Chops and Erosity - Great Lakes Style

[Torie]

Yes, I basically agree, but since we always count county chops, to go beyond that, the issue is not how many CD's are in the UCC per se, but how much population has been fanned out. So many small chops (each penalized of course in the ordinary way), should for this narrow purpose, arguably should be treated the same as one larger chop, focusing on the amount of the population involved. Make sense? To me, there is no policy reason to hate Jimtex's first map versus mine (where I accidentally did a macrochop, given that you grant no population play, and I dropped the ball), simply because he chose to do two smaller chops into the Lansing UCC, versus my bigger one chop, thereby garnering a two point penalty rather than the ordinary one. In other words, both of our maps should have had the same chop score outside the Detroit UCC (4 county chops plus two macrochops), or with my population play regime in effect, 5 chops total.  

In Detroit, an invading chop (or chops  that collectively were a macro-chop) would generate an extra point penalty beyond the chops themselves, as would a smaller chop in, that generated a macrochop out (if you count all macrochops as earning an additional penalty point).

Where I am going here, is to limit the UCC concept to multi county UCC's, which causes the number of chops into the UCC to be added up for population purposes, to ascertain if a macrochop is involved (maybe giving one point penalty per 5%), and deem for this purpose a whole county severance as itself a chop, and having no macrochop penalty for macrochops internal to the UCC. A macrochop (or multi chops that add up to a macrochop) of any county not internal to a multi county UCC, would generate an extra point penalty.

By the way, for inter county erosity purposes (internal county erosity tests remain a work in progress), I am liking your road connectivity proxy more and more. I think it really works. At least it does for the square county zone of this nation.

[muon2]

Yes, I basically agree, but since we always count county chops, to go beyond that, the issue is not how many CD's are in the UCC per se, but how much population has been fanned out. So many small chops (each penalized of course in the ordinary way), should for this narrow purpose, arguably should be treated the same as one larger chop, focusing on the amount of the population involved. Make sense? To me, there is no policy reason to hate Jimtex's first map versus mine (where I accidentally did a macrochop, given that you grant no population play, and I dropped the ball), simply because he chose to do two smaller chops into the Lansing UCC, versus my bigger one chop, thereby garnering a two point penalty rather than the ordinary one. In other words, both of our maps should have had the same chop score outside the Detroit UCC (4 county chops plus two macrochops), or with my population play regime in effect, 5 chops total.  

In Detroit, an invading chop (or chops  that collectively were a macro-chop) would generate an extra point penalty beyond the chops themselves, as would a smaller chop in, that generated a macrochop out (if you count all macrochops as earning an additional penalty point).

Where I am going here, is to limit the UCC concept to multi county UCC's, which causes the number of chops into the UCC to be added up for population purposes, to ascertain if a macrochop is involved (maybe giving one point penalty per 5%), and deem for this purpose a whole county severance as itself a chop, and having no macrochop penalty for macrochops internal to the UCC.  

I get what you are saying, but I think it is a lot harder than you may think. I don't know if you read through the link in the OP that shows how the UCC concept originated for our MI maps. The original rule is quite simple - treat UCCs as an extra object in which to count districts, independent of the county chops. Each modification to that rule adds complexity, so we should see if the complexity is worth the effort in getting the maps "right".

For example, you use the phrase "invading chop" for the Detroit UCC and say it should get a penalty beyond the chop penalty, but that is exactly what the original rule does. Should an invading chop in the GR district get a penalty beyond the chop penalty? I think it should, just like in Detroit, or the UCC idea really doesn't hold any water.

That brings us to Lansing. Should an invading chop get a penalty beyond the chop penalty? The original rule says yes, just like Detroit and GR. I offered an amendment that says it only gets the extra penalty if it's a macrochop which I have applied in this thread.

One could also say it only gets the extra penalty if it's a whole county chop, though that would have to be carefully defined for instances where there was more than one chop into the Lansing UCC. If you go with this latter path, then you are saying Lansing and Calhoun (or any other single county UCC) are treated with the same rule, to wit only whole county chops in single district UCCs incur a UCC penalty. That draws the distinction based on the population of the UCC rather than the number of counties in the UCC as we currently operate the rule.

