DRA stuff

[President Punxsutawney Phil]

McCain (yellow) and Obama (green) each win their districts with exactly 57.3%. The only county split is Mecklenburg.

Interesting.
Did you know that half of North Carolina's population lives in, like ten counties?

[muon2]

In IL over half the population is in three counties (Cook, DuPage, and Lake). How many states don't have half the population in 10 counties or fewer?

[President Punxsutawney Phil]

In IL over half the population is in three counties (Cook, DuPage, and Lake). How many states don't have half the population in 10 counties or fewer?

That is a fascinating question. I think % of counties is better measure personally though.

[President of the great nation of 🏳️‍⚧️]

In IL over half the population is in three counties (Cook, DuPage, and Lake). How many states don't have half the population in 10 counties or fewer?

That is a fascinating question. I think % of counties is better measure personally though.

AL - 9 (13.43%)
AK - 2 (10%/6.9%)
AZ - 1 (6.67%)
AR - 10 (13.33%)
CA - 4 (6.9%)
CO - 5 (7.81%)
CT - 2 (25%)
DE - 1 (33.33%)
FL - 7 (10.45%)
GA - 12 (7.55%)
HI - 1 (20%)
ID - 4 (9.09%)
IL - 3 (2.94%)
IN - 11 (11.96%)
IA - 11 (11.11%)
KS - 5 (4.76%)
KY - 14 (11.67%)
LA - 8 (12.5%)
ME - 4 (25%)
MD - 4 (16%)
MA - 4 (28.57%)
MI - 6 (7.23%)
MN - 6 (6.9%)
MS - 14 (17.07%)
MO - 7 (6.09%)
MT - 5 (8.93%)
NE - 3 (3.23%)
1st counts Unorganized as one borough, 2nd counts it as 10 CAs, which are counted in the % as boroughs
20% of counties or more
10 counties or more
I'll finish this list when I get home.

[President Punxsutawney Phil]

KY Republican gerrymander

(two-party vote)
Calculations reached by (other %/{McCain %-100})+McCain %. This has more margin of error than the exact method but shouldn't deviate too much in terms of numbers.
1 (blue): R+13
2 (green): R+7
3 (purple): R+7
4 (red): R+14
5 (gold): R+20
6 (teal): R+12

[President Punxsutawney Phil]

(two-party vote, using Muon's formula)
1 (black): R+20
2 (green): R+4
3 (purple): R+3
4 (red): R+16
5 (gold): R+25
6 (blue): R+5

[President Punxsutawney Phil]

This is a district in WV drawn to be reliably Democratic. It is 46.5% O, 51.8% McC.

[President Punxsutawney Phil]

PA non-partisan map

(two party vote)
1 (blue): 36.1% White, 45.6% Black, D+33
2 (green): 45.1% White, 32.9% Black, 13.7% Hispanic, D+25
3 (purple): R+2
4 (red): R+9
5 (gold): R+13
6 (teal): R+5
7 (gray): D+6
8 (slate blue): D+0.5
9 (cyan): D+12
10 (pink): D+2
11 (chartreuse): R+12
12 (cornflower blue): R+12
13 (salmon): R+5
14 (olive): D+12
15 (orange): D+5
16 (lime): R+1
17 (dark slate blue): R+7
18 (yellow): R+9

[President Punxsutawney Phil]

KY R gerrymander, 5 seats

(two-party vote)
1 (blue): R+13
2 (green): R+8
3 (purple): R+7
4 (red): R+13
5 (white): R+19

[President Punxsutawney Phil]

