Chops and Erosity - Great Lakes Style

[Torie]

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:



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.  

EROSITY: 113 (includes Lansing UCC not acting as a supercounty for erosity)

I guess if I do what Train did within the Detroit UCC (which really has a lot to commend it I must admit, assuming the drop from 48.5% BVAP in my map (which could get to 50% with a hood chop in Detroit) to the 47% in his is not the difference between the map being legal versus illegal), but not otherwise (so my erosity score would not change much), my map with the GR "fix," has one more chop than this map, 7 rather than 6 (excluding the necessary Wayne County chops). This is a lot of additional erosity to save one chop (the gain being in Train's map the elimination of the Lansing area chop).

[traininthedistance]

I guess if I do what Train did within the Detroit UCC (which really has a lot to commend it I must admit, assuming the drop from 48.5% BVAP in my map (which could get to 50% with a hood chop in Detroit) to the 47% in his is not the difference between the map being legal versus illegal), but not otherwise (so my erosity score would not change much), my map with the GR "fix," has one more chop than this map, 7 rather than 6 (excluding the necessary Wayne County chops). This is a lot of additional erosity to save one chop (the gain being in Train's map the elimination of the Lansing area chop).

I lifted that Detroit configuration from muon's latest (Oakland is a tiny bit different, but the general idea is the same); credit should go to him.  Of course, it's an open question as to whether it would fly.

In general, the lines in the big three counties and elsewhere are pretty much just separate issues that don't impact each other much.  You see a similar thing in Ohio, where "how much to pack the Cleveland district" is an easily separable question from the rest of the map.

[Sol]

Isn't it a VRA violation to not put Southfield in a Black district? Either way, I suspect not doing so would be unpopular, even if not illegal.

[muon2]

Isn't it a VRA violation to not put Southfield in a Black district? Either way, I suspect not doing so would be unpopular, even if not illegal.

No, since the only violation can occur if the black population of the area is unable to elect the candidates of their choice. That analysis must be viewed in the context of the whole state, so if there are a reasonable number of districts where the black minority would be able to elect the candidates of choice, it doesn't matter that certain black populations are excluded from those districts.

As a practical matter, that was done in certain legislative districts in IL in 2011. Politically some black communities were shifted to white districts to make them safer for Dems. Major groups representing black issues supported the Dem plan, since politically the Dems would align with their issues, and the number of districts that would elect the candidate of choice of the blacks was not impacted.

=====

This does raise an interesting thought. In our work on southern states we identified counties that had significant black populations, and like the UCCs, thought that they should be grouped together and covered with the minimum number of districts to preserve their voting strength. In principle one could go though the same exercise with county subunits in Wayne and Oakland and recognize those areas as a unique community of interest.

[muon2]

train made an observation that high erosity in urban areas went along with areas with many small munis. I've been updating and making more accurate my Detroit area muni map, with connections. What I see is that the areas with a lot of links that could contribute to erosity are also those areas with a number of subunits with small population, which can often be used to get populations within limits or otherwise reduce inequality. Effectively the higher erosity in that area acts as a tradeoff with lower inequality and seems consistent with the Pareto principle between those measures.

This is the updated map with connections (after a few hours with some mapping software). I've added the Detroit neighborhood boundaries. The blue lines are local connections within counties. Roads on the border count in both munis for connections. The red lines are highway connections across the county lines. Numbered highways on the county border may be used, but cannot be exclusively used to cross the line. That is there must be state highway entirely on each side to make a connection. Otherwise all the munis along the northern border of Wayne would count a connection by touching 8 Mile Rd (MI 102).

[traininthedistance]

Isn't it a VRA violation to not put Southfield in a Black district? Either way, I suspect not doing so would be unpopular, even if not illegal.

Considerations like that are a major reason why the VRA– as currently put into practice– effectively enshrines Republican gerrymanders in urban areas.  One can speculate that this effect is part and parcel of its enduring popularity.

This is not to say that the VRA is bad law on the whole.  The "candidate of choice" test still has bite in polarized rural areas like South Texas and the Black Belt, and the protections against de facto discriminatory measures like Voter ID laws are still very important in this day and age.  But its effect on metro area lines has, shall we say, been less salutary than intended.

