DRA stuff

[jimrtex]

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).

What happens if large UCC's are treated as a single-county, multi-representative apportionment unit?

Does Log Range represent Log₁₀ of the deviation range in absolute numbers (eg a value of four represents a range of 10,000 persons?

Are the two outlier yellow boxes, Iowa and Massachusetts?

[President Punxsutawney Phil]

(two-party vote)
1 (red): D+10*
2 (green): D+1
3 (blue): D+1
4 (teal): R+2
5 (white): R+18*
6 (gold): D+7
7 (purple): D+9*
Estimated. DRA doesn't want to work with me right now.


I saw the data one or two times though and made educated guesses.

[President Punxsutawney Phil]

Same estimated pvi disclaimer applies here.

[muon2]

I like your neutral offerings better. I'm sure there will be plenty of more relevant gerrymanders when estimates close to 2020 start to come out.

[President Punxsutawney Phil]

I like your neutral offerings better. I'm sure there will be plenty of more relevant gerrymanders when estimates close to 2020 start to come out.

Understood.

[LLR]

[Tim told me i could put this here]

Democratic district (by 60 votes) in a 4-district Wyoming)




However, it's technically not legal because the area to the bottom and left isn't enough to fill a district

[President Punxsutawney Phil]

Florida D gerrymander quasi-D gerrymander

1 (gold): R+21
2 (teal): R+6
3 (gray): R+14
4 (red): R+22
5 (purple): 55.2% White, 31.2% Black; EVEN
6 (blue): R+3
7 (green): EVEN
8 (dark orange): R+12
9 (dark magenta): 48.2% White, 10.9% Black, 34.7% Hispanic; D+5
10 (cyan): 48.7% White, 22.6% Black, 21.9% Hispanic; D+8
11 (slate blue): R+9
12 (aquamarine): R+2
13 (chartreuse): R+3
14 (dark salmon): 55.2% White, 20.1% Black, 19.1% Hispanic; D+5
15 (black): R+12
16 (olive): R+7
17 (yellow green): R+1
18 (dark slate blue): R+1
19 (lime): D+3
20 (maroon): R+16
21 (pink): D+7
22 (white): D+5
23 (gray): 33% White, 36.7% Black, 24.7% Hispanic; D+17
24 (pale violet red): 24.4% White, 15.5% Black, 56.5% Hispanic; D+8
25 (indigo): 24.2% White, 25.2% Black, 46.7% Hispanic; D+19
26 (aquamarine): 8.4% White, 17.3% Black, 72.5% Hispanic; D+5
27 (sienna): 26.7% White, 11.5% Black, 58.6% Hispanic; D+2

[President Punxsutawney Phil]

Michigan fair map

1 (blue): R+1
2 (green): EVEN
3 (purple): R+4
4 (red): D+3
5 (gray) D+9
6 (gold): R+8
7 (teal): D+1
8 (slate blue): D+5
9 (pink): D+2
10 (chartreuse): D+9
11 (aquamarine): D+13
12 (cyan): R+4
13 (dark salmon): 46% White, 48.8% Black; D+23
14 (olive): 43.2% White, 45.4% Black; D+24

[muon2]

Michigan fair map

1 (blue): R+1
2 (green): EVEN
3 (purple): R+4
4 (red): D+3
5 (gray) D+9
6 (gold): R+8
7 (teal): D+1
8 (slate blue): D+5
9 (pink): D+2
10 (chartreuse): D+9
11 (aquamarine): D+13
12 (cyan): R+4
13 (dark salmon): 46% White, 48.8% Black; D+23
14 (olive): 43.2% White, 45.4% Black; D+24

That's more like it. Would you like it scored with the other MI maps we all posted a few years ago?

[President Punxsutawney Phil]

Michigan fair map

1 (blue): R+1
2 (green): EVEN
3 (purple): R+4
4 (red): D+3
5 (gray) D+9
6 (gold): R+8
7 (teal): D+1
8 (slate blue): D+5
9 (pink): D+2
10 (chartreuse): D+9
11 (aquamarine): D+13
12 (cyan): R+4
13 (dark salmon): 46% White, 48.8% Black; D+23
14 (olive): 43.2% White, 45.4% Black; D+24

That's more like it. Would you like it scored with the other MI maps we all posted a few years ago?

Sure.
Funnily enough my FL map also counts as a fair map in the sense it reflects the state's partisan balance (median seat is R+1. 3) and has a good amount of swing districts, though it was drawn as a Democratic gerrymander.