MO 4D-4R map

1 (blue): This district includes practically all of the black precincts in the St. Louis area, along with all of heavily conservative St. Charles County, an area that elected Todd Akin to the House time and time again. The presence of white liberals in St. Louis makes this district Democratic, and safe for William Lacy Clay Jr. (D-St. Louis). 55.9% White, 39.2% Black; D+13
2 (green): This district includes most of the population in St. Louis County, as well as the southern, white half of St. Louis. This configuration makes it a safe Democratic district, screwing over Ann Wagner (R-Ballwin). This would be a prime oppurtunity for the Carnahan name to return to Congress. D+6.
3 (gold): This district includes most of the exurbs to the west of St. Louis, but moves north to include most of Northern Missouri. It is solidly Republican. While no incumbents live here, Blaine Leutkemeyer (R-Jefferson City) would run here, and Sam Graves (R-Independence) might make a quixotic bid here as well. R+12.
4 (slate blue): This district would likely be where Vicky Hartzler (R-Columbia) would run. No incumbents live here, except for Leutkemeyer and Jason Smith (R-Salem), who would both, in all probability would run elsewhere. This district, not surprisingly, would always be solidly Republican. R+19.
5 (red): This district includes almost all of the parts of Metro Kansas City that actually border Kansas, along with some rural areas that reduce the D PVI and help out the 5th. Emanuel Cleaver (D-Kansas City) takes a hit in terms of PVI, but he should be fine. D+2.
6 (purple): This seat is Sam Graves' current one, but it is radically transformed, gaining counties along the Missouri River as well as Columbia, which is quite Democratic. He also gains some areas in Kansas City itself, including some heavily black neighborhoods in Downtown KC. This district moves double-digits to the left, ensuring he will most likely not be re-elected. Sam Graves is screwed. D+2.
7 (gray): This seat changes a bit from its prior configuration, now reaching the southernmost reaches of the Kansas City metro and becoming a long, tall, thick column in terms of shape. It remains solidly Republican, and Billy Long (R-Springfield) retains his political base. He should be fine here. R+17.
8 (teal): This district has all of the counties that border the Mississippi and are south of the St. Louis metro, including Cape Girardeau, home to Rush Limbaugh. It also has a slice of the metro as well, taking in a small part of St. Louis County, and all of Jefferson County. This is the seat of Jason Smith (R-Salem) and this would be his if he wanted it. R+10.
So, in sum, this map is a pretty solid 4D-4R map. Sam Graves likely loses to a KC Metro area D, Ann Wagner retires or makes a quixotic bid in the 2nd or 3rd; Leutkemeyer likely gains hundreds of thousands of constituents in Northern Missouri; and MO has a tied House delegation for years to come.
And yes, that MO-1 is fully legal.

[President Punxsutawney Phil]

A gerrymander of Oklahoma designed to strengethen Markwayne Mullin. OK-2 is now 50% D and 50% R in the partisan average.

[President Punxsutawney Phil]

Non-partisan map of AZ, no VRA

1 (blue): This district includes more than half of Arizona's area, and is compromised of very sparsely populated Northern Arizona. Paul Gosar (R-Prescott) and Ann Kirkpatrick (D-Flagstaff) both live here, but since Kirkpatrick is running for the Senate, Gosar would be not be seriously challenged for this seat. This seat is right in line with the state as a whole in terms of partisanship. R+10.
2 (green): No incumbent lives here, but it is solidly Republican. This moves heavily to the south of the current 2nd, and pulls in heavily conservative Pinal and Chocise counties, before moving north to pick up parts of Maricopa and Yavapai counties. R+15.
3 (red): Southwest Arizona district. Raúl Grijalva (D-Yuma) would have uphill fight for re-election in this district. 53.9% White, 37.1% Hispanic; R+7.
4 (white): This congressional district includes a large chunk of heavily Republican areas to the north and west of Pheonix. This district has no incumbent. R+14.
5 (gold): This seat includes all of Mesa and some Southeastern Maricopa County communities to the south. Matt Salmon (R-Mesa) would be fine here. R+15.
6 (gray): This district stretches from Fountain Hills to Downtown Pheonix. It has a Republican lean. David Schweikert (R-Fountain Hills) takes a hit, and his PVI is halved, but he would nonetheless be favored to win here. R+7.
7 (teal): This district, the most Hispanic and liberal of the Maricopa-area seats, is a genuine swing district, and has a good amount of Downtown Pheonix. Ruben Gallego (R-Pheonix) would have to moderate to make himself viable here. 57% White, 26.1% Hispanic; R+1.
8 (slate blue): This seat takes in some conservative suburbs of Pheonix, but the gaining of some liberal areas in the city drags down the McCain %. This seat is technically majority-minority. Trent Franks (R-Glendale) might have to really work for this seat, more so than his current one. 45% White, 43.5% Hispanic; R+5.
9 (purple): This district includes heavily Democratic Santa Cruz county, but goes north to include most of Tucson and much of its suburbs. A white liberal could easily win here. This is the most Democratic seat on the map, and the most Hispanic one as well. Ron Barber could easily make a comeback here. 57% White, 34% Hispanic; D+2.

