Chops and Erosity - Great Lakes Style

[muon2]

Nelsville is the county seat of Clark County in Wisconsin, not Greenwood, but either way apparently Hwy 29 through northern Clark is not a highway cut  because it does not connect from the Clark county seat to an adjacent county, county seat. That is an example as to why, beyond complexity, picking and choosing state highways to count as cut is problematical, because the WI-03 Clark County jut is an erose feature, and thus the cut of Hwy 29 is a good proxy to pick that erose feature up. Your highway cut metric seems more focused on connectivity between county seats, rather than connectivity in general (hwy 29 does connect to county seats in adjacent counties, so the population around it is connected to those counties, even though Clark's county seat is not in play), and trying to get the best possible proxy for erose shapes. This would be particularly a problem with the county seat is not the largest town or city in a county.

I'm not sure I follow your concern here. My map of WI has hwy-29 connected to US-10 by way of hwy-73 which is entirely in Clark for that stretch. Both Greenwood and Neillsville are on hwy-73 so any path that connects to one of them connects to the other. You can't use hwy-29 to connect Chippewa to Taylor since that would go through Clark, but hwy-64 provides a direct path so hwy-29 is not an issue.

Oh, I see, highway 73 is not an orange line, but still a state highway. Assuming Hwy 29 has nothing to do with the county seat, is cutting it still a chop because it connects the county seats of Marathon and Chippewa, two non adjacent counties?

A chop has to do with the county itself. Then one can ask what connections do the fragments created by the chop have with the neighboring counties as if they were quasi-counties. Once that's done one can assess the cut links that define erosity.

Looking at Clark, it has connections to 5 of its 6 adjacent counties. It lacks a connection to Eau Claire since US-12/hwy-27 dips into Jackson along its path. Now consider a chop that followed the Eau Claire-Chippewa line extended east. That puts all of hwy-29 in the north part of Clark. As a new unit on the map it would have links to Chippewa, Taylor, Marathon, and the south part of Clark. The remainder of Clark in the south would have links to the north part of Clark, Jackson, Wood, and if a secondary path can be considered, Marathon.

Like the pink line in the Kent example, there are two state highway paths that cross the border to Marathon on the way from Neillsville to Wausau. Mapquest says that the one using hwy 29 is fastest so it is the primary link. Once there are two pieces of Clark the question of the use of the secondary highway, hwy-98, comes up.

Either way one resolves hwy-98, there are links established to both parts of Clark. Now it's a matter of counting the number of those links reside on the boundary between two CDs.


I think I should split the chop and erosity conversation off from the MI and WI threads so I'm not responding to similar queries in both. What do you think?

[Torie]

Maybe move all the posts on this topic to a new thread. It's just using WI and MI as examples. You are constructing a hideously complex system, and the issue is balancing all of this against simplicity. In the end, a much clearer statement of how it all works needs to be set forth, but I am concerned about the gaming. It's kind of a mess really. Just like the weighted voting thing - another nightmare.

[muon2]

Maybe move all the posts on this topic to a new thread. It's just using WI and MI as examples. You are constructing a hideously complex system, and the issue is balancing all of this against simplicity. In the end, a much clearer statement of how it all works needs to be set forth, but I am concerned about the gaming. It's kind of a mess really. Just like the weighted voting thing - another nightmare.

Consolidated, and I've added a link in the OP to our discussion about MI with UCCs, chops and erosity from 2013. Some of the erosity discussions there show how there are a number of ways to view the issue, an each one is going to have a weakness one way or another. That's true for the standard compactness algorithms, too.

The twin problems any system has to deal with is 1) how to construct scoring rules that apply equally well in Wayne county as in western MI, and 2) how to avoid too much gaming of those rules. The gerrymandering in MI is in part due to the codification of a set of rules in the late 1990's that had worked well in the hands of a special master, but when given to a legislature under partisan control turned out not to be so protective. I think that the first problem can only be dealt with using some type of system that allows one to change the scale of mapping elements in different areas based on population, otherwise one is able to get away with all sorts of shenanigans in areas where the natural scale of the rules aren't applicable (eg measuring county erosity on Wayne districts). I think the second problem then requires a number of independent mappers to test what games they might play and then see if the fix is worse than the game.

