalty of 1 for 7 CDs in the Detroit cluster and 1 for 2 CDs in the Lansing cluster. That brings the total to 7 chops. That's lower than my other plan despite the extra UCC penalty.

[jimrtex]

The only county connectivity over water is between Mackinac and Emmet, and Mackinac and Cheboygan.  Other counties with borders in the Great Lakes, including Saginaw Bay, Grand Traverse Bay and Keweenaw Bay are not considered connected.

Islands in the Great Lakes are treated as if they were dragged to shore with the mainland portion of the county.  This includes in particular Leelanau, Charlevoix, Mackinac, Chippewa, and Keeweenaw counties.

Land boundaries are measured on the Census Bureaus 500K Cartographic Boundary Files.   The boundary between Emmet and Mackinac, and Emmet and Cheboygan is considered to have zero length.

Point connectivity between counties may not be used, nor may near point connectivity, specifically Shiawasee-Gratiot, and Livingston-Jackson.   If the Shiawassee-Gratiot or Livingston-Jackson borders form part of region boundary, they are included in a length calculation.

There are 3 multi-county Urban County Clusters (UCC) in Michigan:

Detroit: Wayne, Oakland, Macomb, Livingston and St.Clair/
Grand Rapids: Kent and Ottawa.
Lansing: Ingham, Eaton, and Clinton.

Regions are groups of connected whole counties whose population is approximately equal to an integer multiple of the ideal district population (705,974).  The maximum permitted deviation is 5% of the ideal population.   For multi-district regions this is relative to the ideal district population (eg. for a 4-district region, the limits are 3.95 to 4.05, not 3.80 to 4.20).

UCC may not be split between regions, unless the entirety of at least one region is within one region.  As a practical matter, the Grand Rapids and Lansing UCC must be in a region.   Wayne, Oakland, and Macomb counties must be in multi-district regions.

[jimrtex]

My proposed regional plan:



There are 9 regions (the Detroit UCC is divided).

The standard deviation is measured in two ways, between regions, and between districts based on the assumption that mult-district regions will be perfectly split.

The shift is the number of persons who would need to be shifted to balance the regional populations, relative to the ideal district population.  If there are N regions, then there must N-1 interregional shifts, and every region must be connected to the other regions by at least one shift.  This necessarily means that there are not more than one shift between any pair of regions, nor any loops.  

The locations of the shifts may be chosen so as to minimize the amount of shifted population.  In general, links should be drawn directly between regions with a surplus to regions with a deficit.

The total amount of shifts for my map is 9.23% (relative to the ideal district size).  This is equivalent to 65,168 persons.  That is, to equalize the population of the regions chops with 65,168 would be needed.

Shifts that are not necessary to bring regions within a deviation of 0.5% (3,530 of the ideal may be excluded).  Important: Shift amounts may not be adjusted so as to barely bring a region within tolerance.  Once the initial set of links is identified, a link may only be excluded from the minimum shift set.

In my map, the shifts in pink are not necessary to bring all regions into reasonable population balance (0.5% maximum deviation).   The remaining shifts are 8.40% (relative to the ideal district population, which is 59,316 persons.  This represents the total size of county chops necessary to reach practicable population equality (balanced against the objective of not making excessive county splits).

After these shifts were made, the standard deviation among regions would be 0.25%, while the standard deviation among districts, assuming perfect equality within multi-district regions is 0.20%.

The measures of 8.40% and 0.20% are the best measures of practicable equality, indicating the amount of violation of county integrity and the equality achieved.

The inter-regional perimeter is 922 miles.  We can estimate the interior perimeter of the multi-district regions by using a circle with the same area as the region and calculating its radius.  For a 2-district region the interior perimeter is twice the radius of the circle.  For a 4-district region the interior perimeter is four times the radius of the circle.  Based on the two 2-district regions and the one 4-district region, the estimated interior perimeter of 14 districts is 1224 miles.

[muon2]

The Detroit UCC has a population of about 28K less than 6 CDs. That comes to about 4%. Sticking with a maximum deviation of 0.5% and to avoid an unnecessary chop into the UCC, the five counties need to chop out into an adjacent county to make up the shortfall. That forces at least one chop outside the UCC counties.

[jimrtex]

The Detroit UCC has a population of about 28K less than 6 CDs. That comes to about 4%. Sticking with a maximum deviation of 0.5% and to avoid an unnecessary chop into the UCC, the five counties need to chop out into an adjacent county to make up the shortfall. That forces at least one chop outside the UCC counties.

