Chops and Erosity - Great Lakes Style
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muon2
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« Reply #275 on: February 22, 2015, 08:35:10 AM »
« edited: February 22, 2015, 08:37:22 AM by muon2 »

The IL Dems successfully defended state rep districts with 46% BVAP in court, and that was with more compact 50% BVAP districts available. In Cook the data supported a finding that polarized voting was not prevalent to the extent that the black minority would be unable to elect a candidate of choice. It helped that major black groups like the Urban League were supporting the Dems position.

In the OH competition, a threshold of 48% BVAP was used for CDs based on consultation with black community groups. They recognized that a 50% BVAP CD would need to reach into Akron, where as 48% could be put together in Cuyahoga. The Dem map that was filed in response to the Pub plan was between 48% and 50%.

However, a Pub-gerrymandered map that went under 50% BVAP would almost certainly be subject to attack by Dem-leaning minority groups. That is why Pubs stick to the 50% threshold.

Can you get to 48% BVAP without chops of subunits? Can you get there without such a map causing the map score to tank whether using your system, or your system as modified by me?  If Ohio enacted into law "our" system, I suspect that would tend to defang any such lawsuit, because there would be objective reasons per previously enacted law to cut down the BVAP a tad, tied to good map making. That is a different context, from a map that chops here, there and everywhere, but then suddenly does not when it comes to the Cleveland district.

I am falling in love with my system. Smiley  I find it simple and intuitive, focusing on chop size, along with the number of chops, universally applied with just the UCC aggregation overlay.

To get to 48% Cleveland has to be split. OH recognizes city wards as a subunit of municipalities. The OH constitution explicitly states that "such district shall be formed by combining the areas of governmental units giving preference in the order named to counties, townships, municipalities, and city wards." [emphasis added]

In DRA the Cleveland wards are listed by number in the precinct name with the ward precinct indicated by letter. The same notation applies to other OH cities and can be used to guide chops of Akron or Cincinnati. They are especially useful in Columbus which must be chopped.

=====
It is probably useful to run your chop scores on our collection of MI maps and see if they shift the Pareto ranking of any of them.
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Torie
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« Reply #276 on: February 22, 2015, 10:23:56 AM »
« Edited: March 05, 2015, 08:23:41 AM by muon2 »

Thought so. No thank you, when it comes  to securing the 48% BVAP. Yes, when I chopped Columbus I followed the ward numbers, and avoided ward splits.

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

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

MI Torie 2015E


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traininthedistance
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« Reply #277 on: February 22, 2015, 12:27:41 PM »
« Edited: March 06, 2015, 09:10:33 PM by muon2 »

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

MI train 2015C






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

Obviously, I would prefer to ding myself a half point for not having an all-GR district, but in the absence of that rule I'll leave outstate be for now.
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jimrtex
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« Reply #278 on: February 22, 2015, 12:28:51 PM »

To get to 48% Cleveland has to be split. OH recognizes city wards as a subunit of municipalities. The OH constitution explicitly states that "such district shall be formed by combining the areas of governmental units giving preference in the order named to counties, townships, municipalities, and city wards." [emphasis added]
The proposed constitutional amendment will remove city wards.
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muon2
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« Reply #279 on: February 22, 2015, 01:41:44 PM »

I'm surprised at the lack of love for Pareto. Without it flexibility goes down and the pressure to game the system increases. I think there is a role for humans to look at plans, and that requires that they presented with some choices. Why not a Pareto optimized set?

One danger with a total score approach is that it assumes that the categories in the score are calibrated with respect to each other. If they are then a chop point should mean the same as an erosity point. I have somewhat balanced the chop and inequality scores by using actual data from states drawn here. I haven't done anything like that to balance chops and erosity. If I had to guess, the balance between them will depend on the number of districts in the state. In MI a chop point is probably worth 3-4 erosity points, maybe more. I'm looking at the maps drawn here as part of a data set that may determine the right calibration.
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traininthedistance
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« Reply #280 on: February 22, 2015, 02:13:10 PM »

I'm surprised at the lack of love for Pareto. Without it flexibility goes down and the pressure to game the system increases. I think there is a role for humans to look at plans, and that requires that they presented with some choices. Why not a Pareto optimized set?

One danger with a total score approach is that it assumes that the categories in the score are calibrated with respect to each other. If they are then a chop point should mean the same as an erosity point. I have somewhat balanced the chop and inequality scores by using actual data from states drawn here. I haven't done anything like that to balance chops and erosity. If I had to guess, the balance between them will depend on the number of districts in the state. In MI a chop point is probably worth 3-4 erosity points, maybe more. I'm looking at the maps drawn here as part of a data set that may determine the right calibration.

I'm a fan of Pareto.  Perhaps there could be a fail-safe to prevent rewarding, say, just going back to strict 100 percent population equality and letting all else twist in the wind, but barring that the three-prong test seems conceptually sound.

As for how to calibrate erosity, it really does depend on the state.  I also wonder if zoomed muni connections ought to be a fractional erosity point on the grounds that having lots of tiny boros in places where one must cut would have an unduly large influence on the overall erosity score.  It doesn't seem quite right that, say, a quarter of Pennsylvania's entire erosity score could depend on how one navigates the tiny municipalities in Allegheny County, when the larger shapes elsewhere are what "really" matters.

