Chops and Erosity - Great Lakes Style

[muon2]

The fix for Clinton is to allow for population play, and not have to use it to get under the threshold. It seems like a good fix to me. Would you address that precise issue for me?

I don't know what the phrase means, so I can't do anything to systematize it.

It means the difference between the population of a CD and the population of that CD if it were 0.5% off from its "perfect" allocable share of the population. Where that difference is enough to jiggle the lines in a county to get rid of the macro-chop, then it's not a macro-chop, and you need not jiggle the lines, as we did in Clinton above. That leaves out the issue of generating microchops elsewhere to get even more "play," which is one reason why micro-chops need to be penalized out of the box, to shut down that game (which game might well still be worth playing even with some penalty if the macrochop of a multi-county UCC, or even a single county UCC, is right on the cusp (of however one defines a macro-chop, which definitional issue is another issue that I raised above)).

I might add that nobody in their right mind would ever consider the line in Clinton to get rid of the macro-chop to be superior to the clean, less erose looking, line that I drew, with better population equality to boot. Sometimes, such a sad outcome in order to have applicable metrics, might be unavoidable, but at least one can try to mitigate that syndrome.

In my view, your system really incentives game playing when matters are on the cusp, which I consider a major problem. In drawing maps per your system, I have to spend a lot of time game playing. The sad thing is that I will never be as good at is as you are, no matter how hard I try. You have a gift there, you master gamesman you.

Aren't you just saying that if the chop is within a microchop of a macrochop then it's not a macrochop? If so shouldn't I just say that the threshold is 5.5% of the quota? If not, then I still don't understand population play.

Any system that is codified and objective will have cusps that one can take advantage of. Think about all the souls looking for the cusps in the IRS code this time of year. The whole purpose of the Pareto test is to insure that a single game-playing mapper won't knock out reasonable contenders. The humans reviewing the contenders can bring other judgements to bear on the Pareto set, but there needs to be a winnowing to avoid pure subjectivity.

[Torie]

I understand in the case of the MI map, there is no escape from the Detroit UCC penalty, so the issue at least for Train's map and mine is irrelevant. But my concern is more what triggers the macrochop since in other states that might matter, and I certainly would want to penalize an unnecessary macrochop into a multi county UCC, if someone chose to go there in a MI map. Thus I suggested the whole county fix, which perhaps you might wish to address.  

The trigger for a macrochop can either be due to a chop into a selected list of counties (like the ones in UCCs) or it can be due to a population trigger and applied to any county. I'm wary of the first method because I think that will lead to pressure to place chops in counties not on the list. I think we agree that is not a desirable feature.

I didn't follow that there was a specific fix proposed. If it is something that can be made systematic it can be investigated. I still haven't quite seen the problem that would be fixed either.

The image to the left is a macrochop. The one to the right is not.

[Torie]

The fix for Clinton is to allow for population play, and not have to use it to get under the threshold. It seems like a good fix to me. Would you address that precise issue for me?

I don't know what the phrase means, so I can't do anything to systematize it.

It means the difference between the population of a CD and the population of that CD if it were 0.5% off from its "perfect" allocable share of the population. Where that difference is enough to jiggle the lines in a county to get rid of the macro-chop, then it's not a macro-chop, and you need not jiggle the lines, as we did in Clinton above. That leaves out the issue of generating microchops elsewhere to get even more "play," which is one reason why micro-chops need to be penalized out of the box, to shut down that game (which game might well still be worth playing even with some penalty if the macrochop of a multi-county UCC, or even a single county UCC, is right on the cusp (of however one defines a macro-chop, which definitional issue is another issue that I raised above)).

I might add that nobody in their right mind would ever consider the line in Clinton to get rid of the macro-chop to be superior to the clean, less erose looking, line that I drew, with better population equality to boot. Sometimes, such a sad outcome in order to have applicable metrics, might be unavoidable, but at least one can try to mitigate that syndrome.

In my view, your system really incentives game playing when matters are on the cusp, which I consider a major problem. In drawing maps per your system, I have to spend a lot of time game playing. The sad thing is that I will never be as good at is as you are, no matter how hard I try. You have a gift there, you master gamesman you.

Aren't you just saying that if the chop is within a microchop of a macrochop then it's not a macrochop? If so shouldn't I just say that the threshold is 5.5% of the quota? If not, then I still don't understand population play.

Any system that is codified and objective will have cusps that one can take advantage of. Think about all the souls looking for the cusps in the IRS code this time of year. The whole purpose of the Pareto test is to insure that a single game-playing mapper won't knock out reasonable contenders. The humans reviewing the contenders can bring other judgements to bear on the Pareto set, but there needs to be a winnowing to avoid pure subjectivity.

Nope, because it is focused on what the population of a CD actually is, and the play might be either as little as zero, or as much as 1%. Maybe I should express this concept in a formula for you.  Why oh why do lawyers and math gurus have so much trouble communicating with each other? I mean, yes, I am not as smart as you, but then again, my IQ is nevertheless considerably above average.

