MI maps - muon2 scoring

[muon2]

This thread is split from the larger discussion on chops and erosity in the Great Lakes states to hold the scoring of MI maps and the rules used to get the score.

UCC rules

per jimrtex: Urban County Cluster (UCC). A UCC consists of one or more counties within a metropolitan statistical area (MSA).  A county is included in a UCC if at least 40% of the population of the county is in urbanized areas; or if at least 25,000 persons live in urbanized areas.

Yes, MI has a lot of single-county clusters. Here's the map I put together in 2013 as we were developing the UCC concept (which originated because of the Lansing tri-county problem). There are three multi-county UCCs marked in pink, and 11 single-county UCCs in tan. The Grand Rapids UCC supports 2 CDs before a chop occurs, and the Detroit cluster supports 6 CDs before a chop occurs.



I tend to agree that single-county clusters should not count in scoring, but this point was never resolved. The votes cast on this point by the Forum Commission (VA) varied with no majority, and one commissioner voted that multi-county clusters shouldn't affect scoring either, but UCCs could be used as a secondary factor. The VA FC seems to have lost interest as the policies got into technicalities. Of course it's the technical detail where the real work happens.

One way to resolve my Jackson vs Clinton question is to recognize that in small UCCs (less than a CD) the UCC chop penalty only occurs when county lines are followed, as if a county was chopped the normal way. That way a chop of Clinton creates just one chop, not two (no extra for the UCC), but putting all of Clinton in a CD separate from the rest of the UCC also counts as one chop (because it's in a UCC).

The UCC size is defined as the population of the UCC divided by the quota and rounded up to the nearest whole number. The cover of the UCC is the number of districts that include any or all of the UCC. The pack of the UCC is the number of districts that are wholly contained by the UCC. Chop points are assessed for the difference between the cover and size of the UCC, and for the difference between one less than the size and the pack.

Edit: This is in addition to the normal chop score. To test the effect of the two parts of this on scores, I will quote a raw CHOP score without the UCC and additional scores for just the cover, both the cover and pack, and with single-county UCCs included.

[muon2]

The INEQUALITY score for a plan is found by taking the range for a plan and comparing it to the table below.

Range	Inequality
0-1	0
2-10	1
11-100	2
101-400	3
401-900	4
901-1600	5
1601-2400	6
2401-3200	7
3201-4000	8
4001-4800	9
4801-5600	10
5601-6300	11
6301-7000	12
7001-7700	13

I went back to the data set I used to make the table of inequality for range. In that I took as many whole county split states as I could make with the 0.5% maximum deviation and found the average absolute deviation. Like the range it follows an exponentially falling dependence on the average number of counties per district. I then did a regression fit. From that I took a hypothetical state of 72 counties (the average) and determined the expected average deviation one should get as additional districts are added.

Ave Dev	Inequality
0-2	0
2-30	1
30-100	2
100-220	3
220-370	4
370-540	5
540-710	6
710-880	7
880-1050	8
1050-1360	9
1360-1500	10
1500-1640	11
1640-1760	12
1760-1880	13
1880-1990	14
1990-2100	15

For each additional 100 in ave dev, add 1 to inequality. If the average is exactly on the boundary use the lower number.

If this makes sense I can use it in my rescoring of the plans. I can also go to a coarser step size in the table based on the exponential relationship, but I think that is more likely to favor plans with more chops.

Raw CHOP score
This post is modified to reflect the current scoring.

Here's how I would write that into a scoring rule for MI.

Definition: Urban County Cluster (UCC). A UCC is a geographic unit within an MSA. It is made up of those counties in the MSA such that each county has either 25,000 population or 40% of its population in an urbanized area. the geographic subunit of a UCC are its counties.

Definition: Subunit. The geographic subunit of a county are the census-defined county subdivisions. Except for Detroit, the geographic subunit of county subdivisions are the vote tabulation districts (VTD). The geographic subunit of Detroit is city-defined neighborhood cluster, and the subunit of the neighborhood is the VTD.

Definition: Chop. A single chop is the division of a geographic unit between two districts. A second chop divides the unit between three districts. In general the number of chops is equal to the number of districts in that unit less one.

Definition: Microchop. A microchop is a chop where a district has less than 0.5% of the quota in a geographic unit.

Definition: Macrochop. A macrochop exists in a geographic unit when the remainder of a geographic unit after subtracting the population of the largest district in the unit exceeds 5% of the quota.

Definition: The initial map for counties chops consists of UCCs and counties not in UCCs. The CHOP score is determined by counting the chops excluding microchops. In units with a macrochop, the CHOP score is increased by the chops of its subunits. If any of the subunits have a macrochop, its subunits are considered for the purposes of the CHOP score.