Perhaps, actually, keep the muni counting system and have erosity based on the average score of all the districts instead.  That might in one fell swoop get those numbers down to chop size.  This system could be extended to inequality as well, to provide an incentive for districts which aren't just the furthest outliers to get closer to equal.
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jimrtex
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« Reply #281 on: February 22, 2015, 02:37:07 PM »

Links may be eliminated to reduce their number to the minimum necessary to leave all vertices connected (minimum links = number vertices minus one).  We will equalize population along these remaining links.  Thus we are defining the fewest possible chop locations that would produce equality among all regions.  Remember that a link represents a boundary between regions that have connected counties, and thus we can chop a county on the side of the boundary  where population is being shifted from.





Once we have the reduced graph, it is trivial to calculate the population need to equalize the population among them.   There will always be at least two exposed vertices that have only a single link to the rest of the vertices.   Since all equalization for the vertex must be along that link, the amount to be transferred is the deviation of the region's population from the ideal size for the region.



In this example, the flow was calculated in the following order:

Gray (Flint) to Red (Tri-Cities), which makes Gray exposed.
Gray (Flint) to Pink (Detroit), which makes Pink exposed.
Lime (Lansing) to Pink (Detroit), which makes Lime exposed.
Lime (Lansing) to Green (Grand Rapids), no new exposures.
Sky (Southwest) to Brown (Southeast), which makes Sky exposed.
Sky (Southwest) to Green (Grand Rapids), which makes Green exposed.
Green (Grand Rapids) to Red (Northern)

The amount of the flow (ie chop size) is relative to the quota.  The total flow is 8.90% of the quota or 62,804 persons.

When measuring a plan our objective is to not only have the minimum number of chops, but have the fewest persons in chops.

Muon will want to know if an ordinary person could do this.  The initial graph is quite simple.  Simply take a sheet of paper, and indicate the location and population of each region, and draw links between neighboring regions.

To avoid double shifts, shifts should be made from regions with surplus, to regions of deficit.  In this case the shift from Lime (Lansing) and Gray (Flint) to Pink (Detroit) was noted.  And there was enough left over to eliminate the deficit for Red (Tri-Cities).

This meant that the deficit for Brown (Southeast) had to be made up from Sky (Southwest), with the remaining surplus shifted north.

It this instance, there were 14 links.  There are 214 (16384) sets of links.  But we want a graph with 7 links.  That is we have have 14 links, and we want a subset of 7 links, or:
14! / 7! (14-7)! = 3432.  But many of these would exclude some of the vertices.  I think there are 462 7-link subgraphs that link all 8 regions.   It is amenable to brute force attack.

But an ordinary user simply needs to concentrate on reducing inequality among regions.
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muon2
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« Reply #282 on: February 22, 2015, 02:39:46 PM »

I'm surprised at the lack of love for Pareto. Without it flexibility goes down and the pressure to game the system increases. I think there is a role for humans to look at plans, and that requires that they presented with some choices. Why not a Pareto optimized set?

One danger with a total score approach is that it assumes that the categories in the score are calibrated with respect to each other. If they are then a chop point should mean the same as an erosity point. I have somewhat balanced the chop and inequality scores by using actual data from states drawn here. I haven't done anything like that to balance chops and erosity. If I had to guess, the balance between them will depend on the number of districts in the state. In MI a chop point is probably worth 3-4 erosity points, maybe more. I'm looking at the maps drawn here as part of a data set that may determine the right calibration.

I'm a fan of Pareto.  Perhaps there could be a fail-safe to prevent rewarding, say, just going back to strict 100 percent population equality and letting all else twist in the wind, but barring that the three-prong test seems conceptually sound.

As for how to calibrate erosity, it really does depend on the state.  I also wonder if zoomed muni connections ought to be a fractional erosity point on the grounds that having lots of tiny boros in places where one must cut would have an unduly large influence on the overall erosity score.  It doesn't seem quite right that, say, a quarter of Pennsylvania's entire erosity score could depend on how one navigates the tiny municipalities in Allegheny County, when the larger shapes elsewhere are what "really" matters.

Perhaps, actually, keep the muni counting system and have erosity based on the average score of all the districts instead.  That might in one fell swoop get those numbers down to chop size.  This system could be extended to inequality as well, to provide an incentive for districts which aren't just the furthest outliers to get closer to equal.

I could easily graph the average absolute deviation and use it to construct a table of inequality (I have the data). I actually like the mathematics of the average deviation and it does make every district matter. The question is what will be most defensible as a standard, and the court likes to concentrate on the worst cases of voter inequality which is the range. For instance if I have 8 districts with deviations of 0.125% from equality and two at the limit of 0.5%, the average deviation is 0.2%. If the eight close districts are made exact, then the average deviation is cut in half to 0.1%. Yet I think the court would care more that the range stayed the same at 1%, and would think a plan with all 10 districts at 0.2% deviation would be better at reaching OMOV.

Dividing the erosity by the number of districts might be a good calibration, but I think it might reduce erosity too much. There's a mathematical basis to think that the erosity should be divided by the square root of one less than the number of districts (3.6 for MI). I'm hoping some of the analysis of plans here will see where the practical ratio lies.

The problem with erosity around small munis is certainly real, but the are artificial ways to navigate counties to reduce erosity, too. The real geography of political boundaries is always going to force certain choices in a plan, unless one wants to erase them in a splitline fashion.
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jimrtex
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« Reply #283 on: February 22, 2015, 02:40:32 PM »

I'm surprised at the lack of love for Pareto. Without it flexibility goes down and the pressure to game the system increases. I think there is a role for humans to look at plans, and that requires that they presented with some choices. Why not a Pareto optimized set?

