New England redistricting using towns and NECTAs.

[muon2]

Counties don't have the same importance as CoIs in New England as they do elsewhere in the US. Cities and towns take center stage in the New England state. They are more numerous and generally less populated than counties, and if they are the fundamental unit of redistricting in those states, they don't place a lot of constraints on the maps. It's easy to get districts within 0.5% yet gerrymander to accomplish other desires.

If I assume that towns are the fundamental unit to keep whole then other rules would necessarily change. For example, not all towns have state highways through them so connections would be based on any path of local roads that go from one town center to another without passing through any other town. Erosity would be based on how many connections are cut by the line between districts.

UCCs are a construct made of multiple whole counties that reflect a CoI based on an urbanized area within a MSA. Without counties as units for mapping, UCCs don't work as well. However, the Census defines New England City and Town Areas (NECTAs) made of multiple whole towns that coincide with urban areas in a fashion similar to MSAs and counties. NECTAs seem like a natural place to look for CoIs that should be kept intact by redistricting, and splitting NECTAs would count as a chop. Some NECTAs are very large and the Census defines NECTA divisions that might be better than NECTAs in those areas.

Here's an example of the NECTAs for NH placed on a map of the towns. Each color represents a separate NECTA division. The red, orange, and yellow areas are part of the Boston NECTA, but are separate divisions.

[muon2]

As an example of the application of NECTAs and erosity to NH consider these two plans.

Plan A has no NECTA chops. Towns outside NECTAs were adjusted so that each district varies only 8 persons from the population quota (range = 16). The erosity based on cut connections between towns is 35. To eliminate this plan another plan with no NECTA chops and lower erosity or population range would need to be presented.



Plan B reduces erosity by introducing a chop of the Manchester NECTA separating 3 towns. The erosity is brought down to 33 and both districts are exactly at the population quota of 658,235 (range = 0). This plan can coexist with plan A, since A has fewer chops while B is better on erosity and inequality.

[Sol]

What about this?

[muon2]

What about this?

I count an erosity of 30, so that's better from erosity. The question would be how much can lower erosity justify larger population deviations. If there is no limit with these small deviations then yours should be the better plan. If points are assigned to the range, then the tradeoff can be quantified.

[muon2]

To make a more careful count of erosity I put together a map of the connections between the towns. I didn't map all the way through Coos county since that involves dealing with a lot of unorganized townships.



To use this map to find erosity, draw the district boundary line on the map and count the number of links between towns that are cut by the boundary. It also can be used to establish connectivity, and for example my plan A fails that test since Brookfield is not connected to the rest of CD 2; it's only contiguous across a mountain. My plan B with one NECTA chop now calculates to an erosity of 34, and one can see that separating the Portsmouth and Haverhill NECTAs costs a lot in erosity due to the rich connectivity there. Sol's plan recalculates to a 31 erosity using the savings from the short boundary between the Nashua and Haverill NECTA divisions within the Boston NECTA.

Sol's plan has a significantly higher deviation than my plan B, so one might want to know how the deviation compares to erosity. Some time ago I derived an exponential relationship between the likely lowest deviation and number of units (towns in New England) available. Using national averages for counties and districts one can create a score for the inequality based on the average deviation when none of the units is chopped.

Average Deviation	Inequality Score
less than 1	0
1 - 1.6	1
1.6 - 2.5	2
2.5 - 4.0	3
4.0 - 6.3	4
6.3 - 10	5
11 - 16	6
17 - 25	7
26 - 40	8
41 - 63	9
64 - 100	10
101 - 160	11
161 - 250	12
251 - 400	13
401 - 630	14
631 - 1000	15
1001 - 1600	16
1601 - 2500	17
2501 - 4000	18
4001 - 6300	19
6301 - 10000	20

Using this table, my plan B has an inequality of 5 while Sol's plan has an inequality of 11. Sol's plan gives up 6 points of inequality to get 3 points of erosity and avoid a NECTA chop. A local redistricting board could decide if that was a reasonable tradeoff.

[muon2]

I liked Sol's idea of splitting the Boston NECTA into its divisions and using that to reduce erosity. However, his deviation seemed larger than necessary, so with some minor adjustments I produced this similar looking plan C.



The deviation is 8 (inequality score 5) and the erosity is down to 29. This plan would beat both my plan B and Sol's plan since it improves the erosity over both and is no worse than my inequlity. I could push the erosity lower (27) with a slight increase in deviation (inequality 9) by swapping the Cheshire towns for Barnstead and Gilmanton (C'), and that plan could then be coequal with my plan C since one would be better in erosity and the other in inequality.