[Torie]

Yes, the GR UCC "invasion" should get an extra chop penalty; in fact any county that is macro-chopped not internal to a UCC should get such an extra penalty point.

I don't mind, and favor, given this, a penalty point for a macrochop of the Lansing UCC, I just don't like giving two extra penalty points, if the macrochopo is severed into two I chops, like Jimtex did. In this aspect, his map from a policy standpoint, is just as good as mine (where mine had just one macrochop, and had an I chop elsewhere, so we each had four ex-Detroit county chops total). If his map had two chops into the Lansing UCC each of which were a macro-chop, then he earns an extra macrochop penalty point vis a vis my map,  in addition to the two county chops, as would be the case with any county so double chopped.

So the sole purpose of UCC's is with respect to multi county UCC's, with their effect limited to viewing them as one county for purposes of totaling the population involved with the chops (even if in separate counties within the UCC) to see if they rise to the level of a macrochop, on the one hand, and allow internal macrochops on the other without generating an extra penalty point (consistent with the one county theme for this purpose).

One might argue my suggested system is simpler and easier to apply than yours, not harder.

This Lansing thing is great, because it has really fleshed this issue out. Go Lansing!

[muon2]

Yes, the GR UCC "invasion" should get an extra chop penalty; in fact any county that is macro-chopped not internal to a UCC should get such an extra penalty point.

I don't mind, and favor, given this, a penalty point for a macrochop of the Lansing UCC, I just don't like giving two extra penalty points, if the macrochopo is severed into two I chops, like Jimtex did. In this aspect, his map from a policy standpoint, is just as good as mine (where mine had just one macrochop, and had an I chop elsewhere, so we each had four ex-Detroit county chops total). If his map had two chops into the Lansing UCC each of which were a macro-chop, then he earns an extra macrochop penalty point vis a vis my map,  in addition to the two county chops, as would be the case with any county so double chopped.

So the sole purpose of UCC's is with respect to multi county UCC's, with their effect limited to viewing them as one county for purposes of totaling the population involved with the chops (even if in separate counties within the UCC) to see if they rise to the level of a macrochop, on the one hand, and allow internal macrochops on the other without generating an extra penalty point (consistent with the one county theme for this purpose).

One might argue my suggested system is simpler and easier to apply than yours, not harder.

This Lansing thing is great, because it has really fleshed this issue out. Go Lansing!

I'm still not sold that a single macrochopped Clinton is equivalent to a 2 chop Clinton/Ingham when the two chops add to a macrochop. In past thread others, including you, have suggested that two chops into the same entity is less desirable than those two chops moved to two separate entities. Those comments led to a switch from a fragment counting system to a chop counting system. I recognize that the original context of such statements pertained to counties, but shouldn't it apply to UCC's as well?

OTOH, I would note that the single macrochopped county would incur the erosity hit that happens when subunits come into play. If the two chops in the other arrangement are each less than a macrochop, then county subunits would not come into play and the erosity score would stay lower. I'd be fine with that situation where the two county chop has a higher CHOP but a  lower EROSITY.

Of course Lansing rules. As the OP link shows, it was Lansing that generated the whole UCC idea in the first place.

[Torie]

Good point about the erosity bit, which again brings up the issue of not letting the erosity score be dominated by macrochops. The point about macrochops and the erosity score, is not to punish the hell out of macrochops, beyond the chop penalty, but rather to make the macrochops clean, rather than mischievous. If they are clean, except to the extent they make the CD itself more erose (bearing in mind that erosity in highly populated areas should be evaluated on a zoom basis, they should not be punished further. A nice clean straight line macrochop is just fine. Given the policy issues, the highway proxy might not work very well here, unless we focus on highways involved with jagged chops. That straight line I drew in Oakland for MI-11 certainly did not deserve a host of erosity points. There it was harmless, because there had to be a macrochop under your rules (not mine, because internal UCC county macrochops would not be specially penalized). But suppose it was a Lansing situation, where a macrochop could be avoided. Should the roof fall in on the erosity score because of a clean chop? I don't think so. Addendum:  Hey, how about just adding erosity points to the extent the highway cuts for the zoom exercise are in excess of the minimum number of cuts that would be possible per a zoom analysis for a macrochop of the county of the size the proposed map uses?  Would that not solve the problem?