The CHOP score is the sum of the chops of all counties, plus the chops of all subunits in counties with a macrochop. County subunits may not be chopped in counties that do not have a macrochop.

[muon2]

Here are the subunits of Detroit that would be used to compute chops and erosity. The neighborhood clusters have been matched to the extent possible to the DRA precincts. Connections are based on the actual neighborhood cluster boundaries.



NC 1: pop 66,076; BVAP 82.6%
NC 2: pop 81,321; BVAP 91.3%
NC 3: pop 79,779; BVAP 88.7%
NC 4: pop 61,346; BVAP 75.5%
NC 5: pop 74,720; BVAP 27.5%, HVAP 48.8%
NC 6: pop 58,410; BVAP 94.8%
NC 7: pop 88,225; BVAP 83.6%
NC 8: pop 72,117; BVAP 88.1%
NC 9: pop 78,604; BVAP 96.0%
NC 10: pop 53,179; BVAP 93.2%

[muon2]

Here's a map of the cities and villages in the big three counties from 2004. Redistricting in MI is intended to respect these boundaries, so these are the natural subunits of the counties.

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Note that villages are not treated like cities and townships. So for instance Torie separates the village of Holly from Holly township, so that counts as chop of Holly township. It also looks like Lenox township in Macomb is chopped, but it's a microchop so it doesn't affect the chop count.

[muon2]

EROSITY score

Regional connections are defined by the shortest time path between two governmental seats following numbered state or federal highways without passing through a third geographic unit.

The erosity score is the sum of all links cut by district lines in a plan. Links include regional highway connections between counties. In counties with a chop, but not a macrochop, the pieces formed by the chop retain their regional links to adjacent counties and have a local In counties with a macrochop links are included for regional connections to subunits across county lines and local connections between subunits within counties. Point contiguity does not result in a link.

The erosity score for a district is the total number of links severed by its boundary. The erosity score is also equal to the sum of all district scores divided by two, since each severed link would count in two districts individual scores.


So I took some time this morning to put together the complete county connection map for MI. As usual this represents all the regional connections defined by a path between seats of county government that follows state and federal numbered highways. When there is more than one path between two counties, the path is defined by the one that takes the shortest time according to Mapquest.

Technically, I-75 jogs into Emmet county for a brief part just south of the Mackinac bridge, so it can't be on a path between Mackinac and Cheboygan. But I-75 also can't be on a path between Mackinac and Cheboygan since the south end of the bridge is in Cheboygan. There is ferry service across the strait and in mild winters it can run all year, but usually it doesn't. So that leaves no possible link, so the map shows the best alternative which is Mackinac to Cheboygan.



To illustrate the problem with the simplest model for chops and erosity, I used Torie's map at the beginning of the thread. I used black lines to accent the quasi-counties created by the chops and white lines to show the connections cut by the district boundaries. White lines are also added to show links between quasi-counties in the same county (I apologize for the color, but I couldn't find one that provided contrast against all the districts).



The simplest model for erosity measures the number of links cut by a district's boundary, called the cut set. The total erosity for the plan is the total of all district erosities, divided by two since each link is shared by two districts. Here are the erosities for each CD in the plan.

CD 1: 10
CD 2: 11
CD 3: 11
CD 4: 18
CD 5: 9
CD 6: 6
CD 7: 5
CD 8: 12
CD 9: 4
CD 10: 8
CD 11: 5
CD 12: 3
CD 13: 2
CD 14: 4
State: 108/2 = 54

Now consider CD 13. Because it is entirely within Wayne and doesn't border Oakland where the principal highway connects the counties it has a tiny erosity of 2. The shape doesn't matter at all. In fact all the CDs in the big three counties have very low erosities in the simple model since they can usually pack into one or two counties so there just aren't many links to cut.

This is why I claim that a reasonable erosity system has to be able to zoom into high-population chopped counties to measure erosity on a municipal scale. The measure has to be such that the erosities are comparable for similarly formed districts on different scales. Perforce that adds complications to the basic model. Denying the claim accepts that the district erosity disparities in the above example are ok.

However, if the claim is reasonable then the questions become when does one zoom to the next level, and how does one apply the measure at the municipal scale. My proposal is the zoom is triggered when the sum of chops in a county exceeds 5% of the quota. It is based on the notion that a single chop of that magnitude represents a substantial departure from equality of population and is a proxy for a chop into a high density area.

In the big three Detroit counties, the connections look like this:

The blue lines are local connections between munis in a county and the red lines are regional highway connections between munis/counties across county lines. If they are cut they are included in the erosity score. If other counties have a macrochop a similar analysis of local and regional links would apply there as well.