However, as I looked at Sol's plan (or my plan C), it seemed like the way CD 1 wraps around CD 2 created excess erosity. To fix that, I swapped the Keene NECTA for Concord, and adjusted towns to make this plan D.



The deviation is only 1 (inequality 1) and the erosity is down to 24. It would replace my plan C (or C') with better scores in both inequality and erosity. The only plans that could compete would need either perfect equality or lower erosity. My plan B earlier is an example of perfect equality though it has one NECTA chop and much larger erosity, and a local board could then decide if that was worth the trade off.

[muon2]

Here's a look at RI. There are 39 municipalities (towns) and county government doesn't exist in RI. NECTAs don't help here since every town but three are in the Providence NECTA. Hopkinton and Westerly are in the New London NECTA, and New Shoreham is not in a NECTA.

Connections are defined by a path on public roads between two towns that don't pass between any other town. Regular year-round ferry service can also be used to establish a connection and that is used for Block Island (New Shoreham town).



If connections are maintained and the population deviation is minimized I get this plan with near equality. It has an average deviation of 2.5 for an inequality score of 2, and the erosity is 18.

[muon2]

I can also try to minimize erosity for the RI CDs. This plan gets down to an erosity of 7. The average deviation is 466.5 for an inequality of 14.



If I allow the erosity to go up to 8, I can drop the average deviation to 124.5 for an inequality of 11. This is a better total inequality plus erosity than either of the other plans, but all are Pareto optimal since one number can't be made better without the other getting worse.

[muon2]

CT provides some new challenges to the use of NECTAs. There are no counties in CT, so one really should base this on NECTAs instead of UCCs. Within the state two NECTAs (Bridgeport and Hartford) are larger than a CD so they have to be chopped at least once each. The New Haven NECTA is 0.842 of a CD, and attaching it to any of the neighboring NECTAs causes there to be at least one additional chop.

Here's the town map.



For comparison I'll start with Sol's recent offering. It's very compact, but it chops Bridgeport between 3 CDs, New Haven in 2, Waterbury in 2, Hartford in 3, and Springfield in 2. That's a total of 12 chops. The average deviation is 446.8, which translates to an inequality of 14. I'll try to get a connection map soon to calculate erosity. In the meantime, how well can one draw the CDs while minimizing NECTA chops and maintaining compactness?

Massachusetts is a pain, so I'm skipping it for now and moving onto Connecticut. I actually think UCCs work well for CT (and I had them in mind when I did this) so I've made the decision to avoid NECTAs here.

[Sol]

With some initial experimentation, I think eight is the minimum number of chops.

[traininthedistance]

For comparison I'll start with Sol's recent offering. It's very compact, but it chops Bridgeport between 3 CDs, New Haven in 2, Waterbury in 2, Hartford in 3, and Springfield in 2. That's a total of 12 chops. The average deviation is 446.8, which translates to an inequality of 14. I'll try to get a connection map soon to calculate erosity. In the meantime, how well can one draw the CDs while minimizing NECTA chops and maintaining compactness?

It just occurred to me that you're basically de facto double-counting the first chop in any region, by this accounting.  There are three districts in the Bridgeport NECTA, but wouldn't that only be two chops?  If I'm reading your count right, it seems that a map that triple-chopped one region would score better than one which double-chopped two regions, despite the fact that in both cases there are two intrusions on regional boundaries.  I suppose it's possible that this choice is deliberate, but I can't recall where exactly the case for that was made.  (Which I guess might be on me, since I did check out of these discussions for a while.)

Anyway, here is a plan that, I'm pretty sure no matter how you count, is chop-minimizing with regards to NECTAs:



The Bridgeport NECTA is split between 4 (which is all-Bridgeport) and 5; Hartford is split between 1 (which is all-Hartford), 2, 3, and 5.  It is not strictly better than Sol's plan, however, since the average deviation is 448.4, just barely higher (thanks to constraints in Fairfield County), and while most districts are very compact... 2 is not.

...

EDIT: I lied, by fiddling with the boundary between 4 and 5 within the Bridgeport NECTA I was able to get inequality to plummet.  Average deviation is now only 223.2.  The cost is, I would assume, slightly higher erosity for 4, but I think this revised map now leads on two of the three factors.

[muon2]

train - you are right about my chop count. I inadvertently fell back on our old measure. Sol's map should count 7 chops. Your plans have chop counts of 4 by the proper method.