[Torie]

"My proposal is the zoom is triggered when the sum of chops in a county exceeds 5% of the quota."

What does that mean? What is the quota? How does one calculate the numerator and denominator?  And when you "zoom," what additional highways are brought into play?  Every highway connector the "center" of each subunit?

[muon2]

"My proposal is the zoom is triggered when the sum of chops in a county exceeds 5% of the quota."

What does that mean? What is the quota? How does one calculate the numerator and denominator?  And when you "zoom," what additional highways are brought into play?  Every highway connector the "center" of each subunit?

The quota is the population of the state divided by the number of the districts as it has been used on a number of threads including the rules for the VA exercise and the flow chart earlier in this thread. Do I need to put the link to those definitions in every post?

I mentioned two questions. When and how? It is pointless to go into the detail of either, unless you agree that simple doesn't work. If simple does work for you then zooming is irrelevant.

If simple doesn't work I put forward only my answer to when, and it is largely independent of how. When is question about determining what district's erosities need fixing from the simple model. If zooming is needed then how is subsidiary to when, since how is predicated on the situations when it would be invoked. So I need to know what situations I am designing how for.

[Torie]

Oh, I was mixing up cuts and chops. And you treat a multi-county UCC as one county for this purpose, right?  Anyway, as I think I mentioned before, within UCC's smaller unit chops should count, whether or not you have a macro chop into a UCC. So I was focused on erosity measures within a UCC, which I thought was what we were discussing. And outside UCC's, I am still not persuaded why some state highways should count, and not others, and what to do if there are no state highways between adjacent counties. Is that deemed a chop when two counties with no state highway between them are in the same CD? Or do payed county highways count to avoid a chop?  None of this may obtain to WI or MI perhaps (although some state highways are poorly labeled and hard to find on Dave's matting utility.

[muon2]

Oh, I was mixing up cuts and chops. And you treat a multi-county UCC as one county for this purpose, right?  Anyway, as I think I mentioned before, within UCC's smaller unit chops should count, whether or not you have a macro chop into a UCC. So I was focused on erosity measures within a UCC, which I thought was what we were discussing. And outside UCC's, I am still not persuaded why some state highways should count, and not others, and what to do if there are no state highways between adjacent counties. Is that deemed a chop when two counties with no state highway between them are in the same CD? Or do payed county highways count to avoid a chop?  None of this may obtain to WI or MI perhaps (although some state highways are poorly labeled and hard to find on Dave's matting utility.

Let's back up a moment and start with the simple model, identify shortcomings, and propose solutions. For example, let me take your first question about UCCs.

The simple model says all counties are equal and fewer chops are better. The problem is that there's nothing to dissuade mappers from taking whole urban counties and fingering their districts out to a bunch of rural ones, nor to demote a plan that takes a mid-sized urban area like Lansing and splits it right along the county line. The solution was to define the UCC and add to the chop count when the UCC is split.

Now comes implementation in the chop scoring. The next step simple model would count each county chop and count each multi-county UCC chop then add them together. The modeler now asks if there are problems that are undesirable.

Consider that the implementation has to deal with the following situations: a whole county chop of Clinton from Lansing, a small chop of Clinton, and a small chop of a smaller metro one-county UCC like Calhoun. In the simple UCC application the small chop of Clinton would count twice and the other two examples would only each count once. It seems strange to double count a small chop in Clinton, but not Calhoun. But it also would be strange to double count a chop in Calhoun. It looks like the simple UCC model still is weak.

The next fix is to look at the size of the chop, and if it's small it counts the same for Clinton and Calhoun, and the same as a whole county chop into a UCC. However, if the chop is large but not a whole county then having it count twice doesn't bother me. How large is large? I chose 5% of the quota, and initially treating the UCC as a whole unit is a heuristic that gives the desired result. By all means we should see if it causes consequences worse than the simpler preceding step.