[muon2]

It means the difference between the population of a CD and the population of that CD if it were 0.5% off from its "perfect" allocable share of the population. Where that difference is enough to jiggle the lines in a county to get rid of the macro-chop, then it's not a macro-chop, and you need not jiggle the lines, as we did in Clinton above. That leaves out the issue of generating microchops elsewhere to get even more "play," which is one reason why micro-chops need to be penalized out of the box, to shut down that game (which game might well still be worth playing even with some penalty if the macrochop of a multi-county UCC, or even a single county UCC, is right on the cusp (of however one defines a macro-chop, which definitional issue is another issue that I raised above)).

I might add that nobody in their right mind would ever consider the line in Clinton to get rid of the macro-chop to be superior to the clean, less erose looking, line that I drew, with better population equality to boot. Sometimes, such a sad outcome in order to have applicable metrics, might be unavoidable, but at least one can try to mitigate that syndrome.

In my view, your system really incentives game playing when matters are on the cusp, which I consider a major problem. In drawing maps per your system, I have to spend a lot of time game playing. The sad thing is that I will never be as good at is as you are, no matter how hard I try. You have a gift there, you master gamesman you.

Aren't you just saying that if the chop is within a microchop of a macrochop then it's not a macrochop? If so shouldn't I just say that the threshold is 5.5% of the quota? If not, then I still don't understand population play.

Any system that is codified and objective will have cusps that one can take advantage of. Think about all the souls looking for the cusps in the IRS code this time of year. The whole purpose of the Pareto test is to insure that a single game-playing mapper won't knock out reasonable contenders. The humans reviewing the contenders can bring other judgements to bear on the Pareto set, but there needs to be a winnowing to avoid pure subjectivity.

Nope, because it is focused on what the population of a CD actually is, and the play might be either as little as zero, or as much as 1%. Maybe I should express this concept in a formula for you.  Why oh why do lawyers and math gurus have so much trouble communicating with each other? I mean, yes, I am not as smart as you, but then again, my IQ is nevertheless considerably above average.

If in the end it is to be made systematic then it will have be in a formula (with text as needed). I'm leery that you are adding a lot of complexity to address what could be a very small universe of situations. I've been trying to keep KISS in mind to the extent possible.

I understand in the case of the MI map, there is no escape from the Detroit UCC penalty, so the issue at least for Train's map and mine is irrelevant. But my concern is more what triggers the macrochop since in other states that might matter, and I certainly would want to penalize an unnecessary macrochop into a multi county UCC, if someone chose to go there in a MI map. Thus I suggested the whole county fix, which perhaps you might wish to address. 

The trigger for a macrochop can either be due to a chop into a selected list of counties (like the ones in UCCs) or it can be due to a population trigger and applied to any county. I'm wary of the first method because I think that will lead to pressure to place chops in counties not on the list. I think we agree that is not a desirable feature.

I didn't follow that there was a specific fix proposed. If it is something that can be made systematic it can be investigated. I still haven't quite seen the problem that would be fixed either.

The image to the left is a macrochop. The one to the right is not.

We don't disagree about those pictures since my definition would conclude the same, but I don't think that's what you are driving at. A macrochop is not a property of a chop, but of a county or other geographic unit that has been chopped. Are you suggesting that macrochops can only apply to the counties in a UCC? If so, what is the trigger and how do you ameliorate the pressure to dump all chops onto small counties.

[Torie]

I'm done for the night. The only thing that is clear at this point, is that we are both incredibly stubborn men. You love KISS, but have a zillion highways in play for macro-chopped counties for purposes of the erosity score? LOL. My little fixes are kindergarten stuff by comparison. I still have some question outstanding that have not been answered. Perhaps another time.

This cusp stuff pops up more than you perhaps think btw. York township in DuPage was cusp city. And getting rid of I-chops in favor of microchops is also cusp city. Really.

[muon2]

I'm done for the night. The only thing that is clear at this point, is that we are both incredibly stubborn men. You love KISS, but have a zillion highways in play for macro-chopped counties for purposes of the erosity score? LOL. My little fixes are kindergarten stuff by comparison. I still have some question outstanding that have not been answered. Perhaps another time.

This cusp stuff pops up more than you perhaps think btw. York township in DuPage was cusp city. And getting rid of I-chops in favor of microchops is also cusp city. Really.

I thought I had given up on microchops, and I never invoked them as part of any suggestions on train's or your MI offerings.

I'm not wild about the profusion of highways due to macrochops, but I haven't found a better method to address erosity in urban counties. What I am using is easy to code into an algorithm to check plans since the links are fixed before the maps are drawn. Kent has been easy to measure after a lengthy one-time investment of time. Still I'd love to find a better alternative.

[muon2]

I'd like to roll back part of the discussion, so I can see where there is agreement and where questions need to be resolved.

At the level of someone looking at the two MI plans and not knowing any detail did the non-political scores seem reasonable relative to each other?
train: Inequality 10, chop 17, erosity 129
Torie: Inequality 10, chop 19, erosity 108

Let's set aside microchops, since they did not come into play for the MI maps. Perhaps they will return if a need arises.