I divided the Detroit UCC into two regions, both which are within the 5% threshold.  The Wayne-Macomb-St.Clair region is also within a 0.5% deviation.  I indicated the two chops to make up the difference for the Oakland-Livingston region, which is about 1/2 of the total adjustment for the state.

[muon2]

Here's a possible plan that respects the UCCs while minimizing chops.

Let me first show the regional view, using 9 regions to match jimrtex's plan. Populations of each region are indicated as the number of CDs. Necessary population shifts are indicated by colored shapes - the green pentagon indicates a required shift of 4.1% of a CD to get equality. The triangles represent microchops of less than 0.5% of a CD needed to bring two other regions within 0.5% of equality. If I take the required shift in the microchops to be the amount that best equalizes the populations without exceeding 0.5% I would use 0.3% in the light blue triangle and 0.5% in the gold triangle. That would be a total required shift of 4.9%.



The other view is without regions, but looking at the chops directly. Unlike my earlier offerings this plan has no chop penalties for extra chops of UCCs. The chop count is 7, but could be reduced to 6 with if one of the two VRA districts goes under 50% BVAP.



In the west the chop of Kent was required within that region to avoid a bridge chop connecting two otherwise disconnected whole counties. Note, I don't count microchops as chops for the purposes of bridge chops just like they don't count in the chop count. They only count for erosity.



In the SE I chose to recombine the two regions to form two 50% BVAP CDs. If you want to keep the Wayne-Macomb-St Clair part separate you can substitute the borders of my Lansing chop plan for those three counties, then keep CD 11 on this plan the same and attach part of Lapeer onto CD 9.



I returned to the Bloomfield bridge to Pontiac for this plan. On close examination I find that the leap across Dearborn, Dearborn Heights and/or Taylor to get to Inkster (6 mi) and Romulus (10 mi) isn't a much shorter distance and involves crossing over more people than using Bloomfield to go between Southfield and Pontiac (9 mi). Within Wayne I optimized for low erosity and chopped no official neighborhoods within Detroit. The BVAPs  for CD 13 and 14 are 50.4% and 55.1%.

[jimrtex]

I have scored your map in a way that is consistent with how my map was.



I re-arranged the shifts some.  Under my rules, you can not bring the southern district below 1.000 simply to get enough people to get the 0.992 district within 5%.  But you can shift the excess from the purple district - but not execute it.  This increases the shift from the southern district enough to get the 0.992 district within 0.5%.  But the total shift can be reduced more by bringing it in from the north. 

It is conceivable that a claim can be made that this is too much of cheat.   That is, the proposed shifts are: 3,057, 768, 2,562, 1,567, 2,046, 28,923, 2,350, and 705 to provide full equality, and several small shifts were skipped, while two small shifts were done.  The SCOTUS has suggested that consistency is important.

An alternative method would be to only identify shifts among regions that have greater than 0.5% equality, and execute full equality shifts within those regions (in some instances it may be necessary to include intermediate regions).   For your map, the shifts would be among the 4 districts outside the 0.5% and would be either into or out of Livingston and Oakland.  This would increase the shift total to 5.46% (or 38,578 persons).  An argument against this method is that it implies that there is a de minimis population deviation that is permissible, while the SCOTUS has insisted that is not true.

A stronger case might be possible by eliminating all inter-regional shifts.  In that case, Sanilac would have to be moved to a 6-district Detroit region.  This might be necessary regardless.  It would be reasonable to have a rule that simple shifts between two regions must be made if they will improve equality.  While this won't necessarily move the plan away from a local minimum, it will move it towards the local minimum.

What exactly is Michigan's objective?

It is also possible that the two Detroit regions prevent compliance with the VRA.  In a 4-district St.Clair-Macomb-Wayne plan, the Macomb-Wayne district is about 3/7 in Macomb and must include the Gross Pointe's as well as Detroit.  It may be considered a crack.

In a 6-district plan, you might be able to draw 2 majority-minority districts in Wayne, but then the remnant of the county (south, southwest, and west) is going to have to wrap around into Oakland.   But you can probably get a majority-minority district in Wayne-Oakland, plus one in Wayne entirely.

[muon2]

I have scored your map in a way that is consistent with how my map was.