Side note: Chops have nothing to do with state highways. Chops create smaller geographic units (quasi-counties).  Highways are used to find erosity at the boundary of geographic units which may or may not come from a chop.

Second side note: I used 5% of the quota as a threshold for erosity, too. Why? I think the Detroit and Grand Rapids examples illustrate the problem for erosity. I prefer to only keep track of one threshold for both chops and erosity. KISS when I can.

BTW, do my illustrations convince you the the simple erosity model breaks down in densely populated areas?

[Torie]

Let's back up a moment and start with the simple model, identify shortcomings, and propose solutions. For example, let me take your first question about UCCs.

The simple model says all counties are equal and fewer chops are better. The problem is that there's nothing to dissuade mappers from taking whole urban counties and fingering their districts out to a bunch of rural ones, nor to demote a plan that takes a mid-sized urban area like Lansing and splits it right along the county line. The solution was to define the UCC and add to the chop count when the UCC is split.

Now comes implementation in the chop scoring. The next step simple model would count each county chop and count each multi-county UCC chop then add them together. The modeler now asks if there are problems that are undesirable.

Consider that the implementation has to deal with the following situations: a whole county chop of Clinton from Lansing, a small chop of Clinton, and a small chop of a smaller metro one-county UCC like Calhoun. In the simple UCC application the small chop of Clinton would count twice and the other two examples would only each count once. It seems strange to double count a small chop in Clinton, but not Calhoun. But it also would be strange to double count a chop in Calhoun. It looks like the simple UCC model still is weak.

Am I correct that a multi county UCC counts as once county?

The next fix is to look at the size of the chop, and if it's small it counts the same for Clinton and Calhoun, and the same as a whole county chop into a UCC. However, if the chop is large but not a whole county then having it count twice doesn't bother me. How large is large? I chose 5% of the quota, and initially treating the UCC as a whole unit is a heuristic that gives the desired result. By all means we should see if it causes consequences worse than the simpler preceding step.

I am not sure it is unnecessary or wise to have a macro-chop into a UCC count as two chops.

Side note: Chops have nothing to do with state highways. Chops create smaller geographic units (quasi-counties).  Highways are used to find erosity at the boundary of geographic units which may or may not come from a chop.

Second side note: I used 5% of the quota as a threshold for erosity, too. Why? I think the Detroit and Grand Rapids examples illustrate the problem for erosity. I prefer to only keep track of one threshold for both chops and erosity. KISS when I can.

For purposes of creating quasi counties only that might work.

BTW, do my illustrations convince you the the simple erosity model breaks down in densely populated areas? 

Probably, but if chops of subunits are penalized (I think they should be), that should mitigate things. Beyond that, you are down to finding more highway cuts between subunits.

[muon2]

Let's back up a moment and start with the simple model, identify shortcomings, and propose solutions. For example, let me take your first question about UCCs.

The simple model says all counties are equal and fewer chops are better. The problem is that there's nothing to dissuade mappers from taking whole urban counties and fingering their districts out to a bunch of rural ones, nor to demote a plan that takes a mid-sized urban area like Lansing and splits it right along the county line. The solution was to define the UCC and add to the chop count when the UCC is split.

Now comes implementation in the chop scoring. The next step simple model would count each county chop and count each multi-county UCC chop then add them together. The modeler now asks if there are problems that are undesirable.

Consider that the implementation has to deal with the following situations: a whole county chop of Clinton from Lansing, a small chop of Clinton, and a small chop of a smaller metro one-county UCC like Calhoun. In the simple UCC application the small chop of Clinton would count twice and the other two examples would only each count once. It seems strange to double count a small chop in Clinton, but not Calhoun. But it also would be strange to double count a chop in Calhoun. It looks like the simple UCC model still is weak.