Much of the detailed discussion was on macrochops and their effect on chops and erosity. My goals for them were the following:
=A measure for erosity that treats small scale erosity in urban areas the same way as large scale erosity in rural areas.
=A measure that could be coded in a straightforward way into software like DRA and doesn't change for different maps, for example the links between counties form a table that is known well in advance of the Census data, and the Kent links also become a table in software.
=A mechanism to determine if subunits should have subunits considered within them (in MI that means Detroit, but other states aren't as clean as MI - see IL).

A big part of the macrochop mechanism is the threshold to trigger it. Here are the features I was seeking.
=A threshold to determine what areas are sufficiently urban to warrant special treatment.
=A threshold that favors smaller chops over bigger chops.
=A threshold that doesn't particularly favor placing chops in small counties over large counties.

The issues are both whether these all these goals are correct and what should be implemented to achieve them.

The other area of significant discussion was for the implementation of UCCs. We have a detailed description of the UCCs thanks to jimrtex, and they include both multi-county and single county UCCs. In this implementation the following things were true:
=Chops in multi-county UCCs got higher scores over a base value depending on the excess number of districts.
=Chops in multi-county UCCs would count double if they chopped a county and were sufficiently large.
=Chops in multi-county UCCs could not count double if they otherwise maintained whole counties.
=Chops in single-county UCCs could not count double, but could trigger greater erosity if a macrochop was present.
=Avoiding chops in UCCs smaller than a single district could be rewarded with lower erosity (for example Lansing in MI).
=The threshold to determine if a chop could count double was set at the same level as the macrochop to avoid introducing a separate threshold from the one used to trigger the use of subunits to measure erosity.

[muon2]

Since these definitions didn't make it out of the commission, I thought I should copy them here as well.

Definition: Chop. A single chop is the division of a geographic unit between two districts. A second chop divides the unit between three districts. In general the number of chops is equal to the number of districts in that unit less one.

Definition: Chop size. In units with a single chop, the size of a chop is the population of the smaller district within the unit. For districts with more than one chop, chop sizes are measured in order from the smallest populated district in the unit up to but not including the district with the largest population in the unit.

And I'll add these,

Definition: Total chop size. The total chop size of a geographic unit is the sum of the sizes of the chops of that unit. In units with one chop, the total chop size must be less than or equal to half the population of the unit. In units with more than one chop, it is possible that the chop size is greater than half the population of the unit.

Definition: Fragment. A fragment is a contiguous area of a district within a geographic unit. A district may have more than one fragment in a unit if such fragments are discontiguous. A chop may create discontiguous fragments, yet still count as one chop.

And this was the definition of macrochop I used.

Definition: Macrochop. A macrochop is when the total chop size of a geographic unit exceeds of 5.0% of the quota. When a macrochop of a county occurs, the subunits of the county must be considered as if they were units as well. Macrochops may only apply to units with a population of more than 5% of the quota. A single chop can only create a macrochop in units with more than 10% of the quota. A macrochop always exists in units with more than 105% of the quota.

[Torie]

Thanks for the clarification of the macrochop thing. I understand now that the I-chop of Lapeer did not cause the roof to fall in. But what I question is the double chop penalty for each and every macro-chop of counties within a UCC. It seems to me that perhaps there should be an extra chop penalty for a macrochop impinging into a UCC, and other than that, macrochops within a UCC should just count as ordinary chop penalties, albeit creating an extra chop penalty for I chops of subunits. Dealing with erosity in macro-chopped counties remains an open question, along with the global issue of micro-chop penalties (which should be smaller penalties in all events, it is just a matter of whether there should be a penalty at all). I think that needs work.

In any event, playing the Muon2 game, I assume the map below knocks Train's out of the box, because I lose the double chop penalty for both Clinton and Kent counties, at the cost of an additional freebie microchop, at least vis a vis the chop score, thus tying Train's chop score. The map presumably has a higher erosity score than my other one, but there I beat Train's score by large margin, so I have room to spare. Which raises the issue of whether where a map on one metric beats another by a large score, and is very close to a competing map on another metric, whether both should still survive the pareto optimality test. Is it worth quite a bit more erosity to lose one macro-chop?

Thanks for the post above Mike. I will think about it when I have time. I hope you will sincerely consider my population play fix with respect to a macrochop within a county, and not blow it off. I think it is a needed and necessary fix myself, to slow down the game playing, and making maps more erose to the eye, or doing microchops, at in addition the potential the cost of greater population in equality.

MI Torie 2015B

 

[traininthedistance]

because I lose the double chop penalty for both Clinton and Kent counties, at the cost of an additional freebie microchop, at least vis a vis the chop score, thus tying Train's chop score.

Objection, your honor.  I am not on board with any chops being "freebies".

[Torie]

because I lose the double chop penalty for both Clinton and Kent counties, at the cost of an additional freebie microchop, at least vis a vis the chop score, thus tying Train's chop score.

Objection, your honor.  I am not on board with any chops being "freebies".

Yes, I quite agree, and since my map has one micro-chop, and yours has none, that "saves" you map from biting the dust, if micro-chops are given a half point penalty (as I think they should).  But alas you still lose with this micro-chopless wonder:  

MI Torie 2015C

[traininthedistance]

Yes, I quite agree, and since my map has one micro-chop, and yours has none, that "saves" you map from biting the dust, if micro-chops are given a half point penalty (as I think they should).  But alas you still lose with this micro-chopless wonder:  

This despite the fact that your map has– to the naked eye– four chops outside of the Detroit UCC, and mine only has three.  I somehow doubt the public square, as you are so fond of putting it, would have an easy time following.  Very much a "gameable" situation, those "i-chops", n'est-ce pas?