[President Punxsutawney Phil]

Ohio fair map

1 (blue): D+2
2 (green): R+19
3 (purple): D+12
4 (red): R+16
5 (gold): D+5
6 (teal): R+6
7 (gray): R+5
8 (white): R+16
9 (cyan): EVEN
10 (pink): R+2
11 (black): 50.5% White, 44% Black; D+23
12 (cornflower blue): R+7
13 (dark salmon): D+4
14 (olive): D+4
15 (dark orange): R+9
16 (khaki): D+4
The median seats, the 9th and the 10th, average out to be R+1, right in line with the state.

[muon2]

Michigan fair map

1 (blue): R+1
2 (green): EVEN
3 (purple): R+4
4 (red): D+3
5 (gray) D+9
6 (gold): R+8
7 (teal): D+1
8 (slate blue): D+5
9 (pink): D+2
10 (chartreuse): D+9
11 (aquamarine): D+13
12 (cyan): R+4
13 (dark salmon): 46% White, 48.8% Black; D+23
14 (olive): 43.2% White, 45.4% Black; D+24

That's more like it. Would you like it scored with the other MI maps we all posted a few years ago?

Sure.

In order to score your map, I need to recreate it to measure the chops. The scoring rules treat chops more harshly if they exceed 5% of the population of a CD. Some of your county chops look like they slice through townships and cities (which are equivalent to townships in MI). We also treated maps more harshly if they split multiple townships and cities in a single county.

Do you have the population deviations for each CD? That would tell me if I've recreated it correctly.

[President Punxsutawney Phil]

Michigan fair map

1 (blue): R+1
2 (green): EVEN
3 (purple): R+4
4 (red): D+3
5 (gray) D+9
6 (gold): R+8
7 (teal): D+1
8 (slate blue): D+5
9 (pink): D+2
10 (chartreuse): D+9
11 (aquamarine): D+13
12 (cyan): R+4
13 (dark salmon): 46% White, 48.8% Black; D+23
14 (olive): 43.2% White, 45.4% Black; D+24

That's more like it. Would you like it scored with the other MI maps we all posted a few years ago?

Sure.

In order to score your map, I need to recreate it to measure the chops. The scoring rules treat chops more harshly if they exceed 5% of the population of a CD. Some of your county chops look like they slice through townships and cities (which are equivalent to townships in MI). We also treated maps more harshly if they split multiple townships and cities in a single county.

Do you have the population deviations for each CD? That would tell me if I've recreated it correctly.

I don't, but I could (a) email you the drf files or (b) load them later and tell you the deviations.
Which do you prefer?

[muon2]

Michigan fair map

1 (blue): R+1
2 (green): EVEN
3 (purple): R+4
4 (red): D+3
5 (gray) D+9
6 (gold): R+8
7 (teal): D+1
8 (slate blue): D+5
9 (pink): D+2
10 (chartreuse): D+9
11 (aquamarine): D+13
12 (cyan): R+4
13 (dark salmon): 46% White, 48.8% Black; D+23
14 (olive): 43.2% White, 45.4% Black; D+24

That's more like it. Would you like it scored with the other MI maps we all posted a few years ago?

Sure.

In order to score your map, I need to recreate it to measure the chops. The scoring rules treat chops more harshly if they exceed 5% of the population of a CD. Some of your county chops look like they slice through townships and cities (which are equivalent to townships in MI). We also treated maps more harshly if they split multiple townships and cities in a single county.

Do you have the population deviations for each CD? That would tell me if I've recreated it correctly.

I don't, but I could (a) email you the drf files or (b) load them later and tell you the deviations.
Which do you prefer?

You can load them later. However, I can tell your score will suffer from the large number of township/city chops - particularly in the large counties. Townships and cities are subunits, and once more than 5% of a county is chopped into other CDs then each subunit chop counts against the score, just like a county chop. You may want to make some edits first to fix some of the more obvious subunit chops.

Here's the thread with the other scored MI maps.

[President Punxsutawney Phil]

Michigan fair map

1 (blue): R+1
2 (green): EVEN
3 (purple): R+4
4 (red): D+3
5 (gray) D+9
6 (gold): R+8
7 (teal): D+1
8 (slate blue): D+5
9 (pink): D+2
10 (chartreuse): D+9
11 (aquamarine): D+13
12 (cyan): R+4
13 (dark salmon): 46% White, 48.8% Black; D+23
14 (olive): 43.2% White, 45.4% Black; D+24

That's more like it. Would you like it scored with the other MI maps we all posted a few years ago?

Sure.

In order to score your map, I need to recreate it to measure the chops. The scoring rules treat chops more harshly if they exceed 5% of the population of a CD. Some of your county chops look like they slice through townships and cities (which are equivalent to townships in MI). We also treated maps more harshly if they split multiple townships and cities in a single county.

Do you have the population deviations for each CD? That would tell me if I've recreated it correctly.

