Local vs regional road connections

[Torie]

I am revving up my aging and defective and tired old mind to tackle Alabama. And I think I need a shower first. So later.

[jimrtex]

There are 21 minor civil divisions (MCD) in Stark County, 17 townships, and the cities of Alliance, Canton, Louisville, and Massillon. Other municipalities (cities or villages) are shown as the black shadow. (The four other cities are also in black, but I have set the transparency of their MCD status to 0).

Why does the Census only count some munis as MCDs? Is it a historical artifact? It looks like OH treats them all the same, so they should have equal status as county subunits for redistricting.

I thought I understood it from the time of the redistricting contest, but maybe not.

The cites of Alliance, Canton, Louisville, and Massillon are coterminous with the townships of Butler, McKinley, Constitution, and Massillon, respectively.

When an area is incorporated or annexed to an incorporated city, there must be a formal action to change the township boundaries (counties control township boundaries). The unincorporated part of a township may also file for a change. The statute makes a distinction between cities and villages, in that the county shall make a change if requested by a city, but may make a change if requested by a village..

There was a formal agreement between the cities of Canton and North Canton, and Plain and Jackson townships for development of land along a strip of land alongside railroad tracks, northward from Canton to the Summit County line (the area is west of North Canton). The land would be annexed to Canton, but Canton agreed not to seek to seek annexation into McKinley township.

But Plain township definitely excludes North Canton from its zoning and land use maps. I don't know whether North Canton is not in any township, or is part of Plain township, but not subject to its government.

It may be that the census bureau is recognizing the formal organization of the four townships that coincide with the four cities, while trying to include all territory within a county within an MCD.

[muon2]

There are 21 minor civil divisions (MCD) in Stark County, 17 townships, and the cities of Alliance, Canton, Louisville, and Massillon. Other municipalities (cities or villages) are shown as the black shadow. (The four other cities are also in black, but I have set the transparency of their MCD status to 0).

Why does the Census only count some munis as MCDs? Is it a historical artifact? It looks like OH treats them all the same, so they should have equal status as county subunits for redistricting.

I thought I understood it from the time of the redistricting contest, but maybe not.

The cites of Alliance, Canton, Louisville, and Massillon are coterminous with the townships of Butler, McKinley, Constitution, and Massillon, respectively.

When an area is incorporated or annexed to an incorporated city, there must be a formal action to change the township boundaries (counties control township boundaries). The unincorporated part of a township may also file for a change. The statute makes a distinction between cities and villages, in that the county shall make a change if requested by a city, but may make a change if requested by a village..

There was a formal agreement between the cities of Canton and North Canton, and Plain and Jackson townships for development of land along a strip of land alongside railroad tracks, northward from Canton to the Summit County line (the area is west of North Canton). The land would be annexed to Canton, but Canton agreed not to seek to seek annexation into McKinley township.

But Plain township definitely excludes North Canton from its zoning and land use maps. I don't know whether North Canton is not in any township, or is part of Plain township, but not subject to its government.

It may be that the census bureau is recognizing the formal organization of the four townships that coincide with the four cities, while trying to include all territory within a county within an MCD.

Your last statement makes the most sense. IL has a few such city-township combinations such as Springfield which is co-terminus with Capital twp, and both expand with annexations by the city.

The Stark county website lists all the cities and villages and notes that they are governments separate from the townships as established by the voters. It says the munis provide local government services to their residents, so that also makes them seem apart from the townships.

[Torie]

The connection to Choctaw from Chatom would go through the green piece leaving the district. The connection to Choctaw from Leroy follows US-43, AL-56, and AL-17 and goes through the blue piece leaving the district. The original connection cannot be eliminated by the chop so it goes to the green piece the path is in that district as it crosses the county line.

Your second sentence above flummoxes me. There is a highway cut for erosity purposes, since the state highway leaves the district. I don't get the "cannot be eliminated" bit.