In any case, I'll have a new map forthcoming soon which gets the chop count even lower.

[muon2]

Well this part I do like. One of my desires is to crowdsource the development of maps, where people see plans as they are posted and work to improve them. I think that provides the utmost in transparency and public input to the process.

I admit I do prefer two small chops to one macrochop. I think that is driven by my observation that large counties can have their vote diluted or used to dilute other areas by deeply chopping them. Setting a policy goal that smaller chops are preferred tends to keep counties at their natural voting strength. Making that policy based on a hard cut helps defend the use of that policy to allow for greater inequality, since as I read Tennant it's the clear, concrete policy of WV that allowed for deviations from exact equality.

Speaking of inequality, Torie's latest offering has a range of 5983 which translates to an INEQUALITY of 11. In terms of Pareto, it doesn't knock out the earlier maps that have INEQUALITY of 10. I'll let Torie and train debate whether that's good for flexibility or not.

[traininthedistance]

Well this part I do like. One of my desires is to crowdsource the development of maps, where people see plans as they are posted and work to improve them. I think that provides the utmost in transparency and public input to the process.

I admit I do prefer two small chops to one macrochop. I think that is driven by my observation that large counties can have their vote diluted or used to dilute other areas by deeply chopping them. Setting a policy goal that smaller chops are preferred tends to keep counties at their natural voting strength. Making that policy based on a hard cut helps defend the use of that policy to allow for greater inequality, since as I read Tennant it's the clear, concrete policy of WV that allowed for deviations from exact equality.

Speaking of inequality, Torie's latest offering has a range of 5983 which translates to an INEQUALITY of 11. In terms of Pareto, it doesn't knock out the earlier maps that have INEQUALITY of 10. I'll let Torie and train debate whether that's good for flexibility or not.

Well, I obviously have a rosier view of inequality as a co-equal factor with chops and erosity than Torie does– I take OMOV pretty seriously and think we should strive to get as close as practical.  Our disagreement on that point will be pretty predictable.

As for two small chops vs. one macro chop, I'd think that releasing the munis for a macrochop (thereby incurring a big erosity penalty) should be considered sufficient incentive to avoid the issues you worry about, even without double-counting things.

But, on any case, here's a new map that if I've calculated correctly cuts down two chops.  Rearranging things between the Flint, Tri-Cities, and Lansing districts allowed me to turn the Saginaw macrochop into a non-macro chop, at the expense of I think one erosity point in the Lansing district?  Also, by taking advantage of the rule you pointed out w/r/t Kent, I had sufficient flexibility to clean up the lines in Wayne County and split Detroit entirely on community lines, so not only does the chop count go down but presumably erosity as well.

MI train 2015B




Districts 13 and 14 are 51.4 and 51.1% BVAP; inequality ranges from -2555 (District 6, unchanged) to +2893 (District 9), so inequality is still 10.

[Torie]

Well I dealt with the inequality issue by switching out townships in Clinton, and at the cost of grotesque erosity (but I can afford that probably still, even though my map to win gets uglier with each iteration (boo!), I lost the hood chop in Detroit in favor of a micro-chop of Hamtramck.  (Yes, the BVAP for MI-13 drops to 49.1%, but that is still probably legal, inasmuch as there are a fair number of non citizen and/or non voting Hispanics in the CD), so blacks will still be casting a majority of the votes. So assuming micro-chops are freebies, I move back into the lead!  

But yes, this exercise hopefully will persuade Mike that freebie micro-chops are a dog that just won't hunt. It's dead, dead, dead, no matter how hard he tries to give EMR treatment to reanimate it.

MI Torie 2015D


Anyway, this illustrates again a problem with the pareto optimality regime. A map can win with a massive dose of additional erosity, just in order to lose a chop or two. That is what we are seeing here. I am losing a ton of erosity points, just to get rid of two or three chops, including in one iteration, a fair amount of erosity just to get rid of one micro-chop, and in the case of Detroit, massively more erosity (that should not be rewarded). So a total score concept makes some sense, or to be pareto optimal, the variation in the total score cannot exceed a certain amount.

[jimrtex]

I'd like to roll back part of the discussion, so I can see where there is agreement and where questions need to be resolved.

At the level of someone looking at the two MI plans and not knowing any detail did the non-political scores seem reasonable relative to each other?
train: Inequality 10, chop 17, erosity 129
Torie: Inequality 10, chop 19, erosity 108

Let's set aside microchops, since they did not come into play for the MI maps. Perhaps they will return if a need arises.

Much of the detailed discussion was on macrochops and their effect on chops and erosity. My goals for them were the following:
=A measure for erosity that treats small scale erosity in urban areas the same way as large scale erosity in rural areas.
=A measure that could be coded in a straightforward way into software like DRA and doesn't change for different maps, for example the links between counties form a table that is known well in advance of the Census data, and the Kent links also become a table in software.
=A mechanism to determine if subunits should have subunits considered within them (in MI that means Detroit, but other states aren't as clean as MI - see IL).