One danger with a total score approach is that it assumes that the categories in the score are calibrated with respect to each other. If they are then a chop point should mean the same as an erosity point. I have somewhat balanced the chop and inequality scores by using actual data from states drawn here. I haven't done anything like that to balance chops and erosity. If I had to guess, the balance between them will depend on the number of districts in the state. In MI a chop point is probably worth 3-4 erosity points, maybe more. I'm looking at the maps drawn here as part of a data set that may determine the right calibration.
How difficult is to to do a hyperbolic curve fit (of the form y = k/x)?
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muon2
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« Reply #284 on: February 22, 2015, 04:32:45 PM »

I'm surprised at the lack of love for Pareto. Without it flexibility goes down and the pressure to game the system increases. I think there is a role for humans to look at plans, and that requires that they presented with some choices. Why not a Pareto optimized set?

One danger with a total score approach is that it assumes that the categories in the score are calibrated with respect to each other. If they are then a chop point should mean the same as an erosity point. I have somewhat balanced the chop and inequality scores by using actual data from states drawn here. I haven't done anything like that to balance chops and erosity. If I had to guess, the balance between them will depend on the number of districts in the state. In MI a chop point is probably worth 3-4 erosity points, maybe more. I'm looking at the maps drawn here as part of a data set that may determine the right calibration.
How difficult is to to do a hyperbolic curve fit (of the form y = k/x)?


It a question of having enough data from a given state to make a statistically meaningful fit. There's no guarantee that it takes the form y = k/x. I found that the inequality fit better to an exponential with the number of counties per district (or region).
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jimrtex
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« Reply #285 on: February 22, 2015, 04:46:36 PM »

I could easily graph the average absolute deviation and use it to construct a table of inequality (I have the data). I actually like the mathematics of the average deviation and it does make every district matter. The question is what will be most defensible as a standard, and the court likes to concentrate on the worst cases of voter inequality which is the range. For instance if I have 8 districts with deviations of 0.125% from equality and two at the limit of 0.5%, the average deviation is 0.2%. If the eight close districts are made exact, then the average deviation is cut in half to 0.1%. Yet I think the court would care more that the range stayed the same at 1%, and would think a plan with all 10 districts at 0.2% deviation would be better at reaching OMOV.
A court should consider the overall strategy of the state.  In Karcher v Daggett, the court did not reject the use of whole  towns, but that New Jersey was careless and haphazard.  In Vieth v Jubelirer, knew that Pennsylvania had no non-political strategy and demanded exact equality.  In Tennant v Jefferson County Commission, the court accepted West Virginia's reasons, even though they were somewhat rationalization.

Standard deviation says that the plan without the extremes is better (0.2 vs 0.22).

The SCOTUS has accepted an Ohio House plan with two districts outside a 5% deviation.  One was because of the except for a single-county district, but the other was in northeastern Ohio, where the limit in the Ohio Constitution was exceeded, but was necessary to comply with the other rules with regard to counties.

In White v Regester which set the 10% upper limit, the court did note other aspects of deviation distribution.
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muon2
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« Reply #286 on: February 22, 2015, 05:23:14 PM »

I could easily graph the average absolute deviation and use it to construct a table of inequality (I have the data). I actually like the mathematics of the average deviation and it does make every district matter. The question is what will be most defensible as a standard, and the court likes to concentrate on the worst cases of voter inequality which is the range. For instance if I have 8 districts with deviations of 0.125% from equality and two at the limit of 0.5%, the average deviation is 0.2%. If the eight close districts are made exact, then the average deviation is cut in half to 0.1%. Yet I think the court would care more that the range stayed the same at 1%, and would think a plan with all 10 districts at 0.2% deviation would be better at reaching OMOV.
A court should consider the overall strategy of the state.  In Karcher v Daggett, the court did not reject the use of whole  towns, but that New Jersey was careless and haphazard.  In Vieth v Jubelirer, knew that Pennsylvania had no non-political strategy and demanded exact equality.  In Tennant v Jefferson County Commission, the court accepted West Virginia's reasons, even though they were somewhat rationalization.

Standard deviation says that the plan without the extremes is better (0.2 vs 0.22).

The SCOTUS has accepted an Ohio House plan with two districts outside a 5% deviation.  One was because of the except for a single-county district, but the other was in northeastern Ohio, where the limit in the Ohio Constitution was exceeded, but was necessary to comply with the other rules with regard to counties.

In White v Regester which set the 10% upper limit, the court did note other aspects of deviation distribution.

Then the interesting case would be one that compared two congressional plans with 10 districts that meet all state standards equally well except for population deviation. Plan A has 8 exactly equal districts and 2 with a 0.5% deviation (range 1%, average deviation 0.1%, standard deviation 0.22%). Plan B has all 10 districts with 0.25% deviation (range 0.5%, average deviation 0.25%, standard deviation 0.25%). Since these are congressional plans they are governed by the requirement that the populations be as equal as practicable. Though plan B is worse in both deviation measures, I can't help but think that the court would be attracted to it since the disparity between the most populous and least populous districts is reduced.
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jimrtex
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« Reply #287 on: February 22, 2015, 06:08:36 PM »

I could easily graph the average absolute deviation and use it to construct a table of inequality (I have the data). I actually like the mathematics of the average deviation and it does make every district matter. The question is what will be most defensible as a standard, and the court likes to concentrate on the worst cases of voter inequality which is the range. For instance if I have 8 districts with deviations of 0.125% from equality and two at the limit of 0.5%, the average deviation is 0.2%. If the eight close districts are made exact, then the average deviation is cut in half to 0.1%. Yet I think the court would care more that the range stayed the same at 1%, and would think a plan with all 10 districts at 0.2% deviation would be better at reaching OMOV.
A court should consider the overall strategy of the state.  In Karcher v Daggett, the court did not reject the use of whole  towns, but that New Jersey was careless and haphazard.  In Vieth v Jubelirer, knew that Pennsylvania had no non-political strategy and demanded exact equality.  In Tennant v Jefferson County Commission, the court accepted West Virginia's reasons, even though they were somewhat rationalization.