I re-arranged the shifts some.  Under my rules, you can not bring the southern district below 1.000 simply to get enough people to get the 0.992 district within 5%.  But you can shift the excess from the purple district - but not execute it.  This increases the shift from the southern district enough to get the 0.992 district within 0.5%.  But the total shift can be reduced more by bringing it in from the north. 

So I understand, why was the Saginaw to Gratiot shift left as mandatory as opposed to the Flint to Oakland shift? They both seem to accomplish the same goal and the Flint-Oakland shift involves regions that are already making shifts.

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I think that the identification of microchops as a consistent tool partially addresses this argument. It is a neutral criterion and falls within the range of deviations the court has found as a justified state interest. Also, microchops always be added, expanded or contracted to provide exact equality if the plan is found to have too great an inequality by the court without substantially changing the plan.

In MI one can make the case that the microchops must consist of one or more whole MCDs. Requiring their split to achieve exact equality would fall into the same category as requiring the counties to be split in WV.

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We had a lot of discussion of this point earlier in the thread. 2 majority BVAP districts don't fit in Wayne. A link to Oakland for one of the two is necessary. However, if one can make the case that 49.2% BVAP is sufficient to elect the representative of choice, then the two Detroit subregions can be kept separate by linking one BVAP CD to southern Macomb.

[jimrtex]

I have scored your map in a way that is consistent with how my map was.



I re-arranged the shifts some.  Under my rules, you can not bring the southern district below 1.000 simply to get enough people to get the 0.992 district within 5%.  But you can shift the excess from the purple district - but not execute it.  This increases the shift from the southern district enough to get the 0.992 district within 0.5%.  But the total shift can be reduced more by bringing it in from the north. 

So I understand, why was the Saginaw to Gratiot shift left as mandatory as opposed to the Flint to Oakland shift? They both seem to accomplish the same goal and the Flint-Oakland shift involves regions that are already making shifts.

Under my rules, the person submitting the plan must identify N-1 shifts (for a N-region plan) that would bring the plan into full equality.  There must not be two shifts between a pair of regions, or even two paths between a pair of regions.  This is to prevent splitting of shifts so that both are microchops.  That there a N-1 shifts, and all regions must be connected, ensures that there will not be two paths between pairs of regions.

Once the network of N-1 shifts is identified, the amount of shifts can be automatically calculated, since the network of shifts has exposed nodes with only one link, and as these are resolved, additional nodes are exposed.

Which set of shifts is identified is discretionary, but a submitter would be expected to choose a set which minimizes the total shift population.  I think this is a better measure of equality than standard deviation or range, since it also penalizes geographical imbalances (for example, if your region with the 4.1% surplus was across the state from the region with the 4.1% you would have to make much more shifts to reach equality).  As such, it serves as an additional check on gerrymandering.

After identifying the full set of shifts, the submitter of the plan can identify the order in which the shifts are performed, and skip any shifts that are not necessary in order to bring a region within 0.5% tolerance.

So you (or me acting as your agent) chose the Saginaw-Gratiot shift, which resulted in the Saginaw district being within a 0.5% tolerance, so the Genesee-Oakland shift was not needed.
Note, this is quite different than for example just shifting the bare amount necessary to bring the Flint-Saginaw-Midland district within 0.5% error.

The advantage of arranging the shifts in the way I did is that the shift from Oakland-Livingston to Ann Arbor-Battle Creek is 0.33% vs 0.36% from the Southern tier-Kalamazoo.   Since I didn't actually need the shift from the Grand Rapids region to the Southern tier-Kalamazoo, it can be moved to go from Grand Rapids to Ann Arbor-Battle Creek.  This reduces the maximum shift from 5.95% to 5.84%.

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I think that the identification of microchops as a consistent tool partially addresses this argument. It is a neutral criterion and falls within the range of deviations the court has found as a justified state interest. Also, microchops always be added, expanded or contracted to provide exact equality if the plan is found to have too great an inequality by the court without substantially changing the plan.

In MI one can make the case that the microchops must consist of one or more whole MCDs. Requiring their split to achieve exact equality would fall into the same category as requiring the counties to be split in WV.

I don't think the SCOTUS has ever identified a range that was justifiable.

Since the plan can be pushed towards greater or exact equality by making any of the chops, without substantially changing the plan, why make any of them?