A big part of the macrochop mechanism is the threshold to trigger it. Here are the features I was seeking.
=A threshold to determine what areas are sufficiently urban to warrant special treatment.
=A threshold that favors smaller chops over bigger chops.
=A threshold that doesn't particularly favor placing chops in small counties over large counties.

How about a process that uses decomposition and iteration?  This avoids the issue of mixed chop sizes.

Round 1, Whole State division into regions.

(a) Identify whole-county regions that have a population approximately equal to an integer number of districts (say 5% x sqrt(N)).   Counties in a region must be connected.
(b) Each UCC must be contained within one region.
(c) More regions (ie more single-district regions) is better.
(d) If local equality can be improved by shifting a single county without breaking connectivity it must be shifted.
(e) Inequality can be measured
    (i) total deviation; or
    (ii) total shift count, the population that would have to be moved in the minimal number of
         shifts (number regions - 1) to bring all regions to either full equality or 0.5% equality.
(f) Erosity can be measured using simplified boundaries.  Distance is measured node to node, where a node is either a junction of three or more county boundaries, or two county boundaries and the external boundary of the state (states trimmed to the Great Lakes or ocean).

Round 2) Refinement of inter-region boundaries.

(a) Each pair of districts is treated independently.
(b) Shift direction identifies which side of the boundary the chop occurs on.
(c)  Adjustment must be identified shift population from Round 1, +/- 0.25% of quota.
(d) Chop must be within one county, but any county on the boundary that is connected to the other district may be chopped.
(e) No MCDs may be cut.  If shifting a MCD improves equality without breaking contiguity it must be shifted.
(f)  Erosity is measured by simplified internal distance.  Distance along county lines is excluded.
(g) If necessary to split an MCD, then this would be a separate process.  It is preferable to split a county that does not require an MCD split, with one that does.

Round 3) Definition of districts in multi-district regions.

(a) Large cities (eg Chicago and Detroit) may be treated as counties.  Isolated areas of the remnant county may be treated as part of the city-county, or as separate counties.  For example, Hamtramck, Highland Park, and the Grosse Pointe's could be considered part of the Detroit unit, rather than the Wayne unit.   On the other hand, Chicago might divide the remnant of Cook County into two units.
(b) Larger MCDs (say greater than 10% of a quota) shall be split into subunits.
(c) Districts will be defined using subunits (smaller MCDs, and subunits of larger MCDs).
(d) Between districts, at most one MCD may be divided, even if the division uses subunits.
(e) Districts may not multi-span counties (eg only one district may cross the Oakland-Macomb boundary, one between Oakland-Wayne, one between Macomb-Wayne).  The treatment of Detroit and Wayne as separate units does not make an exception (eg Oakland-Wayne and Oakland-Detroit).
(f) Erosity is measured  by internal simplified distance.  Distance along county lines does not count.
(g) District populations should be within 0.5% of quota.   If this is not possible, then subunits would be split in a 4th round.

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Within a UCC, chops up to a threshold are free. 

A cut along county lines within a UCC is still a chop.  A UCC chop does not count as a county chop.

(a) Cutting Clinton is a chop of the Lansing UCC, but not a chop of Clinton.
(b) Cutting along the southern boundary of Clinton is a chop of the Lansing UCC.
(c) Cutting Calhoun is a chop of the Battle Creek UCC, but not a chop of Calhoun.
(d) Cutting a non-UCC county counts as chop of that county.

Chops such as (a), (b), and (d) will tend to be favored because they are smaller.

[traininthedistance]

Okay... let's back this up for a second.  I think there's a fast one being pulled here.

How many chops, exactly, does this map have?  Leave aside the Detroit UCC for a moment (the chops inside it, plus the necessary chop of Lapeer- just ignore that part of the map for a second), there are four chopped counties, and the Grand Rapids UCC is by necessity chopped.  Torie's decision to make the Kent chop a non-macro chop at the expense of putting a chop into Clinton should, certainly, decrease erosity since it means the munis don't get released.

But... uh... that doesn't decrease chops.  And shouldn't it actually increase chops even more, since the Lansing UCC is, in fact, also being chopped here?  So outside of the Detroit UCC (which let's hold constant for a moment), Torie has four county chops and two UCC chops, for a total of six whereas my map has a total of four: the Grand Rapids UCC and only three county chops.

...

EDIT: I see part of it; from muon's scoring of Torie's last map, apparently a UCC chop doesn't actually count as a chop unless it's a macrochop?  That's a tres gameable hitch that I don't think I like one bit.  And still only decrements Torie's chop count by one anyway, not two.