Edit: and since two are required by the NECTA sizes a count of 4 chops equates to 2 chop points.

[Sol]

For comparison I'll start with Sol's recent offering. It's very compact, but it chops Bridgeport between 3 CDs, New Haven in 2, Waterbury in 2, Hartford in 3, and Springfield in 2. That's a total of 12 chops. The average deviation is 446.8, which translates to an inequality of 14. I'll try to get a connection map soon to calculate erosity. In the meantime, how well can one draw the CDs while minimizing NECTA chops and maintaining compactness?

It just occurred to me that you're basically de facto double-counting the first chop in any region, by this accounting.  There are three districts in the Bridgeport NECTA, but wouldn't that only be two chops?  If I'm reading your count right, it seems that a map that triple-chopped one region would score better than one which double-chopped two regions, despite the fact that in both cases there are two intrusions on regional boundaries.  I suppose it's possible that this choice is deliberate, but I can't recall where exactly the case for that was made.  (Which I guess might be on me, since I did check out of these discussions for a while.)

Anyway, here is a plan that, I'm pretty sure no matter how you count, is chop-minimizing with regards to NECTAs:



The Bridgeport NECTA is split between 4 (which is all-Bridgeport) and 5; Hartford is split between 1 (which is all-Hartford), 2, 3, and 5.  It is not strictly better than Sol's plan, however, since the average deviation is 448.4, just barely higher (thanks to constraints in Fairfield County), and while most districts are very compact... 2 is not.

...

EDIT: I lied, by fiddling with the boundary between 4 and 5 within the Bridgeport NECTA I was able to get inequality to plummet.  Average deviation is now only 223.2.  The cost is, I would assume, slightly higher erosity for 4, but I think this revised map now leads on two of the three factors.

I like that a lot, Train!

[muon2]

I took me a while since my ISP was down yesterday, but here is the local connection map for CT. Connections are established between towns when it is possible to go from one town hall to another by all season roads without crossing into another town.



I can use this now to measure the erosity scores for the various submissions so far. Erosity measures the number of connections that are severed by the boundaries between CDs.

Sol's initial map has an inequality of 14, chop excess of 5 and erosity of 55. It is quite compact.

train's first map also has an inequality of 14, but a chop excess of 2 and erosity of 60. It gives up a little erosity to avoid a number of chops.

train's second map does indeed increase erosity to reduce inequality. It has an inequality of 12, still just 2 excess chops (which may well be unavoidable), and an erosity of 64.

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For fun I tried to move the inequality even further down while I was waiting for my ISP to recover. I was able to produce this map with some strange combinations such as Hartford with New London. There is one extra chop of the Hartford NECTA and a chop of Bridgeport and the average inequality is 73.6 (CD 3 is only 1 person from its quota). The inequality is 10, chops are 2 and the erosity has jumped to 73.



If I totally ignore NECTAs and erosity I am able to get down to an average deviation of 3.2 (deviations are +1, +8, 0, -5, -2). NECTAs and erosity certainly help constrain some of the options.

[muon2]

I've modified the train 1 plan to produce a couple options with lower erosity, and I worked on my low inequality plan to get a version lower still. This gives me 6 plans that all have 2 chops over the minimum. I'll put then in order of increasing erosity.

muon2 A: range 0.96%, average deviation 1920.4. Score Inequality 17, Chops 2, Erosity 49.


muon2 B: range 0.30%, average deviation 757.6. Score I 15, C 2, E 52.


train 1: range 0.22%, average deviation 404.8(there appears to be a tiny precinct with 109 people placed in 4 instead of 5, which I have corrected in the numbers here). Score I 14, C 2, E 60.


train 2: range 0.13%, average deviation 266.8 (same correction here). Score I 13, C 2, E 64.


muon2 C: range 0.03%, average deviation 74.6. Score I 10, C 2, E 73.


muon2 D: range 0.02%, average deviation 54.4. Score I 9, C 2, E 75.


All these plans are Pareto equivalent. Should any be discarded from consideration, and why? Is there an obvious favorite, and if so why?

[muon2]

One observation from the set of maps above is that the lowest erosity plans all involved putting both extra chops on the Hartford NECTA. To get a significantly lower inequality I had to move one of those two chops to another NECTA and I put it on the New Haven NECTA. That cost a lot of erosity.

As a second attempt I tried to place the second extra chop on the Bridgeport NECTA to see if that could also give lower inequalities. I found that it did, and with less increase in erosity than I had with the New Haven chop.