Am I correct that a multi county UCC counts as once county?
At this stage I have not put that forward; remember I've backed up. So, I'm going to defer on this, because changes based on your second question can make this moot. I want to solve the problem of the UCC implementation in the score. My hope was that would have bubbled out of the VA work where I could have multiple commissioners reacting to ideas. Even there I had one commissioner vote against any use of UCCs in scoring.

The next fix is to look at the size of the chop, and if it's small it counts the same for Clinton and Calhoun, and the same as a whole county chop into a UCC. However, if the chop is large but not a whole county then having it count twice doesn't bother me. How large is large? I chose 5% of the quota, and initially treating the UCC as a whole unit is a heuristic that gives the desired result. By all means we should see if it causes consequences worse than the simpler preceding step.

I am not sure it is unnecessary or wise to have a macro-chop into a UCC count as two chops.

What I think I discern from your line of questions is a different direction for the use of UCCs than the original proposal in 2013. Let me ask as I did to the commission, should UCCs be used in scoring and should there be a penalty for over-chopping a UCC? If the answer is that there should be a penalty, then let's look at examples to see what heuristic can meet the need.

If the answer is no penalty then we must accept that the carve up of Lansing along county lines is a good solution if it otherwise reduces chops and erosity. My sense was that the majority of us in 2013 did not think is was good (the thread linked in the OP traces that history). This is the map I constructed back then that led to the UCC concept in order to penalize it and is still a good example, setting aside the separate debate on the VRA.

[Torie]

If you have appropriate penalties for erosity within a UCC, that hideous thing you did to Ingham County should not fly. And it might be wise on the matter of multi county UCC's being deemed one county, to limit that to where who whole county is chopped from the UCC, so it is not open season to chop between counties in a UCC, or to do traveling chops within such a UCC.

[muon2]

If you have appropriate penalties for erosity within a UCC, that hideous thing you did to Ingham County should not fly. And it might be wise on the matter of multi county UCC's being deemed one county, to limit that to where who whole county is chopped from the UCC, so it is not open season to chop between counties in a UCC, or to do traveling chops within such a UCC.

I'm not sure erosity saves the day with my Ingham mess. I don't need the microchop from CD 7 to stay within 0.5%, and if it isn't there, the lines are pretty clean and the shape is reasonably compact in the county. Plus that puts the onus on erosity to make up for defects in the chop rule. I've played a bit with the idea of pushing more onto erosity, and my observation is that as one puts more emphasis on erosity to cure all ills, chops can become irrelevant or at best secondary. The balance has to be well crafted for the flexibility of Pareto to remain.

The second problem my example uncovers wasn't intended when I drew it because the UCC definition didn't exist then. The Detroit UCC has a size of 6, and I have 7 CDs covering it (8 including a microchop from CD 7 into Wayne). But since Detroit has so many, is the extra chop the whole county removal of Livingston or the chop into Oakland from CD 10? If I set the UCC rule to only pick up whole county chops then how do I trigger it when there is a intracounty chop as well? What if there are multiple intracounty chops?

That is why the simple punishment for my plan was to charge it an extra chop for the Lansing UCC over and above the one for Ingham (microchops only counting for erosity). In addition it gets charged for the excess chop in the Detroit UCC and I don't have to separate out which district causes the excess. I think that is a fairly elegant solution to deal with my map (and many others that have come up) and it's why this board has devoted so much time to UCCs over the last year and a half.

[Torie]

If you get rid of the microchop into Inghram, indeed two of them (remember, I don't like county tri-chops, and think that should be penalized, with traveling chops probably banned), I don't mind the macrochop really. For Detroit, you have one chop for severing Livingston, and one chop for Oakland, and one chop for Macomb. Chops within UCC counties should count. The only thing UCC's should really do potentially, is penalize whole county severances.

The only really potentially compelling policy reason to go your route, is to discourage mixing urban and rural voters (but only to the extent of one county fragments), as I see it. I am not sure that is per se so terrible at the margins, if it otherwise makes the state map cleaner with fewer chops.