For example the CDs in the Detorit UCC would get erosities that better reflect their shape.
CD 9: 14
CD 10: 35
CD 11: 16
CD 12: 26
CD 13: 31
CD 14: 37

[muon2]

OK let me take a stab at the scores.

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As I responded to Torie, I can be persuaded to go in that direction, but then the inequality score should have the same weight in decision making as chop and erosity scoes.

I've always tended to have a lower tolerance for inequality than folks like jimrtex, so that would certainly get my vote.  The three-pronged Pareto test you mentioned seems at first blush to be an approach I'd strongly approve of.

Thanks for all the other explanations; think I've got it straight now (well, I still need to take a closer look at Illinois regarding the Kalamazoo point, but that's a minor point and I trust I can figure it out without any more help).

...

Taking all these tweaks and suggestions into account... here's Draft 2, new and improved:

MI train 2015A2








You'll note that I also found a super-low-inequality configuration for 1 and 4 (not necessarily the lowest-erosity, mind, but lower than what I had before), and shuffled a precinct or two in Detroit to lower inequality between 13 and 14.  I suspect that one can lower inequality in Oakland at the expense of erosity, but I this is enough maps for today.  Alternate Oaklands and 1/4 borders might be in the offing for tomorrow, though.

Anyway, I'm an idiot and there's a strictly better 1/4 anyway, both on erosity and inequality:

MI train 2015A3


1 is +428, 4 is +155.

Now I'm done for the day.

The political factors are scored, but not used to eliminate any maps. They are provided to the commission to use when they decide on a map.

The PVI-08 for MI is D+4.7, so the expected delegation is 8.3D to 5.7R and the difference is 2.6 which rounds to 3. The political ratings for the districts are CD 1: r, CD 2: d, CD 3: R, CD 4: e, CD 5: D, CD 6: e, CD 7: D, CD 8: d, CD 9: d, CD 10: r, CD 11: R, CD 12: d, CD 13: D, CD 14: D. That's 2R, 2r, 2e, 4d, 4D (UC for uncompetitive, lc for competitive).

SKEW: 1 ( 8[D+d] - 4[R+r] - 3[state] )
POLARIZATION: 18 ( 6[r+d] + 2*6[R+D] )

The population range is +2887 - (-2555) = 5442. This is between 4801 and 5600. The average deviation is 1239.
INEQUALITY: 10 (range), 9 (ave dev)

And now it's time for my supper. More later.

[muon2]

Completing train A

On to chops. I'll use the full UCC protocol which means they act as super counties until they are chopped.

There are three UCCs. Detroit has 5 chops, and is macrochopped releasing the counties. Grand Rapids has 1 chop, and is macrochopped releasing its counties. Lansing is not chopped so it is treated as a single county for erosity. Total is 6 which is the minimum.


On to county chops.
Kent: 1 chop; macrochop releasing munis
Saginaw: 1 chop; macrochop releasing munis
Jackson: 1 chop
Lapeer: 1 chop
Macomb: 1 chop; macrochop releasing munis
Oakland: 2 chops; macrochop releasing munis
Wayne: 2 chops; macrochop releasing munis
Total: 9 county chops

There is 1 muni chop for Detroit and 1 community chop in Detroit. Total 2 chops, so 11 total.
The UCC cover adds 0, UCC pack ads 1 (GR), and the single county UCCs add 2 (Saginaw and Jackson)

CHOP: 11 raw (UC:11, UP:12, US:14)

Next to erosity. I'll use the simpler version for links and cuts as applied to regular chops which generates a lower score and gives more weight to chops over macrochops.

Segment 1/4: 9
Segment 2/3: 9 (8 from munis in the macrochop)
Segment 2/4: 2
Segment 2/6: 1 (muni, but it doesn't matter)
Segment 2/8: 4 (also Kent munis on the border to two counties)
Segment 3/6: 5
Segment 4/5: 12 (11 from munis in the macrochop)
Segment 4/8: 3
Segment 5/8: 3
Segment 5/10: 3
Segment 5/11: 4 (3 along Oakland border)
Segment 6/7: 4
Segment 6/8: 5
Segment 7/11: 1
Segment 7/12: 6 (3 Washtenaw-Wayne, 3 Monroe-Wayne)
Segment 8/11: 1
Segment 9/10:  8 (all within Macomb)
Segment 9/11: 8 (all within Oakland)
Segment 9/13: 3 (connections from Wayne to Macomb and Oakland)
Segment 9/14: 11 (all within Oakland)
Segment 10/11: 1
Segment 10/13: 2
Segment 11/14: 7 (all within Oakland)
Segment 12/13: 7 (all within Wayne, including the links to the district in Detroit)
Segment 12/14: 7 (6 within Wayne, 1 on the border to Oakland)
Segment 13/14: 9 (includes links between Detroit districts, 1 on Oakland border)

EROSITY: 136

[muon2]

Its the relative scores that matter, so let's start comparing the results. I've taken the step of labeling the plans in their posts, so I can keep track of them. I'm using the state, author, year of submission, and a letter.