Standard deviation says that the plan without the extremes is better (0.2 vs 0.22).

The SCOTUS has accepted an Ohio House plan with two districts outside a 5% deviation.  One was because of the except for a single-county district, but the other was in northeastern Ohio, where the limit in the Ohio Constitution was exceeded, but was necessary to comply with the other rules with regard to counties.

In White v Regester which set the 10% upper limit, the court did note other aspects of deviation distribution.

Then the interesting case would be one that compared two congressional plans with 10 districts that meet all state standards equally well except for population deviation. Plan A has 8 exactly equal districts and 2 with a 0.5% deviation (range 1%, average deviation 0.1%, standard deviation 0.22%). Plan B has all 10 districts with 0.25% deviation (range 0.5%, average deviation 0.25%, standard deviation 0.25%). Since these are congressional plans they are governed by the requirement that the populations be as equal as practicable. Though plan B is worse in both deviation measures, I can't help but think that the court would be attracted to it since the disparity between the most populous and least populous districts is reduced.
The "equal as practicable" comes from the Constitution that representative be chosen by the people of the respective states.   If they are to somehow collectively represent the state, while being elected from individual districts, it is the overall equality among the districts that is more important.  In this particular case, the gratuitous dismemberment of communities, as if the commission were re-enacting a 1950s-style urban redevelopment or freeway construction, clearly violates equal protection of voters in those areas.  Equal protection is actually in the Constitution.  The basis for Wesberry v Sanders is fabricated.  See White's concurring opinion.
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muon2
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« Reply #288 on: February 22, 2015, 06:14:39 PM »

Links may be eliminated to reduce their number to the minimum necessary to leave all vertices connected (minimum links = number vertices minus one).  We will equalize population along these remaining links.  Thus we are defining the fewest possible chop locations that would produce equality among all regions.  Remember that a link represents a boundary between regions that have connected counties, and thus we can chop a county on the side of the boundary  where population is being shifted from.





Once we have the reduced graph, it is trivial to calculate the population need to equalize the population among them.   There will always be at least two exposed vertices that have only a single link to the rest of the vertices.   Since all equalization for the vertex must be along that link, the amount to be transferred is the deviation of the region's population from the ideal size for the region.



In this example, the flow was calculated in the following order:

Gray (Flint) to Red (Tri-Cities), which makes Gray exposed.
Gray (Flint) to Pink (Detroit), which makes Pink exposed.
Lime (Lansing) to Pink (Detroit), which makes Lime exposed.
Lime (Lansing) to Green (Grand Rapids), no new exposures.
Sky (Southwest) to Brown (Southeast), which makes Sky exposed.
Sky (Southwest) to Green (Grand Rapids), which makes Green exposed.
Green (Grand Rapids) to Red (Northern)

The amount of the flow (ie chop size) is relative to the quota.  The total flow is 8.90% of the quota or 62,804 persons.

When measuring a plan our objective is to not only have the minimum number of chops, but have the fewest persons in chops.

Muon will want to know if an ordinary person could do this.  The initial graph is quite simple.  Simply take a sheet of paper, and indicate the location and population of each region, and draw links between neighboring regions.

To avoid double shifts, shifts should be made from regions with surplus, to regions of deficit.  In this case the shift from Lime (Lansing) and Gray (Flint) to Pink (Detroit) was noted.  And there was enough left over to eliminate the deficit for Red (Tri-Cities).

This meant that the deficit for Brown (Southeast) had to be made up from Sky (Southwest), with the remaining surplus shifted north.

It this instance, there were 14 links.  There are 214 (16384) sets of links.  But we want a graph with 7 links.  That is we have have 14 links, and we want a subset of 7 links, or:
14! / 7! (14-7)! = 3432.  But many of these would exclude some of the vertices.  I think there are 462 7-link subgraphs that link all 8 regions.   It is amenable to brute force attack.

But an ordinary user simply needs to concentrate on reducing inequality among regions.

I understand this, and I think it makes a good basis for an algorithm. However, what it can't do is evaluate a plan like the one I posted for MI. To do so, it has to reverse engineer regions where none are plainly evident. It is possible to propose regions consistent with the plan, but that choice may not be unique. We take some care in our maps, but what about citizens who propose maps that aren't so careful to minimize chops. I wouldn't want to see them discarded, but I would like to see them scored.

The second issue I have is that it presumes the sanctity of the UCC. I see no reason why excess UCC splits should be viewed as anything more special than excess county splits. In my posted plan, I actually did use regions to devise it. It has eight regions, which is the same number as your graph, but my regions don't respect the UCCs. Shouldn't I get scored based on my regions with perhaps a penalty for violating the UCCs? If you try to score it based on UCCs it would get a prohibitively large penalty for population shifts that you might as well say that UCCs are inviolable. That was never the intent of the UCCs as I understood their development.