Hey, just to cheer you up on this cold, snow everywhere day (we are getting your weather of yesterday now, thanks a lot), what kind of score would my IL-17 get do you think?  If the Dems knew what was coming down in Downstate Illinois, do you think they would have had the chutzpah to go there?

[muon2]

The chop count at the county level for my "bad" plan is 2 in Wayne, 1 in Oakland, 1 in Macomb, and 1 in Ingham, each counts as one chop point. In addition there are microchops in Wayne, Sanilac, Tuscola, Bay, and two in Ingham (one of which can be eliminated without exceeding the inequality limit) and they don't count as chop points. All this was worked out two to three years ago and represents a balance between those who dislike a lot of single chopped counties, those who dislike placing lots of chops in one county, and those who think that large chops should be discouraged in favor of small chops.

I think it is a mistake to revisit this part of the scoring model, but if there is a detailed alternative it can be reviewed. I also think that UCCs have shown value in guiding redistricting plans and there is currently a simple model on the table - add the number of chops in a UCC over the minimum as a penalty. Detailed alternatives are worth review here, too, but they must be compared to the baseline model.

One revision to the simple model is to not apply the penalty to chops in a single county UCC, and that is consistent with most plan reviews to date, though I left it as an open item for the VA exercise. More recently I have offered another specific revision to the UCC implementation - that total chops in a UCC below 5% of the quota don't trigger the UCC penalty.

[muon2]

Hey, just to cheer you up on this cold, snow everywhere day (we are getting your weather of yesterday now, thanks a lot), what kind of score would my IL-17 get do you think?  If the Dems knew what was coming down in Downstate Illinois, do you think they would have had the chutzpah to go there?

The IL Dems showed their willingness to approve districts like that back in 2001 for IL-17. Chutzpah was the DC Dems deciding that they wanted the maximum number of wins in 2012 to regain the majority, and gambled in IL despite the headwinds elsewhere. As Steve Israel said

You must be logged in to read this quote.

I suspect the IL Dems would have been willing to settle for 11 or 12 safe seats rather than gamble on 13 and end up with 10 after 2014.

[Torie]

The chop count at the county level for my "bad" plan is 2 in Wayne, 1 in Oakland, 1 in Macomb, and 1 in Ingham, each counts as one chop point. In addition there are microchops in Wayne, Sanilac, Tuscola, Bay, and two in Ingham (one of which can be eliminated without exceeding the inequality limit) and they don't count as chop points. All this was worked out two to three years ago and represents a balance between those who dislike a lot of single chopped counties, those who dislike placing lots of chops in one county, and those who think that large chops should be discouraged in favor of small chops.

I think it is a mistake to revisit this part of the scoring model, but if there is a detailed alternative it can be reviewed. I also think that UCCs have shown value in guiding redistricting plans and there is currently a simple model on the table - add the number of chops in a UCC over the minimum as a penalty. Detailed alternatives are worth review here, too, but they must be compared to the baseline model.

One revision to the simple model is to not apply the penalty to chops in a single county UCC, and that is consistent with most plan reviews to date, though I left it as an open item for the VA exercise. More recently I have offered another specific revision to the UCC implementation - that total chops in a UCC below 5% of the quota don't trigger the UCC penalty.

Everybody has their own preferences or course, but I am thinking if what the public square thinks. They are not going to like getting away without penalty with subunit chops, and I don't think they will like severing in two smaller population counties en mass in order to avoid a "macro-chop" into one county, nor will they accept microchops not counting at all. And most importantly, is what generates the best maps. Perhaps the macrochop rule generating another penalty point might work out if it generates a good balance vis a vis reduced erosity. I wonder if my macrochop into Jackson effected an offsetting savings in chops versus the intermediate chop which caused MI-07 to be more elongated. Maybe the two maps are equally scored.