[Torie]

I have only four chops, because yes, neither Grand Rapids nor the Lansing UCC's are macro-chopped Lansing per my first map should not have been deemed macro-chopped anyway, because of the population pad issue I am arm wrestling with Mike about, but I digress). You have four chops, three counties, plus a macro-chop of the Grand Rapids UCC. I agree with a one penalty point for a macro-chop of any UCC I think (well one penalty point per macrochop from a CD impinging on the UCC from outside containing an adjacent whole county (although such multi macrochops are unlikely to happen)). Why? Because if not, UCC's, with their big populations, became vulnerable to being a macro-chop dumping ground, because you have so much flexibility when using them, to get rid of smaller chops elsewhere (that was the game I initially played with my Kent macrochop, because it was useful to at once make MI-02 and MI-04 chop-less (MI-04 on its west side), while also reducing erosity). That is my sense of it. Indeed, a macro-chop of any county (unless it is internal within the a multi-county UCC (that should get just one penalty point like any other county), should probably be a two pointer, although almost all counties capable of being macro-chopped will be in  a UCC, since if a single county, that means it needs a population of in excess of 70,000, and probably more like 100,000+, since with 70,000 or so, to be a macro-chopped it would need to be just about exactly bifurcated, which is unlikely to happen.  

[muon2]

I'd like to roll back part of the discussion, so I can see where there is agreement and where questions need to be resolved.

At the level of someone looking at the two MI plans and not knowing any detail did the non-political scores seem reasonable relative to each other?
train: Inequality 10, chop 17, erosity 129
Torie: Inequality 10, chop 19, erosity 108

Let's set aside microchops, since they did not come into play for the MI maps. Perhaps they will return if a need arises.

Much of the detailed discussion was on macrochops and their effect on chops and erosity. My goals for them were the following:
=A measure for erosity that treats small scale erosity in urban areas the same way as large scale erosity in rural areas.
=A measure that could be coded in a straightforward way into software like DRA and doesn't change for different maps, for example the links between counties form a table that is known well in advance of the Census data, and the Kent links also become a table in software.
=A mechanism to determine if subunits should have subunits considered within them (in MI that means Detroit, but other states aren't as clean as MI - see IL).

A big part of the macrochop mechanism is the threshold to trigger it. Here are the features I was seeking.
=A threshold to determine what areas are sufficiently urban to warrant special treatment.
=A threshold that favors smaller chops over bigger chops.
=A threshold that doesn't particularly favor placing chops in small counties over large counties.

How about a process that uses decomposition and iteration?  This avoids the issue of mixed chop sizes.

Round 1, Whole State division into regions.

(a) Identify whole-county regions that have a population approximately equal to an integer number of districts (say 5% x sqrt(N)).   Counties in a region must be connected.
(b) Each UCC must be contained within one region.
(c) More regions (ie more single-district regions) is better.
(d) If local equality can be improved by shifting a single county without breaking connectivity it must be shifted.
(e) Inequality can be measured
    (i) total deviation; or
    (ii) total shift count, the population that would have to be moved in the minimal number of
         shifts (number regions - 1) to bring all regions to either full equality or 0.5% equality.
(f) Erosity can be measured using simplified boundaries.  Distance is measured node to node, where a node is either a junction of three or more county boundaries, or two county boundaries and the external boundary of the state (states trimmed to the Great Lakes or ocean).

Round 2) Refinement of inter-region boundaries.

(a) Each pair of districts is treated independently.
(b) Shift direction identifies which side of the boundary the chop occurs on.
(c)  Adjustment must be identified shift population from Round 1, +/- 0.25% of quota.
(d) Chop must be within one county, but any county on the boundary that is connected to the other district may be chopped.
(e) No MCDs may be cut.  If shifting a MCD improves equality without breaking contiguity it must be shifted.
(f)  Erosity is measured by simplified internal distance.  Distance along county lines is excluded.
(g) If necessary to split an MCD, then this would be a separate process.  It is preferable to split a county that does not require an MCD split, with one that does.

Round 3) Definition of districts in multi-district regions.

(a) Large cities (eg Chicago and Detroit) may be treated as counties.  Isolated areas of the remnant county may be treated as part of the city-county, or as separate counties.  For example, Hamtramck, Highland Park, and the Grosse Pointe's could be considered part of the Detroit unit, rather than the Wayne unit.   On the other hand, Chicago might divide the remnant of Cook County into two units.
(b) Larger MCDs (say greater than 10% of a quota) shall be split into subunits.
(c) Districts will be defined using subunits (smaller MCDs, and subunits of larger MCDs).
(d) Between districts, at most one MCD may be divided, even if the division uses subunits.
(e) Districts may not multi-span counties (eg only one district may cross the Oakland-Macomb boundary, one between Oakland-Wayne, one between Macomb-Wayne).  The treatment of Detroit and Wayne as separate units does not make an exception (eg Oakland-Wayne and Oakland-Detroit).
(f) Erosity is measured  by internal simplified distance.  Distance along county lines does not count.
(g) District populations should be within 0.5% of quota.   If this is not possible, then subunits would be split in a 4th round.

I like this as an algorithm to design a plan, but I tried something similar a year or so ago and had difficulty turning it in to a metric to judge plans. At a minimum it requires the mapper to submit their regions with their plan, and that has the downside of potentially disqualifying plans that were designed without regions. My sense is that isn't as good for public participation.