Region 1 (CD 1) 1.0000
Region 2 (CD 2+4) 1.9950
Region 3 (CD 3) 1.0035
Region 4 (CD 6) 1.0025
Region 5 (CD 7) 0.9920
Region 6 (CD 8 ) 1.0042
Region 7 (CD 5+9+11) 3.0019
Region 8 (CD 10+12+13+14) 4.0010

Shifts 8->5 (0.10%), 7->5 (0.19%), 6->5 (0.42%), 4->5 (0.10%): 0.81%
Shifts 3->2 (0.35%), 4->2 (0.15%): 0.50%
Total shift 1.30% (adjusted for rounding). The red is the only shift that was required on the map.

Why shouldn't this be scored as such, with an additional penalty for the 3 UCC chops?

Alternatively I could claim CD 5 as a 9th region since it is within 5% of the quota. How should that be treated?
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traininthedistance
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« Reply #289 on: February 23, 2015, 12:34:24 AM »

The second issue I have is that it presumes the sanctity of the UCC. I see no reason why excess UCC splits should be viewed as anything more special than excess county splits. In my posted plan, I actually did use regions to devise it. It has eight regions, which is the same number as your graph, but my regions don't respect the UCCs. Shouldn't I get scored based on my regions with perhaps a penalty for violating the UCCs? If you try to score it based on UCCs it would get a prohibitively large penalty for population shifts that you might as well say that UCCs are inviolable.  That was never the intent of the UCCs as I understood their development.

I feel like sanctity of major metro areas was indeed the whole point of UCCs, so I'm obviously not a fan of any plan that tries to make an end-run around them like yours does.  Obviously some splits are mathematically unavoidable, but I would certainly argue in favor of the concept having more teeth than just a garden-variety county chop.  Perhaps an extra penalty for each district that spans the UCC boundary is in fact what the doctor ordered. 

I'd also like to see an erosity calculation for my latest map when you get the chance.
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traininthedistance
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« Reply #290 on: February 23, 2015, 02:10:44 AM »
« Edited: February 23, 2015, 02:20:15 AM by traininthedistance »

Here is a corrected Ohio.  









Dayton and Columbus now have a district entirely within the UCC; this gets Dayton to optimal (and, oh hey, a macrochop in Montgomery is swapped for an I-chop in Miami).  Columbus and Cincy both still have two districts which span the UCC line, but since doing so saves a county cut that is acceptable.  And, of course, all UCCs have the minimum number of districts total, which is the most important thing.

The Columbus chop was fun– trying to keep everything contiguous in Franklin is really unnecessarily hard.  As for Cuyahoga, I did not go for max BVAP but did choose to present what feels like a good "close enough" configuration, it is 44.7% BVAP, and plurality-black by total population.  Obviously the Cuyahoga lines can and should be dealt with separately: figure out what BVAP/erosity balance you need to strike, and just hold it constant with respect to the other maps.
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« Reply #291 on: February 23, 2015, 05:40:16 AM »
« Edited: February 23, 2015, 07:16:06 AM by muon2 »

The second issue I have is that it presumes the sanctity of the UCC. I see no reason why excess UCC splits should be viewed as anything more special than excess county splits. In my posted plan, I actually did use regions to devise it. It has eight regions, which is the same number as your graph, but my regions don't respect the UCCs. Shouldn't I get scored based on my regions with perhaps a penalty for violating the UCCs? If you try to score it based on UCCs it would get a prohibitively large penalty for population shifts that you might as well say that UCCs are inviolable.  That was never the intent of the UCCs as I understood their development.

I feel like sanctity of major metro areas was indeed the whole point of UCCs, so I'm obviously not a fan of any plan that tries to make an end-run around them like yours does.  Obviously some splits are mathematically unavoidable, but I would certainly argue in favor of the concept having more teeth than just a garden-variety county chop.  Perhaps an extra penalty for each district that spans the UCC boundary is in fact what the doctor ordered.  

I'd also like to see an erosity calculation for my latest map when you get the chance.

We will have to agree to disagree here. The UCCs were devised to identify communities of interest and penalize plans that chopped them excessively. Excessively was simply defined as having more districts than the minimum to cover the UCC. Almost all UCCs are less than a whole number of districts, so all those districts must perforce have a UCC-spanning district.

Counties and munis are also CoIs, just like UCCs. Arguably counties and munis are more identifiable and their chops will be more readily noted by the public than a chop of a UCC. Scoring excess UCC chops more severely than excess county chops, especially more than rural county chops is completely counterintuitive to me. It's a way too city-centric view that elevates the urban area over the rural area without justification.

Even considering UCCs is a unique feature of this site compared to any other I've seen. Most only consider established political boundaries, which UCCs are not. Then they rely on subjective communities of interest which can become a crutch for gerrymandering. However, I find that when CoIs can be quantified they can be used to improve a plan. UCCs are an example of that. The limitation of connections between counties to direct numbered highways for calculating erosity is another example. I've built both in to the system, but not so much that they dictate a result.

I can be convinced that a chop is a chop. I can't be convinced that a UCC chop is something more than a chop.
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Torie
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« Reply #292 on: February 23, 2015, 07:39:21 AM »
« Edited: February 23, 2015, 08:28:22 AM by Torie »

Interesting discussion, with my little points not commented upon. Sad That's OK. I take Mike's points, but to me severing off whole a highly populated county in a UCC without an extra penalty, tends to eviscerate the concept of a UCC, and could lead to abuses. We calculate the size of chops already, in a way no other system out there does, but then suddenly, when it comes to UCC's, it doesn't matter so much anymore, with the ratio of the penalty to the population involved in a fan out, in some cases relatively trivial (oh, the irony of the freak out over Jimtex's minor two chops of the Lansing UCC, while just one point penalty accrues for Mike's chop off of the entirety of Livingston).