[traininthedistance]

train made an observation that high erosity in urban areas went along with areas with many small munis. I've been updating and making more accurate my Detroit area muni map, with connections. What I see is that the areas with a lot of links that could contribute to erosity are also those areas with a number of subunits with small population, which can often be used to get populations within limits or otherwise reduce inequality. Effectively the higher erosity in that area acts as a tradeoff with lower inequality and seems consistent with the Pareto principle between those measures.

Yes, but that only actually has an effect on scoring if the most unequal districts happen to be in those metro areas.  If you have a more rural whole-county district which is leading the inequality derby, the tradeoff in places like Oakland and Wayne and Allegheny is rendered irrelevant, which seems wrong.

Another reason to measure inequality by average rather than simply range, perhaps?

[Torie]

train made an observation that high erosity in urban areas went along with areas with many small munis. I've been updating and making more accurate my Detroit area muni map, with connections. What I see is that the areas with a lot of links that could contribute to erosity are also those areas with a number of subunits with small population, which can often be used to get populations within limits or otherwise reduce inequality. Effectively the higher erosity in that area acts as a tradeoff with lower inequality and seems consistent with the Pareto principle between those measures.

Except that if the small subunits are all in a row for example, next to a big subunit, it's not clear to me at all just why chopping between the little units and big unit, in a nice straight line, is really erosity at all. Conversely, chopping between two densely populated subunits of some size, no matter how jagged the line between them, is anti-erosity heaven. It really makes no sense objectively. But maybe that is unavoidable. Hopefully in general, the overall metric, tends to push for straight lines, rather than jagged ones, more often than not, and the size of the subunits per se, will not distort matters too much.

[Torie]

Isn't it a VRA violation to not put Southfield in a Black district? Either way, I suspect not doing so would be unpopular, even if not illegal.

Considerations like that are a major reason why the VRA– as currently put into practice– effectively enshrines Republican gerrymanders in urban areas.  One can speculate that this effect is part and parcel of its enduring popularity.

This is not to say that the VRA is bad law on the whole.  The "candidate of choice" test still has bite in polarized rural areas like South Texas and the Black Belt, and the protections against de facto discriminatory measures like Voter ID laws are still very important in this day and age.  But its effect on metro area lines has, shall we say, been less salutary than intended.

The VRA hurts Pubs in CA. The VRA is good for Pubs if involving blacks, bad in general if involving Hispanics. As black populations in most places slowly disperse outside the South, and erode to the point of no longer triggering the VRA in specific locations, the VRA as it pertains to blacks, will slowly fade away. In CA, the VRA these days, really protects not one black CD from evisceration, save perhaps but one. In NYC, it's down to 2. After the next census, I suspect the VRA will not protect a black CD in Ohio.

[traininthedistance]

train made an observation that high erosity in urban areas went along with areas with many small munis. I've been updating and making more accurate my Detroit area muni map, with connections. What I see is that the areas with a lot of links that could contribute to erosity are also those areas with a number of subunits with small population, which can often be used to get populations within limits or otherwise reduce inequality. Effectively the higher erosity in that area acts as a tradeoff with lower inequality and seems consistent with the Pareto principle between those measures.

Except that if the small subunits are all in a row for example, next to a big subunit, it's not clear to me at all just why chopping between the little units and big unit, in a nice straight line, is really erosity at all. Conversely, chopping between two densely populated subunits of some size, no matter how jagged the line between them, is anti-erosity heaven. It really makes no sense objectively. But maybe that is unavoidable. Hopefully in general, the overall metric, tends to push for straight lines, rather than jagged ones, more often than not, and the size of the subunits per se, will not distort matters too much.

Yes, agreed.  Though of course remember that not all jagged lines are the same: river boundaries are just as good as the surveyor's straightedge, while the fractal insanity that is Columbus city limits is... not.

It's a hard question and no solution is going to get every single case perfectly right.  The highway cut system works perfectly for counties, which tend to all be of comparable size; it works less well when you're drawing around, say, Pittsburgh's city lines, where the sizes of the subunits are anything but comparable.  But I'd still take it over, say, splitline.

[traininthedistance]

Isn't it a VRA violation to not put Southfield in a Black district? Either way, I suspect not doing so would be unpopular, even if not illegal.

Considerations like that are a major reason why the VRA– as currently put into practice– effectively enshrines Republican gerrymanders in urban areas.  One can speculate that this effect is part and parcel of its enduring popularity.

This is not to say that the VRA is bad law on the whole.  The "candidate of choice" test still has bite in polarized rural areas like South Texas and the Black Belt, and the protections against de facto discriminatory measures like Voter ID laws are still very important in this day and age.  But its effect on metro area lines has, shall we say, been less salutary than intended.