In one case, Michigan can say that their objectives are:

Practicable equality with whole-county districts except in larger metropolitan areas; respect for communities of interest as represented by by urban county clustes and compact districts, and popular support.

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We had a lot of discussion of this point earlier in the thread. 2 majority BVAP districts don't fit in Wayne. A link to Oakland for one of the two is necessary. However, if one can make the case that 49.2% BVAP is sufficient to elect the representative of choice, then the two Detroit subregions can be kept separate by linking one BVAP CD to southern Macomb.

Does this work if there is a St.Clair-Macomb district, and then southern Macomb (about 3/7 of a district) plus Detroit?

[jimrtex]

We can improve your original plan by adding Sanilac to a 6-district Detroit region, and then swapping counties in northern lower peninsula.

It might be a requirement that simple swaps such as this could be mandatory, based on SCOTUS decisions such as Kirpatrick v Preisler and Karcher v Daggett, where simple swaps could have improved equality.  In Tennant v Jefferson, different groupings of counties could have produced greater equality and more compactness - but compactness was not one of the West Virginia legislature's objectives.

The two sets of swaps (1) Sanilac, and (2) the northern swaps individually improve equality, and can be considered a series of simple swaps, rather than a complex swap.

The standard deviations is improved from 1.96% (regional) and 1.37% (district) to 0.95% abd 0.48%,

The shift amounts are reduced from 5.95% (full equality) and 4.65% (minimal equality) to 3.50% and 2.83%.    This reduces the displaced population from 32,840 to 19,878.

If we use the alternative measurement with full equalization between regions that are outside 0.5% deviation, the enw plan reduces the shift from 5.46% to 3.12%.  It may be possible to reduce the shift amounts a bit, by changing counties in the northern LP.  Currently there is double shift from the Detroit region to the UP+NWLP region.  In addition, the UP+NWLP region is just outside the 0.5% threshold (0.9949).

The perimeter changes slightly from 1184 (regional) and 1402 (district estimate) to 1178 (regional) and 1454 (district estimate).   

The slight improvement in the regional perimeter is mainly due to the combination of the two Detroit regions vs. the added length to include Sanilac.  The district estimate is due to the added area of Sanilac, and the less favorable treatment of a single 6-district region vs. a 2-district and 4-district regions.

[muon2]

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We had a lot of discussion of this point earlier in the thread. 2 majority BVAP districts don't fit in Wayne. A link to Oakland for one of the two is necessary. However, if one can make the case that 49.2% BVAP is sufficient to elect the representative of choice, then the two Detroit subregions can be kept separate by linking one BVAP CD to southern Macomb.

Does this work if there is a St.Clair-Macomb district, and then southern Macomb (about 3/7 of a district) plus Detroit?

This was my best plan with a southern Macomb-Detroit district. CD 13 is 50.2% BVAP and CD 14 is 49.2% BVAP.



I should also clarify that it isn't possible to have 2 BVAP majority CDs in Wayne that keep the region nesting correct. One can just barely make 2 in Wayne, but the require three additional chops into the county.

[jimrtex]

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We had a lot of discussion of this point earlier in the thread. 2 majority BVAP districts don't fit in Wayne. A link to Oakland for one of the two is necessary. However, if one can make the case that 49.2% BVAP is sufficient to elect the representative of choice, then the two Detroit subregions can be kept separate by linking one BVAP CD to southern Macomb.

Does this work if there is a St.Clair-Macomb district, and then southern Macomb (about 3/7 of a district) plus Detroit?

This was my best plan with a southern Macomb-Detroit district. CD 13 is 50.2% BVAP and CD 14 is 49.2% BVAP.

Presumably you could flip the Oakland districts, so that you keep it within Oakland-Livingston.

I think that looping around Dearborn but picking up Hamtramck is pretty awkward.

I should also clarify that it isn't possible to have 2 BVAP majority CDs in Wayne that keep the region nesting correct. One can just barely make 2 in Wayne, but the require three additional chops into the county.

Presumably this could be adapted to go north into Oakland, which would permit the connection of southern and western Wayne, and then the Grosse Pointes could be added to the eastern Detroit district?

If so, that would seem to be the better solution.  Avoiding cutting the Oakland-Macomb and Oakland-Macomb lines doesn't really seem all that important.