I have always had a bias in all of my maps that were not deliberate gerrymanders, to limiting the fan out of UCC populations. Given all of the additional complexity involved as it is, given this loophole, we might as well dump the concept of UCC's entirely, and except perhaps for micro-chops, macrochops as well. I am not sure it is worth it. A lot is at stake when it comes to just how much of a UCC is fanned out. Finally, I think it is easier for the layperson to understand that the population fanned out from a UCC needs to be minimized within macrochop range, and penalized within increments. The blizzard of rules promulgated here, that give a lot of play in  that regard, in my view is not. Allowing bisections of big cities, that can be mitigated, without penalty, is also a big problem for me.

I must say Train's gerrymanders within the rules of the game, are most skilled. He's really good at it. Smiley  And you can see what happens, without the incremental penalty, in his Ohio map with the Columbus CD (his Cinci UCC also has an excess fan out). His Cleveland district is also very skilled, and, like his Dayton UCC configuation now, does not do an excess fan out (the minimum fan out goes west rather than east, although it may entail some more erosity points as a result), and largely gets where he wants to go, except that within the UCC, that wrap of OH-14 around the west side of Cleveland, would get hit with some extra erosity points perhaps, if that aspect of the system were ever refined.

The way to deal with the pareto optimality controversy perhaps, applicable across states, is to look at the relative percentage deviations in scores in the erosity and chop metrics. That way, if a state is necessarily going to generate a lot of erosity points as compared to chop points, one can correct for that, so that the erosity consideration does not dominate, and is appropriately taken account of. And it should not be a strict total score concept. That limits flexibility way too much. But the gap in the total scores should not be excessive either - yet another iteration of the never ending search for the Goldilocks solution.
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« Reply #293 on: February 23, 2015, 09:33:19 AM »

Interesting discussion, with my little points not commented upon. Sad That's OK. I take Mike's points, but to me severing off whole a highly populated county in a UCC without an extra penalty, tends to eviscerate the concept of a UCC, and could lead to abuses. We calculate the size of chops already, in a way no other system out there does, but then suddenly, when it comes to UCC's, it doesn't matter so much anymore, with the ratio of the penalty to the population involved in a fan out, in some cases relatively trivial (oh, the irony of the freak out over Jimtex's minor two chops of the Lansing UCC, while just one point penalty accrues for Mike's chop off of the entirety of Livingston).

Alas when there are four of us in conversation it is all too easy to address one or two comments in one post, and as that evolves, lose track of other salient points raised.

I've conceded the county microchop in the face of evidence, but on the UCC matter I've seen nothing to sway me. In fact some of the evidence presented on the microchop case makes me firmer on UCC chops. It comes down to the basic notion that a chop is a chop.

Let me elucidate with the comparison you cite. If I'm viewing it as a detached member of the public I see the double chop of Lansing as two chops, I don't see the Livingston chop at all. Then you tell me about UCCs, and that chops into them matter. I then can see that both Lansing and Detroit UCCs are chopped and should each get a point, and maybe Lansing gets two UCC points because it's better to spread the chops around rather than put them all in one place. Either way UCC chops are no stronger than county chops, and in the Lansing case maybe less strong. Recall that some on our VA commission here were not willing to approve UCCs as part of the basic scoring, only as a guide to the selection, putting UCCs in the same category as the political measures.

Then you claim that size matters. Let's recall that the macrochop is primarily the test to determine when subunits matter so that erosity comes out relatively even in urban and rural areas. Erosity is the prime tool to balance the use of chops in gerrymandering. I note that both train and I have pushed down chops, but have not reached your lower erosity scores - that is how it should be. But in the absence of UCCs and if strict subunit integrity is applied, macrochops don't affect the chop count. So we can consider other size metrics to address this.

Jimrtex has a continuous scale for judging chop size, and Torie has a discrete set of steps for chop size scoring (I think, but it hasn't been in a clearly put table, so I may have it wrong). If the effect of the chop size is to say that smaller county chops below some threshold are less than one point, I can see how that might resonate with my rational but detached viewer. But as soon as one says that a chop is magnified beyond the basic one point amount it looks fishy (unless of course everything scales up by some constant factor). When UCCs are in play they already cause county chops to potentially count double (not to mention the typical increase in erosity when one make large chops into them).

The short takeaway is that given that some members of the public may not accept UCCs at all in the scoring since they aren't statutory political units, someone has to show me why UCC chops should be scored more severely than counties. The Livingston vs Lansing example convinces me of the opposite.
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« Reply #294 on: February 23, 2015, 10:35:44 AM »
« Edited: February 23, 2015, 10:54:06 AM by Torie »

Well, we will just have to agree to disagree on UCC's. I don't think all of your complexity is worth it, when there is so much population play with which to play games. Macrochops to trigger some sort of zoom for erosity (in any county) would still be a useful exercise. But otherwise, they would not be extra-penalized anywhere - or they should be penalized everywhere, and based on relative size. Penalize them everywhere, and based on size, or penalize them nowhere. KISS. I am afraid your system gets us the worst of both worlds. You also have this unnecessary overlay of macrochops within UCC's it seems to me, beyond again some intelligently applied zoom test for erosity (which needs to be based on the excess erosity over the minimum).