The VRA hurts Pubs in CA. The VRA is good for Pubs if involving blacks, bad in general if involving Hispanics. As black populations in most places slowly disperse outside the South, and erode to the point of no longer triggering the VRA in specific locations, the VRA as it pertains to blacks, will slowly fade away. In CA, the VRA these days, really protects not one black CD from evisceration, save perhaps but one. In NYC, it's down to 2. After the next census, I suspect the VRA will not protect a black CD in Ohio.

NYC has three black districts, two in Brooklyn and one in Queens.  The VRA is in fact quite good to Pubs for the Queens district, as it provides a reason for that district to take Valley Stream and weaken NY-4, rather than just having it stop at the city line like it should.

[Torie]

Isn't it a VRA violation to not put Southfield in a Black district? Either way, I suspect not doing so would be unpopular, even if not illegal.

Considerations like that are a major reason why the VRA– as currently put into practice– effectively enshrines Republican gerrymanders in urban areas.  One can speculate that this effect is part and parcel of its enduring popularity.

This is not to say that the VRA is bad law on the whole.  The "candidate of choice" test still has bite in polarized rural areas like South Texas and the Black Belt, and the protections against de facto discriminatory measures like Voter ID laws are still very important in this day and age.  But its effect on metro area lines has, shall we say, been less salutary than intended.

The VRA hurts Pubs in CA. The VRA is good for Pubs if involving blacks, bad in general if involving Hispanics. As black populations in most places slowly disperse outside the South, and erode to the point of no longer triggering the VRA in specific locations, the VRA as it pertains to blacks, will slowly fade away. In CA, the VRA these days, really protects not one black CD from evisceration, save perhaps but one. In NYC, it's down to 2. After the next census, I suspect the VRA will not protect a black CD in Ohio.

NYC has three black districts, two in Brooklyn and one in Queens.  The VRA is in fact quite good to Pubs for the Queens district, as it provides a reason for that district to take Valley Stream and weaken NY-4, rather than just having it stop at the city line like it should.

I stand corrected, and you are right on all counts.

[muon2]

train made an observation that high erosity in urban areas went along with areas with many small munis. I've been updating and making more accurate my Detroit area muni map, with connections. What I see is that the areas with a lot of links that could contribute to erosity are also those areas with a number of subunits with small population, which can often be used to get populations within limits or otherwise reduce inequality. Effectively the higher erosity in that area acts as a tradeoff with lower inequality and seems consistent with the Pareto principle between those measures.

Yes, but that only actually has an effect on scoring if the most unequal districts happen to be in those metro areas.  If you have a more rural whole-county district which is leading the inequality derby, the tradeoff in places like Oakland and Wayne and Allegheny is rendered irrelevant, which seems wrong.

Another reason to measure inequality by average rather than simply range, perhaps?

I agree that it lends weight to measurement by average. I'd like to be sure one couldn't get away with one outlier district in population.

[Torie]

train made an observation that high erosity in urban areas went along with areas with many small munis. I've been updating and making more accurate my Detroit area muni map, with connections. What I see is that the areas with a lot of links that could contribute to erosity are also those areas with a number of subunits with small population, which can often be used to get populations within limits or otherwise reduce inequality. Effectively the higher erosity in that area acts as a tradeoff with lower inequality and seems consistent with the Pareto principle between those measures.

Yes, but that only actually has an effect on scoring if the most unequal districts happen to be in those metro areas.  If you have a more rural whole-county district which is leading the inequality derby, the tradeoff in places like Oakland and Wayne and Allegheny is rendered irrelevant, which seems wrong.

Another reason to measure inequality by average rather than simply range, perhaps?

I agree that it lends weight to measurement by average. I'd like to be sure one couldn't get away with one outlier district in population.

Except we are only talking about 3,500 people at most. The problem in not using averages, is that it gives no incentive to balance outside the outlier districts, where one can, without an offsetting disadvantage. The problem in using averages, is that it is not what the courts do, or given what the courts do, what politicians do, to please the courts. But if it's legal either way given some non self serving reason, the courts don't matter (bearing in mind, the only reason to have more inequality, in an objective system, is to get a better score due to other objective, good government, considerations (the courts will understand that, and frankly, tend to love that). I prefer averages, and if one outlier, with better averages or similar averages, avoids a chop or more erosity, I say go for it. In the end, it doesn't matter much either way. What Mike and I are wrestling about, matters a lot more - at least to me.