[muon2]

Not just the VRA, but you split reservations in AZ. That's generally frowned upon in neutral maps. It can be more important to keep reservations together than counties.

[/]

Not just the VRA, but you split reservations in AZ. That's generally frowned upon in neutral maps. It can be more important to keep reservations together than counties.

Does the current map in AZ split any reservations?

[President Punxsutawney Phil]

Not just the VRA, but you split reservations in AZ. That's generally frowned upon in neutral maps. It can be more important to keep reservations together than counties.

Which ones did I split?

[muon2]

Not just the VRA, but you split reservations in AZ. That's generally frowned upon in neutral maps. It can be more important to keep reservations together than counties.

Which ones did I split?

Gila River IR extends from Pinal (pop 8774)  into Maricopa (pop 2994).
Tohono O'Odham IR is primarily in Pima (pop 7174) with a bit in Maricopa (pop 151) and the part you chopped in Pinal (pop 545).
Fort Apache IR is primarily in Navajo (pop 11,199 in the main VTDs) with parts in Apache (pop 555) and the chopped part in Gila (pop 1676 in the 2 main VTDs).

The boundaries of current AZ-1 and AZ-4 keep all of Fort Apache IR in AZ-1. The boundary between AZ-1 and AZ-3 keep all of Gila River IR in AZ-1 and Tohono O'Odham IR in AZ-3.

[Torie]

Not just the VRA, but you split reservations in AZ. That's generally frowned upon in neutral maps. It can be more important to keep reservations together than counties.

Which ones did I split?

Don't feel bad. I did the same thing when I did my first AZ maps. Lewis Trondheim took the paddle to me, and I still feel the sting from that.

[President Punxsutawney Phil]

Not just the VRA, but you split reservations in AZ. That's generally frowned upon in neutral maps. It can be more important to keep reservations together than counties.

Which ones did I split?

Don't feel bad. I did the same thing when I did my first AZ maps. Lewis Trondheim took the paddle to me, and I still feel the sting from that.

I am most focused on cutting county splits generally. Just look at my maps!

[muon2]

Not just the VRA, but you split reservations in AZ. That's generally frowned upon in neutral maps. It can be more important to keep reservations together than counties.

Which ones did I split?

Don't feel bad. I did the same thing when I did my first AZ maps. Lewis Trondheim took the paddle to me, and I still feel the sting from that.

I am most focused on cutting county splits generally. Just look at my maps!

Reducing county splits is good, and if that's the goal the number of splits can be reduced even further. For example, this is a map of OK I posted in 2012 with no county splits and it has 51D-49R for the partisan avg in CD-2. All the CDs are within 0.5% of the quota.



It turns out that many states can be drawn with districts within 0.5% with no county splits except for counties which are larger than a CD. There's even a mathematical relation I derived from posted maps that relates the number of counties in the state, the number of districts, and the typical population deviation.

[President Punxsutawney Phil]

Not just the VRA, but you split reservations in AZ. That's generally frowned upon in neutral maps. It can be more important to keep reservations together than counties.

Which ones did I split?