This plan has a range of 0.14%, average deviation 234.4, and scores I 12, C 2, E 62. This would knock out train 2 from the Pareto competition since it improves both I and E while leaving C the same. I'll call it my new muon2 C.


Much as train did between his two maps I found that swaps between CDs 4 and 5 could lower the inequality and at the expense of some erosity. This plan has a range of 0.03%, average deviation 54.4, and scores I 9, C 2, E 66. It knocks out both my previous plans C and D and I'll call this my new plan D.

[muon2]

I found that I had left off the Worcester NECTA in CT, so I've fixed that in the post above. I caught the problem while working on MA, which is done now. Here's the NECTA map for MA.



I kept the NECTA divisions within the Boston NECTA in separate colors (dark red and pink), so that they could be kept intact as in NH. However, it doesn't make sense to consider the large irregular red area that is the Boston division as a unique area. I would suggest that the full Boston NECTA should be covered by no more than seven CDs (of nine), and each division, except for Boston should be maintained in one CD to the extent possible to avoid a chop. Normal rules apply to the other NECTAs.

To measure erosity I've put together a map showing the towns that are locally connected as well as a magnified view of the Boston area. The green lines show all-year ferry service that can be used to establish a connection, though I don't know that cutting them should count towards erosity.

[muon2]

MA poses some challenges for NECTA-based map drawing. As I noted before the Boston NECTA has embedded in it eight separate NECTA divisions, but the majority of the NECTA is not in a division. Ideally, each NECTA division would be kept intact as we did in NH. To deal with the Boston NECTA the goal would be to cover it with as few CDs as possible. The Boston NECTA makes up 5.9 CDs so theoretically could be covered by six CDs, but since it cuts off the western area from SE MA, there have to be at least seven CDs to cover the Boston NECTA. Since SE MA is under one NECTA, it has to join with Boston and a little from Western MA to get to seven CDs.

The Springfield and Worcester NECTAs both just under one CD, but no combination with adjoining smaller NECTAs works for them either to make a whole CD. There needs to be at least two chops of western NECTAs to avoid an eighth CD going into the Boston NECTA. Such an extra chop of Boston also would likely cause a chop of one of the NECTA divisions.

For connections, I count the year-round ferries as shown in my previous post, but I don't count them towards erosity.

My plan A started by keeping all the CDs under 1000 deviation. The result is a plan with an av dev of 318 which is an inequality score of 13. The erosity is 140 and is most impacted by the boundary between CD 1 and 2 (erosity 18) and the total boundary of CD 8 (erosity 57). Here is the state map and the central Boston area map.




Plan B was created to reduce erosity while letting the deviations rise slightly. I left CD 6 and 7 the same here but there a much larger chop into the Springfield NECTA to get a better boundary for CD 1. The maximum deviation is 2010 as opposed to 665 in plan A. This plan has an av dev of 990 which is an inequality score of 15. The erosity dropped to 114, with the CD 1 boundary down to 10 and CD 8 boundary down to 31.

[Sol]

Those maps look very reasonable, IMO. I prefer option 1 very strongly- a CD-4 on the latter map is quite ugly.

What do the racial stats on CD-7 look like?

[muon2]

Those maps look very reasonable, IMO. I prefer option 1 very strongly- a CD-4 on the latter map is quite ugly.

What do the racial stats on CD-7 look like?

CD-7 (VAP): W-55.7, B-18.1, H-13.4, A-9.4, N-0.2, O-3.3.

Your strong preference for plan A is interesting. I suspect that in MA they would rather link the eastern suburbs of Worcester to Fall River (B) than to Quincy (A). The plan A CD-8 is quite a bit worse than the plan B CD-4 by many measures so that's a key trade off between the two plans. Another alternative is to place Quincy with Cape Cod in CD-9 and put Fall River and New Bedford together, but that requires a chop of the Brockton subdivision.

[Sol]

The weird link from Worcester to Fall River is probably a matter of tradition rather than sense.

Anyway, I like the first map more also because the 8th appears to be a MetroWest district, which I get the sense is a good CoI. Also, I believe Boston is beginning to sprawl into the Worcester area, so that makes sense.

Putting Quincy in with the 9th sounds good, even if it does screw up Brockton.

Perhaps the best way to elucidate it would be to poll Massachusetts Atlasians who have been less involved with this NECTA/UCC discussion and see which they prefer.

[Sol]

Is there an equivalent of UCCs for NECTAs?