[muon2]

The chop count at the county level for my "bad" plan is 2 in Wayne, 1 in Oakland, 1 in Macomb, and 1 in Ingham, each counts as one chop point. In addition there are microchops in Wayne, Sanilac, Tuscola, Bay, and two in Ingham (one of which can be eliminated without exceeding the inequality limit) and they don't count as chop points. All this was worked out two to three years ago and represents a balance between those who dislike a lot of single chopped counties, those who dislike placing lots of chops in one county, and those who think that large chops should be discouraged in favor of small chops.

I think it is a mistake to revisit this part of the scoring model, but if there is a detailed alternative it can be reviewed. I also think that UCCs have shown value in guiding redistricting plans and there is currently a simple model on the table - add the number of chops in a UCC over the minimum as a penalty. Detailed alternatives are worth review here, too, but they must be compared to the baseline model.

One revision to the simple model is to not apply the penalty to chops in a single county UCC, and that is consistent with most plan reviews to date, though I left it as an open item for the VA exercise. More recently I have offered another specific revision to the UCC implementation - that total chops in a UCC below 5% of the quota don't trigger the UCC penalty.

Everybody has their own preferences or course, but I am thinking if what the public square thinks. They are not going to like getting away without penalty with subunit chops, and I don't think they will like severing in two smaller population counties en mass in order to avoid a "macro-chop" into one county, nor will they accept microchops not counting at all. And most importantly, is what generates the best maps. Perhaps the macrochop rule generating another penalty point might work out if it generates a good balance vis a vis reduced erosity. I wonder if my macrochop into Jackson effected an offsetting savings in chops versus the intermediate chop which caused MI-07 to be more elongated. Maybe the two maps are equally scored.

I have always held that subunit chops count towards the chop count. The general model should include this for all states at some threshold with commission defined subunits where none exist otherwise. As I suggested the states with statutory county subdivisions (as used by the Census) where counties are primary (ie not New England) require an additional constraint beyond the general rule, much like VA needs an additional rule to handle independent cities. For example a reasonable constraint in a state like MI is that no county fragment created by a chop can include more than one chopped subunit.

I also think that microchops should generally incur some penalty, but recognize that they are not as problematic as larger chops. I believe, based on the substantial testimony of the public I have reviewed, that minor chops to balance population draw less ire than large divisions of an established geographic area. Since microchops will usually add to erosity, reducing their impact on the chop count meets the goal that the small chop is preferred to the large chop.

Severing two smaller counties to avoid a macrochop in one will increase the chop count. If a plan splits two counties instead of one and reduces erosity then it should be in the mix. I assume this is in the context of its application to UCCs and chop penalties, since that's what I was referencing in my quote above. If you are talking about a two chops to avoid a double penalty in a UCC then its a wash.

[Torie]

Microchops add to erosity because it creates county fragments, and brings more highways into play? Do I have that right? We still have the issue of erosity within more populated counties and UCC's, right, that can host two of three CD's?

Thanks for clearly up that city and township chops count. It is just unclear how much I guess. I suggested a half point. I still don't like trichops, and tend to think the public will not either, since it suggests a gang bang on one county, but perhaps you disagree.

[muon2]

Microchops add to erosity because it creates county fragments, and brings more highways into play? Do I have that right? We still have the issue of erosity within more populated counties and UCC's, right, that can host two of three CD's?

Thanks for clearly up that city and township chops count. It is just unclear how much I guess. I suggested a half point. I still don't like trichops, and tend to think the public will not either, since it suggests a gang bang on one county, but perhaps you disagree.

I strongly prefer a whole number point system. Once one opens the doors to some fractional and some whole values there's a new level of games that happen. I would prefer the amendment that if the sum of microchops in a unit exceeds 0.5% then one chop point is awarded. That will also tend to avoid microchops ganging up in one place.

I put forward two addenda to the most basic UCC penalty rule - multi-county and macrochop threshold. If they work then the problem of chops in larger UCCs is resolved per the chop flowchart. If you see examples where it gives a result more undesirable than the alternative then the addenda should be reconsidered.