Using UCC's is hard to defend to the public. To do it, one needs one simple test. But when you have your byzantine structure (I mean look how long it took me to understand it?), and suddenly you can chop off a big county, with not much of a problem (or zero problem when it comes to chopping off Ottawa County in the GR UCC - does that bother you at all?), while being dumped on for two much smaller chops (beyond the chops themselves), just because it is a UCC, I suspect the public will just roll its eyes. Pity, because I really like the concept - if it can rationally be applied and defended. And again, to answer your question/comment above, the sole role in my system of UCC's is to aggregate the population of the population involved in the chops (with whole county severances counting as chops for purposes of this aggregation concept) of more than one county, where there is more than one county in the UCC, for purposes of counting additional penalties for larger chops, beyond the ordinary chop penalty itself. Otherwise it has no role. All counties are otherwise subject to the same rules. KISS again.

Somehow, we stopped focusing on what makes for good maps by the way on this one. What is the disadvantage of my system, when it comes to good maps? Just how horrible is it when it comes to good maps, to have to minimize within a certain range, the UCC fanout? A lot more total chops, a lot more erosity, of the state as a whole, or what?
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traininthedistance
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« Reply #295 on: February 23, 2015, 11:30:41 AM »

Interesting discussion, with my little points not commented upon. Sad That's OK. I take Mike's points, but to me severing off whole a highly populated county in a UCC without an extra penalty, tends to eviscerate the concept of a UCC, and could lead to abuses. We calculate the size of chops already, in a way no other system out there does, but then suddenly, when it comes to UCC's, it doesn't matter so much anymore, with the ratio of the penalty to the population involved in a fan out, in some cases relatively trivial (oh, the irony of the freak out over Jimtex's minor two chops of the Lansing UCC, while just one point penalty accrues for Mike's chop off of the entirety of Livingston).

I have always had a bias in all of my maps that were not deliberate gerrymanders, to limiting the fan out of UCC populations. Given all of the additional complexity involved as it is, given this loophole, we might as well dump the concept of UCC's entirely, and except perhaps for micro-chops, macrochops as well. I am not sure it is worth it. A lot is at stake when it comes to just how much of a UCC is fanned out. Finally, I think it is easier for the layperson to understand that the population fanned out from a UCC needs to be minimized within macrochop range, and penalized within increments. The blizzard of rules promulgated here, that give a lot of play in  that regard, in my view is not. Allowing bisections of big cities, that can be mitigated, without penalty, is also a big problem for me.

I must say Train's gerrymanders within the rules of the game, are most skilled. He's really good at it. Smiley  And you can see what happens, without the incremental penalty, in his Ohio map with the Columbus CD (his Cinci UCC also has an excess fan out). His Cleveland district is also very skilled, and, like his Dayton UCC configuation now, does not do an excess fan out (the minimum fan out goes west rather than east, although it may entail some more erosity points as a result), and largely gets where he wants to go, except that within the UCC, that wrap of OH-14 around the west side of Cleveland, would get hit with some extra erosity points perhaps, if that aspect of the system were ever refined.

The way to deal with the pareto optimality controversy perhaps, applicable across states, is to look at the relative percentage deviations in scores in the erosity and chop metrics. That way, if a state is necessarily going to generate a lot of erosity points as compared to chop points, one can correct for that, so that the erosity consideration does not dominate, and is appropriately taken account of. And it should not be a strict total score concept. That limits flexibility way too much. But the gap in the total scores should not be excessive either - yet another iteration of the never ending search for the Goldilocks solution.

Hey now, my maps are not "gerrymanders".  They are built with an eagle eye towards driving down chops and preserving the spirit of UCCs; they are conscious of skew but that is a purely defensive posture.  (I will– and did– admit that sending PA-6 into Berks rather than Lancaster was a political decision.  That's really it, though– and it would be a winner in my fantasy world that cares about CSAs too, so it's not even purely political anyway.)

That dig aside, I do strongly endorse the sentiment of this post, and will admit that, as surprising as this would seem to the me of a week ago, I am finding myself more upset at muon's severing of Livingston than I am with your chop of Clinton. To be fair the problems with muon's map are not just confined to that area; it does a spectacularly poor job of respecting all sorts of regions all over the map (the severing of Saginaw from the Tri-Cities, the Kalamazoo-Monroe thing, etc.).  It's really quite a monstrosity.  I would take your latest couple Michigans over it in a heartbeat.

I want to get penalized for my Cincy and Columbus fans, even if I am not being penalized at the moment.  My CD-10 is indeed ugly as sin; that is mostly an artifact of having to wrap around the VRA district and your Lake/Cuyahoga district isn't much better.  As for the bisection of Columbus, it's not the Platonic ideal.  But I haven't found a way to save a county cut in that area without basically splitting the city in half, and in any case those Franklin lines really are just drawn for the sole purpose of evading the insane minefield that is those discontiguous township precincts.  I'd like to care about the size and placement of the Columbus chop– I really can't afford to.
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« Reply #296 on: February 23, 2015, 11:56:03 AM »

Well why don't we return then to the original model for UCCs (ca 2013). It was pretty simple IMO. Here's how it reads.

The size of a UCC is defined as the population of the UCC divided by the quota and rounded up to the nearest whole number. The number of districts in excess of the size of the UCC is equal to the number of additional chop points.