Don't feel bad. I did the same thing when I did my first AZ maps. Lewis Trondheim took the paddle to me, and I still feel the sting from that.

I am most focused on cutting county splits generally. Just look at my maps!

Reducing county splits is good, and if that's the goal the number of splits can be reduced even further. For example, this is a map of OK I posted in 2012 with no county splits and it has 51D-49R for the partisan avg in CD-2. All the CDs are within 0.5% of the quota.



It turns out that many states can be drawn with districts within 0.5% with no county splits except for counties which are larger than a CD. There's even a mathematical relation I derived from posted maps that relates the number of counties in the state, the number of districts, and the typical population deviation.

Yep. It it's easier as the total # of counties/CD ratio increases.

[muon2]

Yep. It it's easier as the total # of counties/CD ratio increases.

But I don't think the mathematical relationship was obvious. In any case, for your neutral offerings, why not concentrate on posting maps that really reduce the number of county splits to the absolute minimum?

[President Punxsutawney Phil]

Yep. It it's easier as the total # of counties/CD ratio increases.

But I don't think the mathematical relationship was obvious. In any case, for your neutral offerings, why not concentrate on posting maps that really reduce the number of county splits to the absolute minimum?

That's more generally a vein of all my mapmaking than something that always come first in every single instance.
Oftentimes I reduce splits (or, as you call it, chops) while accomplishing another aim at the same time, like uniting all of an MSA in one district, and/or partisan gerrymandering and reducing erosity etc. My 12R-3D-1Swing Ohio gerrymander is a textbook example.

This is a Republican gerrymander of Ohio that reduces county splits.
District 1 (blue): 46.1% Obama, 52.9% McCain; 53% Dem, 47% Rep.
District 2 (green): 45.7% Obama, 52.9% McCain; 48.8% Dem, 51.2% Rep.
District 3 (teal): 49.3% Obama, 49.2% McCain; 49.5% Dem, 50.5% Rep.
District 4 (white): 47.2% Obama, 50.8% McCain; 54% Dem, 46% Rep.
District 5 (cyan): 42.1% Obama, 56% McCain; 43.4% Dem, 56.6% Rep.
District 6 (pink): 46.8% Obama, 50.9% McCain; 57.9% Dem, 42.1% Rep.
District 7 (chartreuse): 48.3% Obama, 49.6% McCain; 55% Dem, 45% Rep.
District 8 (gold): 38.1% Obama, 60.3% McCain; 40.2% Dem, 59.8% Rep.
District 9 (slate blue): 62.6% Obama, 35.8% McCain; 66.1% Dem, 33.9% Rep.
District 10 (red): 49.2% Obama, 49.5% McCain; 48.4% Dem, 51.6% Rep.
District 11 (dark salmon): 46.1% White, 45.6% Black; 79.9% Obama, 19.3% McCain; 80.9% Dem, 19.1% Rep.
District 12 (gray): 49.8% Obama, 48.8% McCain; 49% Dem, 51% Rep.
District 13 (black): 61.8% Obama, 36.2% McCain; 71.8% Dem, 28.2% Rep.
District 14 (olive): 51.3% Obama, 47.3% McCain; 53.2% Dem, 46.8% Rep.
District 15 (blue): 50.9% Obama, 47.6% McCain; 53% Dem, 47% Rep.
District 16 (dark orange): 52.8% Obama, 45.8% McCain; 58% Dem, 42% Rep.

In my nonpartisan map Toledo and Akron MSAs are kept within one district and all of Cleveland and Cincinnati are as well.  Erosity is also quite low. (editing lines in the Columbus area could lower it even farther).