I don't, but I could (a) email you the drf files or (b) load them later and tell you the deviations.
Which do you prefer?

You can load them later. However, I can tell your score will suffer from the large number of township/city chops - particularly in the large counties. Townships and cities are subunits, and once more than 5% of a county is chopped into other CDs then each subunit chop counts against the score, just like a county chop. You may want to make some edits first to fix some of the more obvious subunit chops.

Here's the thread with the other scored MI maps.

Well the reason you might see some townships chopped is because I was looking at DRA's municipal lines tool very closely to avoid municipal splits.
Does one take precedence over the other?

[muon2]

Well the reason you might see some townships chopped is because I was looking at DRA's municipal lines tool very closely to avoid municipal splits.
Does one take precedence over the other?

DRA shows lines for Census places. Those include cities which are equivalent to townships, and villages which are subsidiary to townships. There is a nice map on the thread I linked that show the county subunits for Wayne, Oakland and Macomb counties.

On DRA you can tell what are subunits by the voting district (precinct) number.  In MI the first three digits are the county number. The next four digits are the county subunit, either township or city. The remaining digits identify the voting district in that subunit.

[President Punxsutawney Phil]

Well the reason you might see some townships chopped is because I was looking at DRA's municipal lines tool very closely to avoid municipal splits.
Does one take precedence over the other?

DRA shows lines for Census places. Those include cities which are equivalent to townships, and villages which are subsidiary to townships. There is a nice map on the thread I linked that show the county subunits for Wayne, Oakland and Macomb counties.

On DRA you can tell what are subunits by the voting district (precinct) number.  In MI the first three digits are the county number. The next four digits are the county subunit, either township or city. The remaining digits identify the voting district in that subunit.

Wait so that is what they truly mean by 'city and town lines'?

[muon2]

Well the reason you might see some townships chopped is because I was looking at DRA's municipal lines tool very closely to avoid municipal splits.
Does one take precedence over the other?

DRA shows lines for Census places. Those include cities which are equivalent to townships, and villages which are subsidiary to townships. There is a nice map on the thread I linked that show the county subunits for Wayne, Oakland and Macomb counties.

On DRA you can tell what are subunits by the voting district (precinct) number.  In MI the first three digits are the county number. The next four digits are the county subunit, either township or city. The remaining digits identify the voting district in that subunit.

Wait so that is what they truly mean by 'city and town lines'?

Yes. In MI some are county subdivisions and others are just Census places that don't count as separate county subdivisions. Each state is different based on their own laws. DRA just loaded the place shapes for all states and didn't distinguish between types of municipalities. Wikipedia is usually accurate about which munis fall into which category. If you use Wikipedia as a reference for MI, it's townships and cities that matter for the chop count.

[President Punxsutawney Phil]

Well the reason you might see some townships chopped is because I was looking at DRA's municipal lines tool very closely to avoid municipal splits.
Does one take precedence over the other?

DRA shows lines for Census places. Those include cities which are equivalent to townships, and villages which are subsidiary to townships. There is a nice map on the thread I linked that show the county subunits for Wayne, Oakland and Macomb counties.

On DRA you can tell what are subunits by the voting district (precinct) number.  In MI the first three digits are the county number. The next four digits are the county subunit, either township or city. The remaining digits identify the voting district in that subunit.

Wait so that is what they truly mean by 'city and town lines'?

Yes. In MI some are county subdivisions and others are just Census places that don't count as separate county subdivisions. Each state is different based on their own laws. DRA just loaded the place shapes for all states and didn't distinguish between types of municipalities. Wikipedia is usually accurate about which munis fall into which category. If you use Wikipedia as a reference for MI, it's townships and cities that matter for the chop count.

Any chops you see as being particularly easy to fix?

[President Punxsutawney Phil]

[muon2]

Thanks, much nicer.

To give you a sense of the scoring and some changes you might consider, I'm just going to describe your CD 4. It is involved with 5 county chops: Eaton, Ingham, Isabella, Montcalm, and Saginaw. The Eaton and Saginaw chops each exceed 5% of a CD so they are macrochops. That means the disposition and boundaries of the individual subunits in those counties matter. This has the practical effect of treating them like the urban areas around Detroit and increases the erosity score that describes the shape of the district. Let me talk about each of the chops separately.

The Eaton and Ingham chops are what we call a "traveling chop". That means the same two districts chop more than one county. The rules can score it, but it's actually illegal under MI law, and can't be used unless required by federal law. There is an easy fix: put all of Ingham in CD 4, and shift the city of Eaton Rapids and the township immediately north to CD 4, too. Then shift Grand Ledge and the township around it out of CD 4. The traveling chop is gone and the total number of chopped counties drops to 4.