MI Torie 2015B

This looks like it is the same in southern and eastern MI, so I'll copy the scores from there.

INEQUALITY 12 (range), 12 (ave dev) (range 6649, ave dev 1672) [10/9 in Torie A]
CHOP 13 raw (UC 14, UP 15, US 17) [12/13/14/16 in Torie A]
EROSITY 94 (changes 1/2:5[3], 1/4:5[7], 2/3:2[9], 2/4:4[7], 3/4:3[2], 3/5:0[1], 3/8:3[8], 4/5:4[3], 4/8:1[0], 5/8:1[2], net -12) [106 in Torie A]

Eliminating the macrochops had a big effect on erosity, a increase in chop, and an increase in inequality.

[muon2]

MI Torie 2015C

I'll compare this one to Torie B.

INEQUALITY 12 (range), 12 (ave dev) (range 6739, ave dev 1671) [12/12 in Torie B]
CHOP 12 raw (UC 13, UP 14, US 16) [13/14/15/17 in Torie B]
EROSITY 95 (changes 1/2:6[5], 1/4:5[5] 2/4:4[4], net +1) [94 in Torie B]

This seems like reasonable trade. Inequality went down, the chop went down and erosity gained only 1.

Edit: On closer inspection there is a precinct of Rose in Ogemaw and a precinct of Cadillac in Wexford that was left in CD 2. The second one is important, since without it CD 2 is outside the allowed deviation in population. With shifts in Kent moving the northern tier of townships plus Cedar Springs to CD 2 and Sparta with its surrounding township to CD 3 both are brought into range. That brings the INEQUALITY back up to 12 on both measures.

[muon2]

Let's check the score on train's plan B and compare to train A3.

But, on any case, here's a new map that if I've calculated correctly cuts down two chops.  Rearranging things between the Flint, Tri-Cities, and Lansing districts allowed me to turn the Saginaw macrochop into a non-macro chop, at the expense of I think one erosity point in the Lansing district?  Also, by taking advantage of the rule you pointed out w/r/t Kent, I had sufficient flexibility to clean up the lines in Wayne County and split Detroit entirely on community lines, so not only does the chop count go down but presumably erosity as well.

MI train 2015B




Districts 13 and 14 are 51.4 and 51.1% BVAP; inequality ranges from -2555 (District 6, unchanged) to +2893 (District 9), so inequality is still 10.

SKEW 1 (D) (6D, 2d, 2e, 2r, 2R)
POLARIZATION 20

INEQUALITY 10 (range), 11 (ave dev) (range 5448, ave dev 1620) [10/9 in train A]
CHOP 10 raw (UC:10, UP:11, US:13) [11/11/12/14 in train A]
EROSITY 126 (changes 4/5:3[12], 4/8:6[3], 5/8:2[3], 5/11:4[4], 7/11:1[1], 7/12:5[6], 7/14:1[0], 8/11:1[1], 9/11:7[8], 9/13:4[3], 9/14:11[11], 11/14:7[7], 12/13:7[7], 12/14:7[7], 13/14:6[9] net -10) [136 in train A]

The Saginaw change was the main winner for erosity, and chops went down though inequality rose.

[muon2]

MI Torie 2015A

Political leaning by district (in order): r, r, r, e, D, e, D, d, d, r, r, d, D, D; 0R, 5r, 2e, 3d, 4D.
SKEW: 1 (R)
POLARIZATION: 16

Population range 4990, average deviation 1257
INEQUALITY: 10 (range), 9 (ave dev)

UCC scores
Detroit cover 6, pack 5; no penalties
Grand Rapids cover 2, pack 0; 1 for pack
Lansing cover 2, pack 0; 1 for cover
Saginaw, Jackson; 2 for single county
Total UCC chops 7

County chops
Kent 1; macrochop
Clinton 1; macrochop
Jackson 1
Saginaw 1
Lapeer 1
Macomb 1; macrochop
Oakland 2; macrochop
Wayne 2; macrochop
Total county chops 10

Local chops
Detroit 1;
Detroit neighborhood; 1
Total local chops 2

CHOP: 12 raw (UC:13, UP:14, US:16)