Yes, the whole issue of erosity still needs to be addressed in urbanized areas. To me the fundamental way to see this is that the zoom scale changes as the density changes. That's consistent with my observation of public reactions, too. An erose river boundary in a rural area can be of far less import as an erosely shaped but much smaller scale carve up of an urban county. The trick is determining when to zoom. I'm still curious as to your reaction to the three Kent plans I prepared - should they count the same in erosity, or not?

[Torie]

Chops and Erosity part 3 of 3.

A zoom into Kent replaces counties with cities and townships, and seats of county government with the town hall or city hall. In the map below the halls (nodes) are marked roughly with blue dots and the lines indicate the connections (links) between them. Villages are shown on the map, but they are not considered subunits of the county for redistricting purposes.

Yellow lines indicate connections where the path between units uses a state highway at the boundary, and blue lines are connections made solely with local roads. Yellow lines generally include local roads to get from the hall to the nearest state highway, so what matters is the status of the road as it crosses the town or city line.



One thing to note is that there are a number of nodes that are only connected locally. This includes the cities of Cedar Springs, Rockford, and East Grand Rapids, and the townships of Spencer, Vergennes, and Bowne. These units are considered to be connected by local links, so cutting those links would also count towards erosity. For other local links, scoring can either count them or not, so the calculation will be made both ways.

Here's a zoom into plan A. The chop cuts 8 yellow lines (including the Byron Twp to Ottawa link), and 3 blue lines to locally connected units for a total of 11 cut links. If all local cuts were counted the total would rise to 19.



Here's a zoom into plan B. The chop cuts 9 yellow links (including two to Ottawa), and 5 required blue links for a total of 14 cut links. If all local cuts were counted the total would rise to 20.



Here's a zoom into plan C. The chop cuts 8 yellow links (including one to Ottawa), and 2 required blue links for a total of 10 cut links. If all local cuts were counted the total would rise to only 12.



Counting the chops in Kent would keep plan C in the mix with a lower erosity than plan B or A. Since all three plans have the same chop count, but differ in erosity, the inequality doesn't come into play. Plan C is the lone surviving plan of the three.

Not sure what the other roads that are not blue or yellow are, and you didn't tell me, and I don't see them drawn, but to my "erosity eye," the golf score I would give to each plan with 0 being best, and 10 being worst, is as below. Plans A and B are pretty disgusting, but plan A more so by a bit, because the carve out into the county is deeper and narrower by a bit. The two little cities on the edge in the northern part of the county going back and forth vis a vis Plans A and B are about a wash, based on what percentage of their perimeter is exposed over 50% to one CD as opposed to the other. Plan C is of course far more desirable. So the most "accurate" measure in this case, is just to use "other roads" and exclude and render irrelevant yellow and blue roads. The next best is to include all roads. Just using yellow roads really sucks because then A=C, which is ludicrous.



These options however below appear to me to be the fairest of them all, perhaps the second one given where the CD lines are to the east.

[Torie]

Microchops add to erosity because it creates county fragments, and brings more highways into play? Do I have that right? We still have the issue of erosity within more populated counties and UCC's, right, that can host two of three CD's?

Thanks for clearly up that city and township chops count. It is just unclear how much I guess. I suggested a half point. I still don't like trichops, and tend to think the public will not either, since it suggests a gang bang on one county, but perhaps you disagree.

I strongly prefer a whole number point system. Once one opens the doors to some fractional and some whole values there's a new level of games that happen. I would prefer the amendment that if the sum of microchops in a unit exceeds 0.5% then one chop point is awarded. That will also tend to avoid microchops ganging up in one place.

I put forward two addenda to the most basic UCC penalty rule - multi-county and macrochop threshold. If they work then the problem of chops in larger UCCs is resolved per the chop flowchart. If you see examples where it gives a result more undesirable than the alternative then the addenda should be reconsidered.