 I don't think UCC's are the same as counties. They are so much bigger. I don't think folks would fret that if say the Detroit UCC were a bit less than 6 CD's, that there was one chop in Macomb, and another in Livingston, as opposed to just one larger chop into Macomb, with one less chop elsewhere in the state.

Anyway, the policy issues have been nicely elucidated here. That's progress.

[Torie]

Speaking of highway cuts and erosity short of a macrochop, is the map below the best way to limit erosity? Is St. Johns (the county seat) or East Lansing (the partial portion thereof in Clinton), the most populated, the highway node to use for Clinton County? For Kent to Montcalm, do you use the most direct route in terms of mileage to get from the Kent County node of GR to the node of Montcalm, even if it is by minor county roads (close call which route is shorter in this instance)?   Not that it matters necessarily in this instance, but is the node for Montcalm the centrally located county seat of Stanton, or the non centrally located but larger city of Greenville?

[jimrtex]

I messed up.  I switched Mecosta, but used the population of Osceola.  Clare and Mason are slightly too large to improve equality with a simple swap.

This is based on the plan named Train 2015 B, with an adjustment.  As originally proposed, it required a double shift to transport the excess population from Saginaw Bay district to Detroit.  But a transfer of Osceola from Saginaw Bay to Lansing, reduces the difference between those two districts, and permits a direct transfer from Lansing to Detroit.  Overall, the shifted population is 6.6% of a quota.

[muon2]

Speaking of highway cuts and erosity short of a macrochop, is the map below the best way to limit erosity? Is St. Johns (the county seat) or East Lansing (the partial portion thereof in Clinton), the most populated, the highway node to use for Clinton County? For Kent to Montcalm, do you use the most direct route in terms of mileage to get from the Kent County node of GR to the node of Montcalm, even if it is by minor county roads (close call which route is shorter in this instance)?   Not that it matters necessarily in this instance, but is the node for Montcalm the centrally located county seat of Stanton, or the non centrally located but larger city of Greenville?

What I did was take the seat of county government, specifically the building where the board of commissioners meets, and ask Mapquest to find the shortest path between them. I also required that the path be state highways except for the short distances on local roads between the building and the highway. In a full blown system this only has to be done once and then mark which road was used as the link. It can then be used as a reference for all the maps.

I looked at using the largest population center, but I found a definition of a single building to be easier to implement. Population centers have the problem of crossing county lines, so what if the largest center has its city hall in a different county, it greatly complicates what I enter in Mapquest.

[traininthedistance]

My interpretation is that you count the number of districts in the UCC. Whether or not those districts spill into other counties, or even other UCCs doesn't affect the counting within the UCC. Basically, put blinders on and just address each UCC on its own. It's no different than with county chops, where it doesn't matter how many other counties a district extends into, one just focuses on the county in question.

Excellent.  That certainly helps one draw nicer lines in Western PA (take a look at District 4!), if it's okay to have two districts span the UCC boundary.  

To wit:









Salient features:

* Within Philadelphia, all the lines are along ward boundaries.  The portion of PA-8 is a macrochop (as is necessary); the portion of PA-7 is not.  PA-2 is 60% BVAP; PA-1 is minority-majority by total population, but not by VAP.
* Obviously, the split of Allegheny and Berks are macrochops, and the portion of PA-7 in Montgomery is also one– these are all necessary.  Every other chop is an I-chop (though Carbon and Bedford are both in the ~6K range, which is pretty small).
* PA-9, without the roughly ~6K of people from Bedford, is tantalizingly close to being whole counties, as it would be -4,800 or so.  I tried to see if you could get the other deviations low enough such that it could fit into a 1% range, but no dice, not without chops elsewhere. (The combo Lehigh+Northampton+Carbon is just a tiny bit further away, as well.)
* There is, I'm pretty sure, a configuration of districts in the T which would lower inequality at the expense of erosity.  District 3 would even look prettier, but 10 and 5 would be a *lot* worse.  I think it also might have required another chop, or turning the SW I-chops into a macrochop, or something else?  There's a reason I abandoned it.  In any case, I might reconstruct it later but I doubt it would be preferred.
* Really, I think that the general shape of this map is hard to beat, though fine-tuning might still be possible.  The biggest point of contention, obviously, would be whether to split Berks or Lancaster between 6 and 16.  Without exhaustively researching every configuration (the proliferation of tiny boros in PA make infra-county erosity measures a BEAR), the erosity seems similar, and this arrangement should better respect the fact that Berks is part of the Philadelphia CSA, something that isn't technically a part of the UCC framework but IMO deserves consideration somehow.