Oakland would not have a whole district, but would have two districts with a majority. and one with a substantial minority, and there are 5 county cuts for 6 districts:

Sanilac (part), St.Clair, northern Macomb, northern Oakland;
Southern Macomb;
Livingston, western Oakland;
Southeastern Oakland, northern Wayne;
Eastern Wayne;
Southern and Western Wayne.

[muon2]

Presumably this could be adapted to go north into Oakland, which would permit the connection of southern and western Wayne, and then the Grosse Pointes could be added to the eastern Detroit district?

If so, that would seem to be the better solution.  Avoiding cutting the Oakland-Macomb and Oakland-Macomb lines doesn't really seem all that important.

Oakland would not have a whole district, but would have two districts with a majority. and one with a substantial minority, and there are 5 county cuts for 6 districts:

Sanilac (part), St.Clair, northern Macomb, northern Oakland;
Southern Macomb;
Livingston, western Oakland;
Southeastern Oakland, northern Wayne;
Eastern Wayne;
Southern and Western Wayne.

That's close to what I posted in my realization of the 6 CD region. You can swap Sanilac for Lapeer. If you want a CD entirely within Macomb then either CD 10 comes down to the Wayne line in SE Oakland, or Wayne is made more erose by wrapping CD 12 around Inkster and/or Romulus. The chop count is the same either way.

I returned to the Bloomfield bridge to Pontiac for this plan. On close examination I find that the leap across Dearborn, Dearborn Heights and/or Taylor to get to Inkster (6 mi) and Romulus (10 mi) isn't a much shorter distance and involves crossing over more people than using Bloomfield to go between Southfield and Pontiac (9 mi). Within Wayne I optimized for low erosity and chopped no official neighborhoods within Detroit. The BVAPs  for CD 13 and 14 are 50.4% and 55.1%.

[jimrtex]

This is my plan adjusted to used a 6-district Detroit region.  Since I had distributed the surplus that resulted from the Oakland-Livingston deficit, I had to make more extensive changes.   Overall, there was considerable increase in equality, at the cost of some increase in perimeter.

I think that these last two plans demonstrate that a 6-district Detroit region must be used.   It also demonstrates while a 4.1% deviation is permissible under the rules, it is not practicable to do so and achieve comparable equality to other plans.   That is, the 5% limit for region plans is not enforcing that as a de minimis standard.

Overall, the standard deviation from 2.46% (regional) and 1.76% (district) to 1.51% and 0.98%, respectively.   The shift amounts decreased from 9.23% (total) and 8.40% (minimal) to 5.43% and 4.65%, respectively.   This latter value is equivalent to 32,837 persons, or about 1/3 of 1% of Michigan's population.

The perimeter increases from 999 (inter-regional) and 1224 (estimated inter-district) to 1100 and 1385, respectively.

[jimrtex]

This is a test of the 5x5x5x5 aggregation method using UCC.   Each multi-county UCC will be included in one group.   For example, in the first round the Detroit UCC has a sum modulo 5 of 10, which is a multiple of 5 and will be treated as a group.  Lansing UCC has a sum modulo 5 of 6, and will be inlcuded in a group with counties which have sum modulo 5 of 4 (or 9, etc.), even though Clinton could ordinarily be paired with Shiawassee.

[muon2]

Here's the way I would interpret the use of UCCs within regions.

Within a state the number of regions equals the number of districts less the number of extra districts in UCCs. For example in MI the Detroit UCC calls for at least 6 CDs and the Grand Rapids CD calls for at least 2 CDs. That's an excess of 5+1=6 CDs. So the number of regions in MI is 14-6=8. Then one can say that regions shall be constructed so that no UCC is split between regions.

Except for cases where regions would have to shift population twice to get from a region of excess population to one of low population, the total shift percentage directly related to the average absolute deviation. In particular the shift times two is equal to the average deviation times the number of regions. It seems simpler to avoid the need to identify a specific shift plan since there are often more than one possible and the different options are equivalent. So I would use the average absolute deviation of the population of the regions, and require that any region of excess population be adjacent to one or more regions with less than ideal population such that the populations could be equalized.

[muon2]

Here are two revised regional plans that could represent improvements. The first is an improvement of my original 8 region plan. It shifts Sanilac and Lapeer and a couple other areas up north. Lapeer is shifted to improve compactness. The average deviation is 0.951% which should equate to a shift of 3.80%. I can get that down to 0.896% (3.58% shift) by readjusting the boundary of the northern district producing a less compact shape for the red region.