Yes, the whole issue of erosity still needs to be addressed in urbanized areas. To me the fundamental way to see this is that the zoom scale changes as the density changes. That's consistent with my observation of public reactions, too. An erose river boundary in a rural area can be of far less import as an erosely shaped but much smaller scale carve up of an urban county. The trick is determining when to zoom. I'm still curious as to your reaction to the three Kent plans I prepared - should they count the same in erosity, or not?

Just to be clear, the sole purpose of the macro-chop, other than if into a multi county UCC (or maybe a single county UCC which is unresolved), which adds a point, is to create a quasi county and put more roads in play, right? Will any paved road do between two counties, as long as it is paved, for cut purposes? And a chop of a county subunit counts the same as a chop of a county, unless a microchop. Is that correct?

I just can't interest you in penalizing trichops I take it. On that one, I would really be surprised if the public did not prefer such penalties, so that one county does not become the toxic waste dump of the state.

Looked at the 2002 Illinois CD plan. The downstate CD's that were really out there, did not involve  the St Louis burb based one, but the other two that reached down into the southern portion of the state, that were really way, way out there.

[muon2]

Not sure what the other roads that are not blue or yellow are, and you didn't tell me, and I don't see them drawn, but to my "erosity eye," the golf score I would give to each plan with 0 being best, and 10 being worst, is as below. Plans A and B are pretty disgusting, but plan A more so by a bit, because the carve out into the county is deeper and narrower by a bit. The two little cities on the edge in the northern part of the county going back and forth vis a vis Plans A and B are about a wash, based on what percentage of their perimeter is exposed over 50% to one CD as opposed to the other. Plan C is of course far more desirable. So the most "accurate" measure in this case, is just to use "other roads" and exclude and render irrelevant yellow and blue roads. The next best is to include all roads. Just using yellow roads really sucks because then A=C, which is ludicrous.

The blue/other roads are all non-state highway links. Some blue roads must be used because a subunit had no state highway links from any direction. The other roads were the remaining non-state highway links. My sense is that in urbanized areas one should use all the links, which corresponds to your total.

The bigger question is how much do the wiggles in Kent matter when looking at the whole of districts 2 and 3. In the simple model they both have the same erosity. In fact in most compactness models all three plans would be nearly the same because the Kent pieces and boundary are small compared to the area of the whole districts, especially for CD 2.

If the zoom for erosity matters to the total score then one could just add the total, but that would more than double the erosity for those districts (from 7 and 13 respectively). It seems like the balance would be to add some fraction of the total (rounded) in Kent to the erosity for the district. How much difference point-wise would you expect to see between B and C?

[Torie]

Oh for erosity, per CD, one point is probably enough, so the max total for Kent would say be 2 for erosity, and then you would prorate based on the number of highway cuts (O cuts being zero, and the max number without subunit chops being 2), and yes, then generating fractional points.   Or the max number could be scaled based on population perhaps. The thing is, is that plans are competing, so any plan that chops Kent would need to match the score of the other competing plan unless the amount of population in each chop varied, and that variance gained a score advantage elsewhere. It's a complicated issue.

[muon2]

Let me pose another question to your erosity eye. How would you rate your CDs 9-14 above on erosity compared to CD 3, 5 and 8?

[Torie]

I will post the scores in the next post (patiently waiting for my screenshot of the map to print out), but in my defense, if the constraint were just getting BVAP above 50%, the Oakland county lines would have been drastically revised.

Btw, you sure that you don't want to reward avoiding any subunit chops in a county? It seems to me with the 0.5% population play, it is rather incumbent on the map maker to avoid any such chops, rather than doing a microchop of a subunit, unless it increases erosity by some more than de minimus degree. On that one, I suspect the public square would agree with me. I feel almost compelled to avoid such subunit chops given the population play myself. If I don't, I feel totally suffused with guilt. Think about that one some more please. Even the gerrymanders seem quite sensitive to that issue as you know, unless the stakes are high enough not to.

[Torie]

Let me pose another question to your erosity eye. How would you rate your CDs 9-14 above on erosity compared to CD 3, 5 and 8?