[traininthedistance]

Oh, hey, here's a better Berks:



I think, if I've counted correctly, the infra-Berks erosity drops from 15 to 14 (though I guess technically that's clawed back by the Montgomery-Berks line now counting twice?), and it looks prettier, and the inequality is even lower!  6 is +255 and 16 is +90.  Of course, under the current scoring there's no reward for getting closer to even for anything except the furthest outliers, which makes that irrelevant.  Should it be irrelevant?  I don't think it should be, though switching to a different inequality measure (perhaps the average of the deviations or something could work?) is not necessarily a hill I care to die on.

[Torie]

What I did was take the seat of county government, specifically the building where the board of commissioners meets, and ask Mapquest to find the shortest path between them. I also required that the path be state highways except for the short distances on local roads between the building and the highway. In a full blown system this only has to be done once and then mark which road was used as the link. It can then be used as a reference for all the maps.

I assume that you mean state or US highways, right?

[muon2]

What I did was take the seat of county government, specifically the building where the board of commissioners meets, and ask Mapquest to find the shortest path between them. I also required that the path be state highways except for the short distances on local roads between the building and the highway. In a full blown system this only has to be done once and then mark which road was used as the link. It can then be used as a reference for all the maps.

I assume that you mean state or US highways, right?

yes

[Torie]

What I did was take the seat of county government, specifically the building where the board of commissioners meets, and ask Mapquest to find the shortest path between them. I also required that the path be state highways except for the short distances on local roads between the building and the highway. In a full blown system this only has to be done once and then mark which road was used as the link. It can then be used as a reference for all the maps.

I assume that you mean state or US highways, right?

yes

Thanks, and is a double chop of a county by one CD banned, or just count as an extra chop. For Kent, it probably pays unless penalized to do a double chop (otherwise one needs to do a microchop of a subunit to get the erosity down, unless microchops are freebies). Granted, the way you use zoom, for macrochopped counties, that itself would probably (maybe not always) add to erosity.

[Torie]

Given that the UCC, county and subunit chops are absolutely the same (just the Detroit hood micro-chop when it comes to subunit chops), I think Jimtex's map version 3 to the left is the winner per Muon2's rules, from a chopped highway county erosity standpoint (and an equality standpoint too), vis a vis the "best" Torie map to the right, because it has one less chopped highway that matters.  Why? Because there apparently is no state highway between Clare and Misaukee counties! Therefore, the maps are tied in highway chops as between MI-01, 02 and 04, rather than the Torie map being ahead by one less highway chop. Thus, that one saved highway chop between MI-02 and MI-03 in Kent, because the state highway from GR in Kent to Stanton in Montcalm does not have to go through MI-02 to get to MI-04, is the tie breaker. Good stuff.

[muon2]

I think Jimtex's map version 3 to the left is the winner, from a chop standpoint (and an equality standpoint too), vis a vis the "best" Torie map to the right, because it has one less chop.  Why? Because there apparently is no state highway between Clare and Misaukee counties!  Good stuff.

I assume you mean cuts, not chops. I use chops to describe the partition of a geographic unit and cut links to determine erosity.

By a double chop do you mean two districts that share two different counties or a district that pokes into one county in two discontiguous places? I think of the first as a running chop, and I prefer to exclude those. The second incurs no chop penalty but can increase erosity - train has such a chop in Kent.

[Torie]

I assume you mean cuts, not chops. I use chops to describe the partition of a geographic unit and cut links to determine erosity.