Erosity by segment
seg 1/2: 3
seg 1/4: 7
seg 2/3: 9 (3 on county line, 6 internal Kent)
seg 2/4: 7 (2 on Kent county line)
seg 2/6: 1
seg 3/4: 2
seg 3/5: 1
seg 3/6: 3
seg 3/8: 8 (3 without the Clinton macrochop)
seg 4/5: 3
seg 5/8: 2 (1 without the Clinton macrochop)
seg 5/10: 3
seg 5/11: 3
seg 6/7: 1
seg 6/8: 1
seg 7/8: 3
seg 7/11: 1
seg 7/12: 6
seg 8/11: 1
seg 9/10: 6
seg 9/11: 10
seg 9/13: 6
seg 11/12: 1
seg 12/13: 13
seg 13/14: 8 (CD 13 in neighborhood 10 has two discontiguous pieces which adds one to erosity)

EROSITY: 106

This could drop if the Clinton macrochop became just a chop. The change of Saginaw from train's map, eliminating the macrochop, reduced that segment 4/5 from 12 to 3. The erosity within the Detroit UCC dropped compared to train's map. The chop went up, so both plans would survive a Pareto test.

[muon2]

This plan has the same problem with CDs 1,2,3 and 4 as Torie C. To score it I'll make the same adjustment I described there.

Well I dealt with the inequality issue by switching out townships in Clinton, and at the cost of grotesque erosity (but I can afford that probably still, even though my map to win gets uglier with each iteration (boo!), I lost the hood chop in Detroit in favor of a micro-chop of Hamtramck.  (Yes, the BVAP for MI-13 drops to 49.1%, but that is still probably legal, inasmuch as there are a fair number of non citizen and/or non voting Hispanics in the CD), so blacks will still be casting a majority of the votes. So assuming micro-chops are freebies, I move back into the lead!  

MI Torie 2015D


Anyway, this illustrates again a problem with the pareto optimality regime. A map can win with a massive dose of additional erosity, just in order to lose a chop or two. That is what we are seeing here. I am losing a ton of erosity points, just to get rid of two or three chops, including in one iteration, a fair amount of erosity just to get rid of one micro-chop, and in the case of Detroit, massively more erosity (that should not be rewarded). So a total score concept makes some sense, or to be pareto optimal, the variation in the total score cannot exceed a certain amount.

The Detroit plan to Hamtramck looks like an equivalent of the Orchard Lake jut. However, I can't get the populations to match (CD 12=+196, CD 13=+6984, CD 14=-3504), so I can't score it. Are there microchops in there, as you suggest? I can't cover the gap with just one to Hamtramck. A zoom with town lines would help.

edit: I found a precinct in Hamtramck that gets CD 14 to +2075 as you have. However, the precinct population is 5579, so it's too big to be a microchop. That doesn't fix my CD 12/13 discrepancy, but both are within limits with the precinct move.

Yes, sorry about that. The chop in Hamtramck was too big (I kept looking so hard for less black precincts to cut, and obviously was trying too hard). The only micro-chop I could find that worked is as below (leaving MI-13 at its absolutely max legal population). BVAP is 48.5%, still probably legal given the 7.5% HVAP population (but cutting it close perhaps).  So equality goes to hell, but hey, it's only a secondary tie breaker.

INEQUALITY 12 (range), 11 (ave dev) (range 6743, ave dev 1527) [12/12 in Torie C]
CHOP 12 raw (UC 13, UP 14, US 16) [no change from Torie C]
EROSITY 99 (changes 13/14:12[8] net +4) [95 in Torie C]

There's no longer a microchop savings here, but if there was some credit the CHOP would drop accordingly. The range was about the same as Torie C, but the ave dev improved enough to gain a point, but at the expected cost in erosity.

[muon2]

Anyway, for scoring,  "your" map is below (as best I could draw it), avoiding subunit chops, assuming that they are penalized in the chop score (as they should be). I must admit "your" MI-04 achieves absolute perfection.


MI jimrtex 2015A

It wasn't really "my" map.  I found a map on the Internet, and was using it for example.  You've jumped ahead to the next step.  But your going back and forth about whether it is better to split Eaton or Ingham illustrates a weakness of a single comprehensive stage.  It become exceedingly complex when trying to consider where the boundary should be between Grand Rapids and Lansing, when it is somehow tied to the division of Hamtramck.   If your statewide map had been approved, then there could be a simple focused discussion on where to get 13,647 persons, where all the options might be considered.

The switch of Osceola (not Missaukee) was automatic.  When a single county on a boundary can be switched and improve the equality between the two districts, then it is shifted.  The algorithm is simple.   Determine counties in the more populous district that have less population than the difference.   Choose the one that reduces the difference the most, while not breaking contiguity.

I had noticed that the shift of Missaukee would produce a 3rd district within 0.5% bounds.  I'll submit it as a joint effort.