[traininthedistance]

I have only four chops, because yes, neither Grand Rapids nor the Lansing UCC's are macro-chopped. You have four chops, three counties, plus a macro-chop of the Grand Rapids UCC. I agree with a one penalty point for a macro-chop of any UCC I think. Why? Because if not, UCC's, with their big populations, became vulnerable to being a macro-chop dumping ground, because you have so much flexibility when using them, to get rid of smaller chops elsewhere (that was the game I initially played with my Kent macrochop, because it was useful to at once make MI-02 and MI-04 chop-less (MI-04 on its west side), while also reducing erosity). That is my sense of it. Indeed, a macro-chop of any county (unless it is internal within the a multi-county UCC (that should get just one penalty point like any other county), should probably be a two pointer, although almost all counties capable of being macro-chopped will be in  a UCC, since if a single county, that means it needs a population of in excess of 70,000, and probably more like 100,000+, since with 70,000 or so, to be a macro-chopped it would need to be just about exactly bifurcated, which is unlikely to happen.  

Your Grand Rapids UCC is, in fact, macrochopped, even if Kent itself is not macrochopped.  Remember that the UCC starts out as a super-county; a Grand Rapids macrochop is literally unavoidable.

I would argue, in addition, that your Clinton chop ought to count as a chop of the Lansing UCC, as well. Isn't that the whole point of UCCs in the first place?

[muon2]

I have only four chops, because yes, neither Grand Rapids nor the Lansing UCC's are macro-chopped. You have four chops, three counties, plus a macro-chop of the Grand Rapids UCC. I agree with a one penalty point for a macro-chop of any UCC I think. Why? Because if not, UCC's, with their big populations, became vulnerable to being a macro-chop dumping ground, because you have so much flexibility when using them, to get rid of smaller chops elsewhere (that was the game I initially played with my Kent macrochop, because it was useful to at once make MI-02 and MI-04 chop-less (MI-04 on its west side), while also reducing erosity). That is my sense of it. Indeed, a macro-chop of any county (unless it is internal within the a multi-county UCC (that should get just one penalty point like any other county), should probably be a two pointer, although almost all counties capable of being macro-chopped will be in  a UCC, since if a single county, that means it needs a population of in excess of 70,000, and probably more like 100,000+, since with 70,000 or so, to be a macro-chopped it would need to be just about exactly bifurcated, which is unlikely to happen.  

The Grand Rapids UCC is two counties and larger than a CD, so it is always macrochopped. The individual counties in that UCC are not necessarily macrochopped. It's a distinction that only comes into play for the Lansing UCC in MI.

Recall these are the implementation effects of the UCCs in this model.

=Chops in multi-county UCCs got higher scores over a base value depending on the excess number of districts.
=Chops in multi-county UCCs would count double if they chopped a county and were sufficiently large.
=Chops in multi-county UCCs could not count double if they otherwise maintained whole counties.
=Chops in single-county UCCs could not count double, but could trigger greater erosity if a macrochop was present.
=Avoiding chops in UCCs smaller than a single district could be rewarded with lower erosity (for example Lansing in MI).
=The threshold to determine if a chop could count double was set at the same level as the macrochop to avoid introducing a separate threshold from the one used to trigger the use of subunits to measure erosity.

I personally think that a whole county chop is better than a partial county chop, and I think that most public viewers would see it that way, too. But I also think a small chop is better than a big chop. What this system does is balance those two such that a whole county chop into a UCC is equal to a small chop into a UCC county. A large chop that is not whole county is judged to be worse than either of those other alternatives and gets a higher score.

I think that's a good balance, but others may not. What weight would you give to those three scenarios?

[traininthedistance]

Recall these are the implementation effects of the UCCs in this model.

=Chops in multi-county UCCs got higher scores over a base value depending on the excess number of districts.
=Chops in multi-county UCCs would count double if they chopped a county and were sufficiently large.
=Chops in multi-county UCCs could not count double if they otherwise maintained whole counties.
=Chops in single-county UCCs could not count double, but could trigger greater erosity if a macrochop was present.
=Avoiding chops in UCCs smaller than a single district could be rewarded with lower erosity (for example Lansing in MI).
=The threshold to determine if a chop could count double was set at the same level as the macrochop to avoid introducing a separate threshold from the one used to trigger the use of subunits to measure erosity.

I personally think that a whole county chop is better than a partial county chop, and I think that most public viewers would see it that way, too. But I also think a small chop is better than a big chop. What this system does is balance those two such that a whole county chop into a UCC is equal to a small chop into a UCC county. A large chop that is not whole county is judged to be worse than either of those other alternatives and gets a higher score.

I think that's a good balance, but others may not. What weight would you give to those three scenarios?

Basically I am on board with those effects with the exception that I would strike the "and were sufficiently large" clause from part 2.  I'm fine with macrochops triggering erosity penalties (and thereby being discouraged), but I do think that for chop counts (single or double), the KISS principle of "a chop is a chop is a chop" is the road I'd take.

[traininthedistance]

Anyway, this illustrates again a problem with the pareto optimality regime. A map can win with a massive dose of additional erosity, just in order to lose a chop or two. That is what we are seeing here. I am losing a ton of erosity points, just to get rid of two or three chops, including in one iteration, a fair amount of erosity just to get rid of one micro-chop, and in the case of Detroit, massively more erosity (that should not be rewarded). So a total score concept makes some sense, or to be pareto optimal, the variation in the total score cannot exceed a certain amount.