Note this is over and above any chops for counties, townships, cities, etc. Macrochops would then only function to determine zoom down from the county level to measure erosity. The simple rule avoids trying to determine a maximum number of districts, so anyone's map can be scored easily without disqualification. It keeps me happy since I oppose disqualification for UCC violations precisely because they aren't generally understood, but think a penalty is fine.
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« Reply #297 on: February 23, 2015, 12:10:23 PM »

While everyone is dissing my Livingston chop map, understand that it is just an entry. If it stays on the Pareto frontier it goes on to a committee of real humans who decide things like whether Saginaw should stay with Midland or if Kalamazoo to Monroe is a bridge too far. They can determine if the South Lyon/Brighton/Howell urbanized area, which is separate from the Detroit urbanized area, means that Livingston can be split off as much as other CSA counties like Monroe and Washtenaw that happen to have an older center that qualified them for their own MSA.
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Torie
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« Reply #298 on: February 23, 2015, 01:33:43 PM »
« Edited: February 23, 2015, 02:02:38 PM by Torie »

Well why don't we return then to the original model for UCCs (ca 2013). It was pretty simple IMO. Here's how it reads.

The size of a UCC is defined as the population of the UCC divided by the quota and rounded up to the nearest whole number. The number of districts in excess of the size of the UCC is equal to the number of additional chop points.


Note this is over and above any chops for counties, townships, cities, etc. Macrochops would then only function to determine zoom down from the county level to measure erosity. The simple rule avoids trying to determine a maximum number of districts, so anyone's map can be scored easily without disqualification. It keeps me happy since I oppose disqualification for UCC violations precisely because they aren't generally understood, but think a penalty is fine.

That does not address excess fan out of up to the population of up to half of a CD applying just your metric - far too much. My system of incremental points per macrochop based on excess fan outs, does. We fret over macrochops, of about 35,000 people, but can play around with another 300,000 in fan out potentially, at will.

The way to solve that issue to make everyone happy is to use your metric, that no more CD's are in the UCC than the nearest whole number rounded up, but add that 1)  the number of whole CD's entirely within the UCC must be the nearest whole number to the quota rounded down (thus Dayton, Columbus and Grand Rapids, must have one CD wholly within them, and Cincy must have two, Cleveland 2, etc), and 2) where there is an excess over the minimum using either metric (I have that excess in the Cleveland UCC, because the Akron CD butts in, while OH-14 butts out, so I have 4 CD's in the UCC, while anything over 3 CD's in the UCC, with a least 2 CD's entirely in the UCC, counts as an excess), the number of people involved in the excess that are equal to a macrochop and over, are penalized on a per macrochop incremental basis (my Akron incursion is below a macrochop, so no problem but the chop itself).

Basically my system, for example, requires (unless one is willing to rack up penalty points) that where a UCC has over 1 CD in population, but less than two, one of the CD's must be entirely within the UCC (subject to the macrochop pad), and in all events, focuses on the number of people involved in the excess, rather than just giving same penalty whether it involves 40,000 people or 300,000 people, etc. It's that simple really. The rest just comes down to simple chop counts, be they macro, I's, or micros, scored however one agrees to score them (about which we we are all arm wrestling too, because we are all so "disagreeable." Smiley ) You know I'm right Mike - yes you do. Smiley

Indeed same system should apply for all counties really, if big enough in population to trigger all of this. It is just that only multi county UCC's potentially trigger a whole number higher than one for the quota and are looked at as one unit, so the formula gets a bit more complicated in application. For all other single counties with populations of below a quota of one, whether UCC's or not, there is no rounding down (that number would be zero), and so we are left with having no more CD's in other counties but one, and where there is more than one CD, one gets a penalty point per macrochop increment, over and above the normal I chop penalties, plus a triggering of the zoom lens for erosity evaluation, scored based on the number of cuts over the minimum possible.
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traininthedistance
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« Reply #299 on: February 23, 2015, 02:03:50 PM »
« Edited: February 23, 2015, 02:25:16 PM by traininthedistance »

They can determine if the South Lyon/Brighton/Howell urbanized area, which is separate from the Detroit urbanized area, means that Livingston can be split off as much as other CSA counties like Monroe and Washtenaw that happen to have an older center that qualified them for their own MSA.

That is an interesting point.  I'd rather go in the opposite direction, and keep Monroe/Washtenaw in the greater Detroit area in keeping with my respect for CSAs; barring the adoption of that I've stuck to the next best thing and kept them with each other at least.  

This has the effect that, for a hypothetical Michigan UCC map where Monroe/Washtenaw are part of a Greater Detroit UCC, Torie's and my maps would be optimally respectful of those lines save for the midsize Lapeer chop, which is a pretty good outcome all things considering!  And, yes, I realize that Flint is actually part of the CSA too, though it's further away: good thing the Lapeer chop is with the Flint district.  I suppose a maximally-CSA-compounding plan would actually throw the Thumb in with Saginaw/Bay City/Midland... hm, that's an idea worth exploring.  Won't score optimally, but worth exploring all the same.

I realize that mocking up a scoring system for taking into account CSA concerns gets to be a pretty hairy bear pretty quickly, so I understand that it won't get into the final chop schema; but it's the sort of thing I try to keep in mind, and I would hope that whatever regime eventually gets decided on would keep CSA ideals as an important criterion for the "human" part of the process, as well as allowing sufficient flexibility that CSA-protecting maps get to make it through to the Pareto frontier.

(One fringe benefit, as you might guess, to my Michigan plan is that I keep Kalamazoo and Battle Creek together, which is in keeping with my CSA-mindful mentality.  That wasn't even the primary motivation for my lines in that part of the map; I cared more about minimizing county cuts in 6/7/8 as well as keeping the two sides of Holland together, but it's a nice benefit.  Is it worth the additional erosity and UCC fan, in comparison to Torie's map?  Eh.  If it was just a matter of keeping Kalamazoo/BC and Holland/Holland together, probably not.  But since it saves county cuts further down the line in Central MI, that helps tip the scales.)
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