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INEQUALITY 11 (range), 9 (ave dev) (range 5977, ave dev 1257) [11/9 in Torie D]
CHOP 12 raw (UC 14, UP 16, US 17) [12/13/14/16 Torie D]
EROSITY 112 (changes 1/2:5[6], 1/4:5[5], 2/3:10[2], 2/4:5[5], 3/4:4[2], 3/5:1[0], 3/8:5[3], 4/5:4[4], 4/8:0[1], 5/8:0[1], 5/10:4[3], 5/11:4[3], 8/11:1[1], 10/11:11[10] net +13) [99 in Torie D]

Shifting the chop from Saginaw to Ingham doesn't affect the raw CHOP, but does increase the UCC cover count, though if single county UCCs are counted it's a wash. Note that Kent is now a macrochop so erosity increases there, plus the other shofts tend to hurt erosity as well.

Shifting the chop from Clinton to Eaton increases the ave dev INEQUALITY to 10 and leaves the CHOP the same. The EROSITY drops to 110.

Edit: The chop into Ingham decreases the Detroit UCC pack from 5 to 4 so the UP score goes up an additional 1 beyond the 1 for GR.

[Torie]

Mike could you explain UC, UP and US again? I know what UP means, but defining them here again would be helpful. Thanks.

[muon2]

UC - raw score plus UCC multicounty cover
UP - UC plus UCC pack
US - UP plus UCC single county cover

cover and pack are defined in the OP. I hope that helps.

[Torie]

UC - raw score plus UCC multicounty cover
UP - UC plus UCC pack
US - UP plus UCC single county cover

cover and pack are defined in the OP. I hope that helps.

Thank you. That single county UCC cover rule sort of forces chops to go outside UCC's, resulting in something like the below, then doesn't it (where I lose chops into Saginaw and the Lansing UCC's)? Do you think that is a good policy? I really think that the cover and pack rules, should only be triggered when one reaches macrochop size myself, but putting that aside, and focusing on just single county UCC's, where, in a state like Michigan, with so many single county UCC's, it sort of forces gang banging when it comes to chops to be directed towards non UCC counties. I don't think non UCC folks will be happy with that. It also "forces" more erosity of course, although I don't think the map below is an erosity disaster - just substandard.

MI Torie 2015F

[muon2]

I certainly didn't say all the UCC rules are good, and I anticipate that any of them may force unintended preferences in maps. These were all suggested in the longer thread. I hope this will give us all a chance to see what impacts each of the UCC rules would have on the plans we've drawn. I'll be working may way through the others on the big thread as I get time.

[muon2]

On the originating thread I posed a map that required a microchop to complete CD7, but otherwise all chops were in the big three counties. In this version (muon A2) I placed the microchop in Washtenaw in a way to keep Milan intact in CD 7. All other chops are in the big three counties. CDs 13 and 14 are both over 50% BVAP (though CD 13 is 50.02%) and the neighborhoods are kept intact.

MI muon2 2015A2



SKEW 3 (R) (4D, 1d, 4e, 5r, 0R)
POLARIZATION 14
INEQUALITY 11 (range), 13 (ave dev) (range 6021, ave dev 1764)
CHOP 9 raw (UC 10, UP 12, US 13)
EROSITY 119

The chop score remains very low, even with all sorts of UCC penalties. However placing all those chops comes with a cost in erosity despite the nice lines in Oakland and Macomb. Erosity in the urban area remains a strong tool to keep this plan from knocking out others, though the low chop score would probably keep it as a Pareto equivalent of other top plans.

Another interesting feature is the very low polarization score - there are 4 very competitive districts, and nothing completely safe for the Pubs with (only 1 is better than R+3.3 and that one is R+4.8 ). However that competitiveness created a skew to the Pubs since it took a couple of lean D districts and moved them to highly competitive (3 are at D+1).

The UCC single county chop score (US) could be decreased by putting the microchop somewhere other than Washtenaw. However, I like the idea of keeping a city together, so I'll keep it in Wastenaw for this version. In any case I'm not sold on the single UCC score so it's a useful exercise to keep it there for that reason, too.

I've cross posted this map on the chops and erosity thread for discussion about policy aspects as opposed to scoring aspects for this thread.

[muon2]

Here's the rescore of muon2 B

Here's my plan to reduce chops in MI without relying on microchops. I used a UCC chop of whole county Livingston and a threshold of 47% BVAP for the Detroit CDs. This allowed the removal of one chop in Oakland and a chop outside of the Detroit UCC.

The Muskegon chop is a macrochop and the townships are used to determine cut links there. The other two outstate chops are small. The chop in Ionia isn't a microchop, but it could be if it were moved to the SW corner of Eaton. However if microchops get no advantage as county or UCC chops then to place it there would be counterproductive, despite a better shape.

The Detroit CDs are 48.3% and 47.5% BVAP for CDs 13 and 14 respectively. It's quite possible that the BCVAP in CD 13 is over 50% since there is a 7.5% HVAP population and a large Arab population which would have high non-citizen rates.