By a double chop do you mean two districts that share two different counties or a district that pokes into one county in two discontiguous places? I think of the first as a running chop, and I prefer to exclude those. The second incurs no chop penalty but can increase erosity - train has such a chop in Kent.

I corrected my text to clarify what I meant  about 30 minutes ago: yes I was discussing highway erosity cuts, not political jurisdiction chops (as to which chops the maps are tied). Presumably it is clear now.

I meant discontiguous chops in the same county between the same two CD's, not multi county chops between the same two CD's (which yes should be banned, along with traveling chops). Discontiguous chops in the same county might facilitate avoiding a sensitive county level highway cut between districts. Where it does, one balances that advantage against whatever the zoom erosity impact is, I guess.

You like my idea of just adding zoom points that are in excess of the minimum for the size of the overall chop, so that aspect of the scoring does not swamp the county highway cut score aspect of the erosity evaluation?

[jimrtex]

This is a plan I created in 2013:

[Torie]

Which plan do you like best now, Jimtex?

[jimrtex]

Which plan do you like best now, Jimtex?

I am going to present and score several, and then we can compare.  Perhaps you will try to create your own plan.

[Torie]

Which plan do you like best now, Jimtex?

I am going to present and score several, and then we can compare.  Perhaps you will try to create your own plan.

I did, and compared it to "yours" above, as modified by me.  

If you are using some scoring system other than Muon2's, except maybe for penalizing microchops, matters however will descend into further chaos than they are now however.  One scoring system at a time should be tested, is my suggestion. Muon2 isn't applying his zoom thing anyway I don't think, which is perhaps the most problematical part of his system until further refined, other than what we discussed about uber penalizing double chops that add up to a microchop of a multi county UCC.

[jimrtex]

Which plan do you like best now, Jimtex?

I am going to present and score several, and then we can compare.  Perhaps you will try to create your own plan.

I did, and compared it to "yours" above, as modified by me.  

If you are using some scoring system other than Muon2's, except maybe for penalizing microchops, matters however will descend into further chaos than they are now however.  One scoring system at a time should be tested, is my suggestion. Muon2 isn't applying his zoom thing anyway I don't think, which is perhaps the most problematical part of his system until further refined, other than what we discussed about uber penalizing double chops that add up to a microchop of a multi county UCC.

I am proposing a simpler, alternate scoring system.

By focusing on regions containing whole UCC's you get something that is more Iowa-like with 8 regions.

Erosity is measured by the simplified internal border length.  This avoids the whole issue of road connectivity. 

I do use connectivity as a constraint on a limited basis, but only as a substitute for pure contiguity.  For example, Gratiot and Shiawassee are contiguous, while Saginaw and Clinton are not.  I define Gratiot and Shiawassee as not being _connected_, and therefore you can not have a region (or district) that goes directly between Gratior and Shiawassee.  However, if the Gratiot-Shiawassee boundary is part of a region boundary you are charged for it (about 3/4 of a mile).

The equality measurement is the amount needed to bring the regions into substantial equality.  It in effect is a measure of the total chopped population.  It avoids the whole issue of chop size calculation.

[Torie]

Somehow I knew that is what you would do.  For erosity, would not a map with juts containing now much area, but a lot of population, garner far less of a penalty, as compared with what makes for the minimum line length of more rural districts large in area, unless you somehow take a ratio of line length to population for subsets of each CD? Your method really emphasizes overall equality in population. That will tend to result I suspect in "uglier" maps. Anyway, it will be interesting to compare what your map looks like that gets the high score with your system vis  a vis Mike's, and get forumite reaction to it. Good luck!

[Torie]

My interpretation is that you count the number of districts in the UCC. Whether or not those districts spill into other counties, or even other UCCs doesn't affect the counting within the UCC. Basically, put blinders on and just address each UCC on its own. It's no different than with county chops, where it doesn't matter how many other counties a district extends into, one just focuses on the county in question.

Excellent.  That certainly helps one draw nicer lines in Western PA (take a look at District 4!), if it's okay to have two districts span the UCC boundary.  