My non-partisan map of Ohio.
District 1 (blue): This seat shifts heavily to the left. Steve Chabot's district moves 8 points to left. Driehaus could easily mount  comeback here. D+2
District 2 (green): Eastern Cincinnati suburbs paired with some heavily Republican rural areas to the east. Brad Wenstrup (R-Cincinnati) would likely run and win here, but Chabot could run here as well. (R+19)
District 3 (purple): This district has parts of the heavily Democratic downtown core of Columbus along with some suburbs to the west and east. Joyce Beatty (D-Columbus) would naturally run here. D+12.
District 4 (red): Parts of Northwest and North-central Ohio along with some rural areas around Lima, which are stomping grounds of Jim Jordan (R-Lima). This seat would be his. R+14.
District 5 (yellow): This district contains the entirety of the Toledo MSA, along with a small part of Senec County added for population purposes. This seat has two incumbents, Bob Latta (R-Bowling Green), and Marcy Kaptur (R-Toledo). Kaptur would easily win. D+7.
District 6 (teal): This seat is composed of rural Southeastern Ohio, and goes north to preserve its rural character and stay out of the Columbus MSA. Bill Johnson (R-Marietta) gets about one point of added security, and his seat becomes R+6.
District 7 (black): This district has the entirety of the Canton–Massillon MSA, which has more than half of the district's population. It becomes more Democratic due to shifting southeast. R+3.
District 8 (slate blue): This seat takes in some suburbs of Dayton and Columbus, and some turf to the north. R+15.
District 9 (cyan): This district takes in the coastal counties of Erie and Lorain, but becomes Republican-leaning due to it gaining Medina and Wayne. Bob Gibbs (R-Avon) lives here and would likely run here, though Jim Renacci (R-Cleveland) could mount a bid for this seat too. R+2.
District 10 (pink): This seat retains its character as a Dayton-centered seat, though its center of gravity moves north. It is still safe for Mike Turner (R-Dayton). R+1.
District 11 (chartreuse): This is the sole VRA seat on the map. It is 47.8% White, 43% Black. Marcia Fudge (D-Cleveland) would obviously run here. D+28.
District 12 (cornflower blue): This district takes up the northern parts of the Columbus MSA. It would easily reelect Pat Tiberi (R-Columbus) again and again. R+10.
District 13 (dark salmon): This seat includes heavily blue-collar Mahoning and Trumbull counties, but also upscale Republican areas in Ashtabula, Gaugea, and Lake counties, minimizing its D lean. Tim Ryan (D-Akron) would run either here or in the 16th; he would be fine in either district. D+3.
District 14 (firebrick): This district envelopes the 11th, and lies mostly within Cuyahoga county. David Joyce (R-Columbia Heights), who was drawn into the 11th, could mount a bid for the seat, but would be at a definite disadvantage in this suburban Cleveland congressional district. D+2.
District 15 (dark orange): This seat has the southern parts of the Columbus MSA, and two-fifths of the area of Franklin County itself. Steve Stivers (R-Columbus) would be comfortable here. R+7.
District 16 (navajo white): This seat is essentially the entire Akron MSA with the addition of a small part of Cuyahoga for population purposes. Tim Ryan (D-Akron) would be right at home in this district. D+3.

[President Punxsutawney Phil]

Yep. It it's easier as the total # of counties/CD ratio increases.

But I don't think the mathematical relationship was obvious.

I was saying that as a general rule, the more counties you have, the less likely you are to have to split one for population equality. It's not really a formula per se.

[muon2]

Yep. It it's easier as the total # of counties/CD ratio increases.

But I don't think the mathematical relationship was obvious.

I was saying that as a general rule, the more counties you have, the less likely you are to have to split one for population equality. It's not really a formula per se.

I'm saying that it is more than a general rule and it does fit to a formula.

A region is a group of whole counties with a whole number districts within the required variance form the quota. A district of whole counties is a region with 1 district. Two districts that are whole counties except that they share a chopped county are effectively a region with 2 districts. Extending that to a whole state, each chop reduces the number of regions in a plan by one.

It turns out that there is a strong correlation between the average number of counties per region in a plan and the inequality. A few years ago we drew up inequality-minimizing plans with no chops and without regard to erosity. I summarized those results for the Forum Redistricting Commission thread in this post.