MI muon2 2015B

SKEW 1 (R) (5D, 2d, 2e, 4r, 1R) [3R in muon2 A2]
POLARIZATION 18 [14 in muon2 A2]
INEQUALITY 10 (range), 11 (ave dev) (range 5425, ave dev 1599) [11/13 in muon2 A2]
CHOP 8 raw (UC:9, UP:10, US:11) [9/10/12/13 in muon2 A2]
EROSITY 116 [119 in muon2 A2]

If the lowered BVAP is permissible, this beats muon2 A2 in all categories except polarization which is not used as a primary score.

[muon2]

Here is a revised map of MI, which minimizes the GR UCC chop, saving 4 penalty points in my system, over the map where MI-03 goes to Ionia and Barry. Under such a system, it's a winner if it does not generate more than three additional erosity points. Does it (say compared to Jimtex's map to the left below? I tend to doubt it generates more than two additional erosity points, but that is just a guess. I tried chopping Ottawa in lieu of Kent, but it was an erosity disaster, so no go.

Actually I count 18 cuts for MI-04, and avoid the highway extra highway cut in Kent (saving two cuts), but there are three more cuts between MI-02 and MI-03 between counties (5 total, rather costly that, as compared to Jimtex's map, with but two), so there is a net increase of one erosity point, (two behind Jimtex's map in that department). So the map is a winner in total score, however meaningful that is vis a vis a strict pareto optimality regime (which I don't think I  favor, if the total score however calculated varies by more than a certain amount).

MI Torie 2015E

I found a precinct error so the deviations of CD 2 and 3 are -1740 and -2372.

SKEW 1 (R) (4D, 3d, 2e, 4r, 1R)
POLARIZATION 17
INEQUALITY 11 (range), 11 (ave dev) (range 5977, ave dev 1512) [12/11 in Torie D]
CHOP 12 raw (UC 13, UP 13, US 15) [12/13/14/16 in Torie D]
EROSITY 115 [99 in Torie D, 106 in Torie A]

The change to protect the UCC pack in GR is expensive in erosity. Torie D had no macrocrop in  Kent and it had an erosity of 2 on the border between CD 2 and 3. The switch back to a macrochop ran the erosity on that border up to 14. Compare this chop in Kent to the one in Torie A which was also a macrochop, but was very rectangular and the border erosity was 9. This plan is more irregular than Torie A in Kent and the erosity is consistent with that.

I come up with a perimeter erosity of 16 for CD 4: 6 with CD 1, 5 with CD 2, 1 with CD 8, and 4 with CD 5.

[Torie]

The change to protect the UCC pack in GR is expensive in erosity. Torie D had no macrocrop in  Kent and it had an erosity of 2 on the border between CD 2 and 3. The switch back to a macrochop ran the erosity on that border up to 14. Compare this chop in Kent to the one in Torie A which was also a macrochop, but was very rectangular and the border erosity was 9. This plan is more irregular than Torie A in Kent and the erosity is consistent with that.

This is a policy problem. By the way, I abandoned my thought that the cover rule only comes into play with whole county UCC severances. It won't work, as I will elucidate. The only way to protect UCC's adequately, is with a population based transference rule, or potentially a ban rule (maxi-pack rule is a requirement). Otherwise, UCC raids will tend to be rewarded, per the above, for example. When I have time (I don't know, buy hey I completed my assignments for the Columbia County DA, so I have my pro bono hours and then some, and can complete my application to become a NY lawyer), I will lay out the conundrums using Mike's "hideous" MI map, that chops the Detroit UCC to bits, while being rewarded for it.

[traininthedistance]

The change to protect the UCC pack in GR is expensive in erosity. Torie D had no macrocrop in  Kent and it had an erosity of 2 on the border between CD 2 and 3. The switch back to a macrochop ran the erosity on that border up to 14. Compare this chop in Kent to the one in Torie A which was also a macrochop, but was very rectangular and the border erosity was 9. This plan is more irregular than Torie A in Kent and the erosity is consistent with that.

This is a policy problem. By the way, I abandoned my thought that the cover rule only comes into play with whole county UCC severances. It won't work, as I will elucidate. The only way to protect UCC's adequately, is with a population based transference rule, or potentially a ban rule (maxi-pack rule is a requirement). Otherwise, UCC raids will tend to be rewarded, per the above, for example. When I have time (I don't know, buy hey I completed my assignments for the Columbia County DA, so I have my pro bono hours and then some, and can complete my application to become a NY lawyer), I will lay out the conundrums using Mike's "hideous" MI map, that chops the Detroit UCC to bits, while being rewarded for it.