Isabella is a nice straight, simple chop. The chop intercepts the state highway connections from Mt Pleasant (county seat) to the county seats of both Midland and Gratiot, so it actually improves the erosity score. Well designed chops should do that.

Montcalm is a chop that creates two pieces. This tends to increase erosity, since each piece has a separate connection. A better design would chop out of CD-4 the 4 southernmost townships of Montcalm as well as the two western townships immediately north of those four. That arrangement serves to reduce the overall erosity.

Saginaw is another macrochop that will increase erosity by it's nature. There is also in CD 4 a precinct of a township west of Saginaw city that was chopped, and that increases the chop score by 1. Better is to leave that precinct out of CD 4 but use the township kitty-corner to the NW corner of Genesee instead.

See what you think of that, and if you want to make any of the changes I suggest. You may want to look at getting rid of those macrochopped counties, too.

[President Punxsutawney Phil]

Michigan (statewide): 56.9 Obama, 41.5 McCain; 47.5 Dem, 52.5 Rep. (Ave: 52.7 Dem)
1 (black): 53.8 Obama, 44.4 McCain; 50 Dem, 50 Rep. (Ave: 52.4)
2 (green): 56.7 Obama, 41.7 McCain; 45.6 Dem, 54.4 Rep. (Ave: 51.6)
3 (purple): 40.6 Obama, 57.7 McCain; 30.1 Dem, 69.9 Rep. (Ave: 36.2)
4 (red): 47.7 Obama, 50.5 McCain; 39.9 Dem, 60.1 Rep. (Ave: 44.2)
5 (gold): 58.5 Obama, 39.7 McCain; 50.1 Dem, 49.9 Rep. (Ave: 54.8 )
6 (teal): 53.7 Obama, 44.7 McCain; 44.6 Dem, 55.4 Rep. (Ave: 49.6)
7 (gray): 60.5 Obama, 37.9 McCain; 50.3 Dem, 49.7 Rep. (Ave: 55.9)
8 (slate blue): 57.6 Obama, 40.7 McCain; 48.4 Dem, 51.6 Rep. (Ave: 53.4)
9 (cyan): 70.2 White, 19.2 Black; 63.5 Obama, 35.2 McCain; 52.4 Dem, 47.6 Rep. (Ave: 58.4)
10 (pink): 55.3 Obama, 42.8 McCain; 48.6 Dem, 51.4 Rep. (Ave: 52.5)
11 (chartreuse): 50.9 White, 42.4 Black; 69.7 Obama, 29.2 McCain; 58.4 Dem, 41.6 Rep. (Ave: 64.4)
12 (cornflower blue): 59.8 Obama, 38.4 McCain; 51.7 Dem, 48.3 Rep. (Ave: 56.2)
13 (white): 43.8 Obama, 54.5 McCain; 34.2 Dem, 65.8 Rep. (Ave: 39.4)
14 (olive): 36.3 White, 52.6 Black; 80 Obama, 19 McCain; 70.5 Dem, 29.5 Rep. (Ave: 75.7)
Note: the (Ave:) is the two-party vote in 2008 averaged with the Dem/Rep numbers in DRA.

[muon2]

Population deviations would be helpful. Even better would be to turn on city and town lines for the Detroit area. In this case an enlargement of the Grand Rapids area with town lines would be helpful to assess the map.

[muon2]

The SW part of your most recent MI plan is looking much better. Here's some analysis and thoughts on scoring for the northern part of that same plan.



I've redrawn just the three northern CDs (1 black, 2 green, 4 red). There are three chops between them:  CDs 1 and 4 chop Gladwin, and CDs 2 and 4 chop Grand Traverse and Kent. Note that this is another traveling chop between CDs 2 and 4 even though the chops are quite separated.

The little white lines show links that are cut between units in the plan. These add up to measure ersoity. Mostly they are between counties that are connected by state highways (see the map in the previously linked thread) or between the parts of chopped counties in different districts. Kent is macrochopped, so the links are local connections between subunits within Kent. There are 11 cut links between CDs 1 and 4, and 11 cut links between CDs 2 and 4, for a total erosity of 22.



I've redivided the same northern area to show how the scores could be reduced. CD 1 is whole counties and there is only one chop between CDs 2 and 4 in Montcalm. In addition the Grand Rapids UCC (Kent + Ottawa) is down to the minimum number of CDs. So this plan has an overall reduction of the CHOP score by 3.

There are now 3 cut links between CDs 1 and 2, 7 cut links between CDs 1 and 4, and 5 cut links between CD 2 and 4. This makes the erosity from those district boundaries equal to 15, so it reduces the EROSITY score by 7.

[President Punxsutawney Phil]