Let's add to the discussion the I in SPICE: Inequality.

Definition: Quota. The quota is the total population of a state divided by the number of districts rounded to the nearest whole number.
Definition: Deviation. The deviation is the difference between the population of a district and the quota. Negative numbers indicate a district that has a population that is smaller than the quota.
Definition: Range. The range is the difference in population between the largest and smallest district in a plan.
Definition: Average Deviation. The average deviation is the average of the absolute values of the deviations for all districts in a plan.

Background: SCOTUS has set two different standards for districts. Legislative and local districts must be substantially equal and that has been interpreted to be a range not exceeding 10% of the quota. Congressional districts must be as equal as practicable, and for some time that was assumed to mean that only exact equality would do. However, the recent WV case makes it clear that a range of up to 1% of the quota is acceptable when driven by other neutral redistricting factors. Greater than 1% might also be acceptable, but 10% would presumably not be because that is set by a different standard. It's an evolving area in the law.

Item 6. All plans for congressional districts shall have a range not exceeding 1% of the quota. All other plans shall have a range not exceeding 10% of the quota except when otherwise limited by state law.

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



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

The average state has about 72 counties and if one divides that number into 2, 3, 4, etc. districts then one can use the fit from the data in the graph to predict a likely range. That in turn can be built into a table.

Item 7. 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

This score reflects the expected improvement one should get by adding chops to a plan. So adding it to the chop score creates an automatic balance between chops and inequality. It also provides for a Pareto choice vs erosity where plans with no chops are likely (eg IA).

[President Punxsutawney Phil]

Yep. It it's easier as the total # of counties/CD ratio increases.

But I don't think the mathematical relationship was obvious.

I was saying that as a general rule, the more counties you have, the less likely you are to have to split one for population equality. It's not really a formula per se.

I'm saying that it is more than a general rule and it does fit to a formula.

A region is a group of whole counties with a whole number districts within the required variance form the quota. A district of whole counties is a region with 1 district. Two districts that are whole counties except that they share a chopped county are effectively a region with 2 districts. Extending that to a whole state, each chop reduces the number of regions in a plan by one.

It turns out that there is a strong correlation between the average number of counties per region in a plan and the inequality. A few years ago we drew up inequality-minimizing plans with no chops and without regard to erosity. I summarized those results for the Forum Redistricting Commission thread in this post.

Let's add to the discussion the I in SPICE: Inequality.

Definition: Quota. The quota is the total population of a state divided by the number of districts rounded to the nearest whole number.
Definition: Deviation. The deviation is the difference between the population of a district and the quota. Negative numbers indicate a district that has a population that is smaller than the quota.
Definition: Range. The range is the difference in population between the largest and smallest district in a plan.
Definition: Average Deviation. The average deviation is the average of the absolute values of the deviations for all districts in a plan.

Background: SCOTUS has set two different standards for districts. Legislative and local districts must be substantially equal and that has been interpreted to be a range not exceeding 10% of the quota. Congressional districts must be as equal as practicable, and for some time that was assumed to mean that only exact equality would do. However, the recent WV case makes it clear that a range of up to 1% of the quota is acceptable when driven by other neutral redistricting factors. Greater than 1% might also be acceptable, but 10% would presumably not be because that is set by a different standard. It's an evolving area in the law.

Item 6. All plans for congressional districts shall have a range not exceeding 1% of the quota. All other plans shall have a range not exceeding 10% of the quota except when otherwise limited by state law.

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



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

The average state has about 72 counties and if one divides that number into 2, 3, 4, etc. districts then one can use the fit from the data in the graph to predict a likely range. That in turn can be built into a table.

Item 7. 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

This score reflects the expected improvement one should get by adding chops to a plan. So adding it to the chop score creates an automatic balance between chops and inequality. It also provides for a Pareto choice vs erosity where plans with no chops are likely (eg IA).

Cool. Please link me the thread in which this exercise was done.