Would you want this ban to include single-county UCCs?  Especially if you do, there will be cases where maxi-pack on all UCCs is physically impossible (such as, say, SEPA) and I presume the rules would then just only allow those maps with minimum UCC chops.  As mentioned in passing earlier, I especially anticipate trouble in Central Florida.

Also, as for rewarding for UCC chops, try comparing my most recent "serious" alternative (which is the same as Train B outstate, and completely respects UCC cover, though it still does not pack Grand Rapids), but adopts muon's 47% BVAP chop-minimzing Detroit).  That should ease your mind somewhat, once muon scores it?

As always, I tend to be more put off by cover violations than by pack violations, though the latter is non-ideal and I'm happy to have it dinged in the scoring.  I will once again point to western PA as a case where violating pack can lead to nicer lines without materially damaging the spirit of the UCCs.

[muon2]

Here's the most recent Torie plan before I go to the rest of train's work.

UC - raw score plus UCC multicounty cover
UP - UC plus UCC pack
US - UP plus UCC single county cover

cover and pack are defined in the OP. I hope that helps.

Thank you. That single county UCC cover rule sort of forces chops to go outside UCC's, resulting in something like the below, then doesn't it (where I lose chops into Saginaw and the Lansing UCC's)? Do you think that is a good policy? I really think that the cover and pack rules, should only be triggered when one reaches macrochop size myself, but putting that aside, and focusing on just single county UCC's, where, in a state like Michigan, with so many single county UCC's, it sort of forces gang banging when it comes to chops to be directed towards non UCC counties. I don't think non UCC folks will be happy with that. It also "forces" more erosity of course, although I don't think the map below is an erosity disaster - just substandard.

MI Torie 2015F

SKEW 2 (R) (4D, 3d, 1e, 5r, 1R) [1 (R) in Torie E]
POLARIZATION 18 [17 in Torie E]
INEQUALITY 11 (range), 10 (ave dev) (range 5977, ave dev 1458) [11/11 in Torie E]
CHOP 12 raw (UC 12, UP 12, US 13) [12/13/13/15 in Torie E]
EROSITY 122 [115 in Torie E]

As anticipated the erosity rose by 7 in order to remove the cover penalty and one of the two single county UCC chops.

[muon2]

Well, if 47% BVAP is going to be okay, then my map can take advantage of that too.

MI train 2015C






Nothing is changed outstate; in the Detroit area the Oakland chop is eliminated, as is presumably several points of erosity– and also a point of inequality!  We're down to 9 here.  District 13 is 47.5% BVAP; District 14 is 48.3%.

Obviously, I would prefer to ding myself a half point for not having an all-GR district, but in the absence of that rule I'll leave outstate be for now.

There were some adjustments in population that I found due to two precincts: CD 5 (+2041), CD 9 (+2099), CD 10 (+1716), CD 13 (-2959). With that I'll compare it to train B which matches the outstate area.

SKEW 1 (D) (5D, 3d, 2e, 3r, 1R) [1 (D) in train B]
POLARIZATION 18 [20 in train B]
INEQUALITY 10 (range), 11 (ave dev) (range 5058, ave dev 1577) [10/11 in train B]
CHOP 9 raw (UC 9, UP 10, US 12) [10/10/11/13 in train B]
EROSITY 125 [126 in train B]

Good news! Both CHOP and EROSITY decreased with the Detroit UCC rearrangement. Polarization came down, too. The only negative is dealing with the sub-50% BVAPs, but given the SKEW the Dems should like it overall.

[muon2]

For Michigan for example, it might be useful to draw a map with the absolutely minimum number of chops, using your system as modified, and mine, where we still disagree, and see how many erosity points it has versus say my map, and see what that ratio is.

I feel pretty confident that this map is as chop-minimizing as you can get, vis-a-vis the Torie UCC rules:

MI train 2015D


Bay, Jackson, and Lapeer are all I-chops.

The Detroit districts are, as last time, drawn to the 47% BVAP standard; another chop of Oakland would be necessary if you wanted to break 50%.

No, it's not a serious suggestion.  

It also violates the bridge connection rule. That rule forbids linking any two whole counties solely through a chopped county. Bay is a chopped county acting as a bridge from Midland to Arenac. I'll score it anyway and compare it to train C which is the same around Detroit.

SKEW 1 (R) (6D, 1d, 2e, 3r, 2R) [1 (D) in train C]
POLARIZATION 20 [18 in train C]
INEQUALITY 10 (range), 11 (ave dev) (range 5383, ave dev 1613) [10/11 in train C]
CHOP 9 raw (UC 9, UP 9, US 11) [9/9/10/12 in train C]
EROSITY 124 [125 in train C]

The erosity went down a point, in part because the Kent chop is relatively clean and since CD 6 went to its most compact form. The only cost was in polarization and a Pub skew.