[traininthedistance]

train made an observation that high erosity in urban areas went along with areas with many small munis. I've been updating and making more accurate my Detroit area muni map, with connections. What I see is that the areas with a lot of links that could contribute to erosity are also those areas with a number of subunits with small population, which can often be used to get populations within limits or otherwise reduce inequality. Effectively the higher erosity in that area acts as a tradeoff with lower inequality and seems consistent with the Pareto principle between those measures.

Yes, but that only actually has an effect on scoring if the most unequal districts happen to be in those metro areas.  If you have a more rural whole-county district which is leading the inequality derby, the tradeoff in places like Oakland and Wayne and Allegheny is rendered irrelevant, which seems wrong.

Another reason to measure inequality by average rather than simply range, perhaps?

I agree that it lends weight to measurement by average. I'd like to be sure one couldn't get away with one outlier district in population.

The way to police outliers, then, is to keep the hard cap appropriately strict.  I think plus or minus 0.5%, as we've been using, is a good standard.  I wouldn't cry over something even a little tighter, but what we have now is probably ideal.

[traininthedistance]

A midnight snack for thought:

I'm taking a desultory spin at Florida, for God knows what reason, and... uh... I'm not sure that penalizing for UCC fans is much value added in this state.



That's a fan.  Pity.

(map is very much a work in progress)

[muon2]

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.

[muon2]

A midnight snack for thought:

I'm taking a desultory spin at Florida, for God knows what reason, and... uh... I'm not sure that penalizing for UCC fans is much value added in this state.



That's a fan.  Pity.

(map is very much a work in progress)

If there's interest in going outside the Great Lakes states with their well defined county subdivisions, I should open a new thread. I anticipate different issues in states like FL.

[traininthedistance]

A midnight snack for thought:

I'm taking a desultory spin at Florida, for God knows what reason, and... uh... I'm not sure that penalizing for UCC fans is much value added in this state.



That's a fan.  Pity.

(map is very much a work in progress)

If there's interest in going outside the Great Lakes states with their well defined county subdivisions, I should open a new thread. I anticipate different issues in states like FL.

This thread is getting pretty huge; that would be for the best.

This is not to say that we should necessarily get bogged down in those weeds right now, but it's a topic I'm sure we'll all want to discuss sooner or later.

[muon2]

Here's a test case to try to understand the role (or not) of microchops and their potential interaction with single and multi-county UCCs.

MI muon2 2015A


There are no chops except in the big three counties and Detroit neighborhoods are whole. There is an extra chop of the Detroit UCC, instead of in Lansing like with Torie's plans. There is also an extra chop in Oakland to bring CD 14 over 50% BVAP, much like the IRL map. The study is in CD 7, which is slightly under the 0.5% threshold below quota, but within a microchop of the quota.

The neighboring CDs are above quota and could be used to bring CD 7 up. One could move two townships on the eastern edge of Kalamazoo (pop 3276), the southwestern township of Eaton (pop 3150), or Rockwood in Wayne (pop 3289) to make all the districts within deviation of quota.

Without the last shift identified above the CHOP score would be 7 for UCCs, 7 for counties, and 1 for Detroit. That's a low score of 15. It could go down to 14 if a 47% BVAP in Wayne would satisfy the VRA allowing an Oakland chop to be eliminated. For comparison trainB was a CHOP of 16.

But that doesn't include the fix to CD 7. If it is a pure non-scoring microchop, then the above paragraph applies. If it is full scoring chop then it matters which of the three UCC choices I use. In Wayne or Eaton it creates an additional UCC chop as well as a county chop, but in the single-county UCC Kalamazoo, there would be no UCC chop. That seems strange to me. If it gets a fractional score as suggested by Torie, that leaves the question of the UCC penalty up in the air.

Should the three choices outlined above score equally on CHOP or not? Should the fact that it's a microchop matter for either the UCC or the county chop? If it matters, should it only matter for one of the two possible scores?

Edit: It should say 8 UCC chops, not 7. I was focusing on the microchop impact, and forgot to count the whole county chop from CD 8 in the Detroit UCC.

I'm cross posting this here for discussion as to whether this map is good policy despite the chops to the Detroit UCC and whther it should be in the mix of maps that would go to a commission.

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 8 raw (UC 9, UP 11, US 12)
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).