To wit:









Salient features:

* Within Philadelphia, all the lines are along ward boundaries.  The portion of PA-8 is a macrochop (as is necessary); the portion of PA-7 is not.  PA-2 is 60% BVAP; PA-1 is minority-majority by total population, but not by VAP.
* Obviously, the split of Allegheny and Berks are macrochops, and the portion of PA-7 in Montgomery is also one– these are all necessary.  Every other chop is an I-chop (though Carbon and Bedford are both in the ~6K range, which is pretty small).
* PA-9, without the roughly ~6K of people from Bedford, is tantalizingly close to being whole counties, as it would be -4,800 or so.  I tried to see if you could get the other deviations low enough such that it could fit into a 1% range, but no dice, not without chops elsewhere. (The combo Lehigh+Northampton+Carbon is just a tiny bit further away, as well.)
* There is, I'm pretty sure, a configuration of districts in the T which would lower inequality at the expense of erosity.  District 3 would even look prettier, but 10 and 5 would be a *lot* worse.  I think it also might have required another chop, or turning the SW I-chops into a macrochop, or something else?  There's a reason I abandoned it.  In any case, I might reconstruct it later but I doubt it would be preferred.
* Really, I think that the general shape of this map is hard to beat, though fine-tuning might still be possible.  The biggest point of contention, obviously, would be whether to split Berks or Lancaster between 6 and 16.  Without exhaustively researching every configuration (the proliferation of tiny boros in PA make infra-county erosity measures a BEAR), the erosity seems similar, and this arrangement should better respect the fact that Berks is part of the Philadelphia CSA, something that isn't technically a part of the UCC framework but IMO deserves consideration somehow.

Train, do you think you did your best to minimize your intra Philly UCC erosity zoom score between CD's? It may be that the PA-08 jut into Philly is not a macrochop, which gives you a freebie, which is itself an issue in the scoring system (maybe all chops into a county except microchops, should be zoomed, but penalized only for the excess subunit connector cuts (Philly hoods in this case) over the minimum for the size of the chop), but I wonder about PA-07 going into Berks rather than Chester. 

[jimrtex]

This is a connectivity map.



Connectivity is not used as part of an erosity measure, but rather as a more stringent criteria than literal contiguity for placing adjacent counties in the same district.   Connectivity would be defined before any maps were drawn.

To be connected, counties must be contiguous.   In general there must be a direct, non-circuitous way to travel between the counties, particularly considering the distribution of the population.  There is no requirement that the route be entirely in the two counties, but if the route goes through other counties it should not be through population concentrations, or drawn in a way to evade the population concentrations.

Continuity of land use may also be considered.  If the land on both sides of the boundary is crop lands, or urban development, the boundary itself is likely artificial.

The length of the border may be considered.  If the direct distance between the end points of the boundary is greater than 20% of the square root of the land area of the smaller county, the counties should generally be considered connected, unless there is a substantial reason not to, such as a substantial physical barrier.     If the direct distance between the end points of the boundary is less than 20% of the square root of the land area of the smaller county, a justification for connectivity may be needed.  If another county intrudes near the boundary, this may be a consideration.  For example the jog up of the northern boundary of Ottawa County cuts the length of the Muskegon-Kent boundary from 12 to 6 miles, but you have an area that is 12 miles wide to both the east and west of the boundary in the two counties.

On the map, green links are between connected counties.  Orange links are where the boundary is entirely in the Great Lakes.  These counties are not considered to be connected.    The links between Mackinac and Emmet and Cheboygan use the bridge.

The red dots are where four counties have a common junction point, or a near common junction point.  Point contiguity or near-point contiguity is not considered connected.

The yellow links are counties I would consider to be connected, but I could see someone arguing that they are not.  Red links are counties I would not consider to be connected, and would need stronger justification to change.

In general, we should be liberal in the granting of connected status.   It is only intended to restrict the most tenuous instances of literal contiguity.  It is not part of the measurement of erosity, or an indication of community of interest.

[muon2]

Is it better to have the two scoring systems in the same thread, or would it be clearer to follow if they were in separate threads? I can split them if our three primary posters here think it useful. Maps can be cross posted as needed if they are split.