In this second plan I have made some adjustments to jimrtex's most recent regional plan. The erose shape of the Grand Rapids region largely disappears when it is split into two CDs. The average deviation is 1.007% which converts to a 4.03% shift.

[jimrtex]

Here's the way I would interpret the use of UCCs within regions.

Within a state the number of regions equals the number of districts less the number of extra districts in UCCs. For example in MI the Detroit UCC calls for at least 6 CDs and the Grand Rapids CD calls for at least 2 CDs. That's an excess of 5+1=6 CDs. So the number of regions in MI is 14-6=8. Then one can say that regions shall be constructed so that no UCC is split between regions.

I think that in Alabama, splitting the Birmingham UCC into two regions is the better solution.

While it may be that a 6-district Detroit region is better overall (mainly because the Oakland-Livingston region ends up with such a large error), I don't think it should automatically be precluded.

Except for cases where regions would have to shift population twice to get from a region of excess population to one of low population, the total shift percentage directly related to the average absolute deviation. In particular the shift times two is equal to the average deviation times the number of regions.

It is precisely this situation that the shift percentage identifies - regional bias, whether deliberate or simply carelessness.

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It is pretty simple to create a shift plan:



Which is the shift plan I used for your map.  

For your plan which I modified to have 8 regions, there are 16 links.  There are:

16! / 7! 9! combinations of 7 links, which is 11,440.  But most combinations are not valid because they don't link all 8 regions.  It would be reasonable to either provide a simple interface:

(1) All regions initially shown with unsaturated color.
(2) Click on two adjacent regions, and a link is created, and the regions are shown with a saturated color.
(3...) Click on two adjacent regions, one already connected, one not and add to the set of connected regions and set of connecting links.

Or the whole process could be automated.

I don't see much difference, other than one of style, between:

(1) "require that any region of excess population be adjacent to one or more regions with less than ideal population such that the populations could be equalized"; and
(2) A hint that such plans would be scored higher.

[jimrtex]

Here are the pairings for the first round of mergers.  The groups are somewhat large with less simple pairs.  I think this is due to three factors:

(1) Relative large number of counties which have a number of units modulo 5 equal to 4, and a relative small number of counties which have a number of units modulo 5 equal to 1.  With a remainder of 4 a pairing can only occur with a county with  a remainder of 1.

(2) Square configuration of counties in the lower peninsula reduces connections.  In the upper peninsula connections are somewhat limited since all counties are along the shoreline.

(3) Use of UCC may force somewhat larger groupings.  Since 5 of the 10 counties in multi-county UCC have a number of units modulo 5 equal to 4, this may combine with (1).

[muon2]

Personally I think the groupings algorithm is a different concept than that of UCCs in either regions or chop counts. Adding a third mechanism complicates the attempt to build a rule-based framework.

[jimrtex]

Personally I think the groupings algorithm is a different concept than that of UCCs in either regions or chop counts. Adding a third mechanism complicates the attempt to build a rule-based framework.

Here it is being used as a mechanism to generate a compact UCC-compatible plan.   At worst it will provide a quasi-independent mechanism for generating an alternative plan to those submitted by you and I (and possibly others).   And besides, I was halfway through generating this when you posted the last two alternative plans.  I'll comment on those, before doing the next round

You are correct that if there was a mechanism for the voters in the atoms to negotiate their groupings, or perhaps this could be done with a cellular automaton, there would be no need for UCC or forming districts from collections of counties.

[jimrtex]

This is your modified plan.

The SD increases from 0.95 (regional) to 1.27%, and 0.48% (district) to 0.80%.

Shift counts increase from 3.50% to 3.87% full equality); 2.83% to 3.04% (shifts necessary to get to regions withing 0.5%); and 3.12% to 3.29% (full equality among regions initially outside the 0.5% threshold).

The perimeter improves from 1178 (regional) to 1114 miles, and 1454 (district estimate) to 1390.




This is a variant that tweaks the border between the northern two districts, producing a negligible change in compactness, an improvement in equality, but an increase in the amount of intercounty shifts.

If the SCOTUS adopts a reasonable definition of practicable equality, then this plan is better.   If not, then perhaps the other is better.

[jimrtex]

This is Muon's proposed revision, excluding the southern changes.  It is a slight improvement in equality, and surpringly to me, an improvement in compactness.

[muon2]

The southern changes should further improve both equality and compactness.