This doesn't faze me, in large part because chops just fundamentally bother me a lot more than erosity.  And, also, because a lot of that erosity is, to be frank, artifical erosity, in particular the fact that a fairly straight line within Oakland which passes by small-sized towns and boros is more "erose" than something which heat-seeks the larger square towns, even if the actual squiggliness is not appreciably different.  (Also, outside of metros, when district lines are cut across a perfect grid of counties rather than offset rows of squares).

What I do take as a potential problem, though, and this is a backtrack from other things I've said earlier, is trying to use inequality as a co-equal factor and then gerrymandering to all hell with perfectly equal population.  That would be an issue, and yeah, does present an issue with the inequality measures.  What to do about that, other than just accede to your idea that inequality below a bright-line threshold just shouldn't matter?

This is perhaps a bit of a kludge, but let me float this trial balloon: perhaps, the inequality and erosity scores be combined into one number which can then be set against chops (which I continue to consider the most important factor in my mapmaking) in a two-prong pareto test.  How to balance the two would take some trial and error; I would certainly give erosity the lion's share of the impact but exactly how much is an open question.

[muon2]

Recall these are the implementation effects of the UCCs in this model.

=Chops in multi-county UCCs got higher scores over a base value depending on the excess number of districts.
=Chops in multi-county UCCs would count double if they chopped a county and were sufficiently large.
=Chops in multi-county UCCs could not count double if they otherwise maintained whole counties.
=Chops in single-county UCCs could not count double, but could trigger greater erosity if a macrochop was present.
=Avoiding chops in UCCs smaller than a single district could be rewarded with lower erosity (for example Lansing in MI).
=The threshold to determine if a chop could count double was set at the same level as the macrochop to avoid introducing a separate threshold from the one used to trigger the use of subunits to measure erosity.

I personally think that a whole county chop is better than a partial county chop, and I think that most public viewers would see it that way, too. But I also think a small chop is better than a big chop. What this system does is balance those two such that a whole county chop into a UCC is equal to a small chop into a UCC county. A large chop that is not whole county is judged to be worse than either of those other alternatives and gets a higher score.

I think that's a good balance, but others may not. What weight would you give to those three scenarios?

Basically I am on board with those effects with the exception that I would strike the "and were sufficiently large" clause from part 2.  I'm fine with macrochops triggering erosity penalties (and thereby being discouraged), but I do think that for chop counts (single or double), the KISS principle of "a chop is a chop is a chop" is the road I'd take.

So you would judge all three scenarios equally, right? The original UCC surcharge idea (ca 2013) would cost any plan that chopped Clinton 2 points. My model reduced that penalty for small chops of Clinton, but left the large chop penalty at 2. To meet what I think you are saying for Lansing I can imagine a statement like this: "The UCC penalty only exists if there is not another county chop penalty that would give that same result."

If try to apply that to the other UCC's I foresee difficulties. Consider the GR UCC. My statement would imply that a clean split along the Kent/Ottawa line counts the same as a chop through Kent. What if the plan chops both Kent and Ottawa, between three districts - there would be already 2 county chops, so how does one assess a penalty for the extra district in the UCC? That would seem like the UCC minimum of two really didn't have any effect.

Now consider the Detroit UCC. I can draw a plan that has the same number of divisions of each of the counties as the offerings here so far, yet has 7 districts instead of 6. Oakland already has one chop more than the minimum. Given that, how does one determine whether the county chop penalty eliminates the need for an extra UCC penalty?

[Torie]

Oh, one penalty point for the chop off of the whole county of Ottawa (I keep forgetting that is in the UCC), and a second two pointer if Kent is also macro-chopped? I think that is OK.

I go the opposite way with chops - they are all different, but all in some degree bad, and it should affect the chop count.

My regime tentatively:

Chops:

0.25 points for a microchop of a subunit

0.5 points for an I chop of a subunit, or a microchop of a county.

1.0 points for an I chop of a county, or an I chop or macrochop of a county which is between counties in a UCC, or a macrochop of a subunit.

In addition to the points above, an additional 1.0 points for each macro-chop into a UCC [county (other than internal county macrochops within a multi-county UCC]), or the severing of a whole county from a UCC.

For county or subunit chops, only one is allowed per boundary between CD's.

No traveling chops are allowed.

Erosity:

No penalty for a microchop, an I chop creates a quasi county, putting another highway into play (two potentially if in a "bad" corner and big enough in area), and a macrochop puts subunit highways into play, but maybe with a maximum number of penalty points, so it does not swamp the overall erosity score for the whole state, which is a particular problem when there are a lot of small subunits  (maybe a half point per additional highway put into play, with maybe a maximum of say 4 penalty points (the exact number is an empirical matter of what makes for better maps, with the point being to encourage clean macrochops rather than jagged ones, so with clean macro-chops, we want the point count to be considerably less than 4, say typically 1.5 to 2 points total, the idea being that a clean chop gets maybe only 40% as many points as a butt ugly one). There is a potentially serious problem with gerrymandering when it comes to messy macrochops (again more in play perhaps with smaller subunits), that needs some serious punishment if one goes there.