That was my interpretation in 2013. My thought is to apply the same idea for Pike. However instead of a chop due to districts, the township is chopped by East Sparta, but the rule would act the same way. The regional connection from Pike to Tuscarawas on OH-800 is interrupted by the "chop" from East Sparta. Since OH-800 is in Pike township at the county line, the connection goes from Pike to Tuscarawas and not from East Sparta to Tuscarawas. A local connection exists between Pike and East Sparta.

And I am even more underwater here. Let's go back a step. If a state highway does not go through a subunit node that is on the county line, what happens? Does it still count as a highway cut? Why does East Sparta come into this? As you say, there is no state highway going directly from Tuscarawas to East Sparta because Pike intervenes, and even if it did not, there is no state highway going from Tuscarawas to East Sparta. East Sparta seems irrelevant to me. And it seems to me, there should be a highway cut counted even if the highway does not go through the node, but I am not sure about that.  It's the conundrum of a highway that just wings a subunit, versus one that goes through the middle, but misses the node, because the node is in an odd place.

If the highway does go through the Pike node, I do think that a subunit surrounded by a subunit (as East Sparta is by Pike), should be ignored for highway cut counts. One should not avoid a highway cut merely because the highway goes through an intervening subunit. In fact, that might be a general rule even if the subunit is not surrounded.

But I have no confidence at all, I am really understanding what you want me to understand. Sorry about that.

[muon2]

I think the confusion goes back to the fact that the connection is defined by a whole path, not a road on the border. A connecting path may or may not be cut by a district boundary. If a district boundary cuts a connecting path then it adds to erosity. For nodes in different counties that path is made of state highways such that no other geographic unit is intercepted by the path. For counting erosity the county line only matters if it's the same as a district boundary.

Let's make sure we are on the same page with AL before we go to OH.


nb. The highways I describe aren't marked on the map. AL-17 is the road north from Chatom through Millry, AL-56 goes east from Chatom to Wagarville, and US-43 goes between Wagarville and Leroy (it's marked in Clarke county).

In chopped Washington AL there are two subnodes. One for the blue district in Washington at the county offices in Chatom. One is for the green district centered in Leroy. For Chatom the node is on AL-56 just west of AL-17. For Leroy the node is on US 43 (using either the high school or post office since it doesn't have an incorporated city government). So far so good?

To test for connections to Choctaw I must find a path of numbers state of US highways that goes from each of those nodes to Butler, the county seat of Choctaw. Without the chop there is a path from Chatom to Butler that goes north on AL-17 after a short piece of AL-56 in Chatom. It says in the two units (whole county Washington and Choctaw) so it's a connection. If it gets cut by a district boundary it adds to erosity. Does this work as an description of how I test for a connection?

In the chopped county I can use the same path from the blue subunit with its node at Chatom. In the chopped county that path goes through the green subunit, so it fails to stay in the two units I seek to connect (the blue Washington subunit and Choctaw). This is probably the first puzzling part.

The path from Leroy to Butler goes SW on US-43, west on AL-56 and north on AL-17. In the chopped county that path goes through the blue subunit, so it fails to connect the units I seek to connect (the green Washington subunit and Choctaw). If the preceding paragraph was puzzling, this may also be.

Recall that we have established that a connection exists between the two counties when they are whole. Yet when the chop is in place I can't draw a connection between either node and Choctaw without going through the other subunit. That leaves me with the four choices I outlined earlier:

A. Remove the connection since the path goes through both subunits on its way to Choctaw from either subunit node. It would not count towards erosity then.

B. Establish the connection to the blue subunit since the path goes more directly through its node and it is otherwise locally connected farther west along the county line. It would count towards erosity since it is cut at the county line between two districts.

C. Establish the connection to the green subunit since the path crosses from that subunit at the county line. It would not count towards erosity since Choctaw is also in the green district so it isn't cut.

D. Create two connections to replace the original connection, since without a regional connection both subunits can claim local connections to Choctaw. One of the two connections would now be cut and count towards erosity.

Since there was a connection that could contribute to erosity without the chop, I don't like the idea that no connection to Choctaw remains after a chop. That invites chop games to eliminate connections (I think jimrtex observed this a few years ago when I started defining erosity). It's enough that the chops can be strategic to reduce erosity without eliminating connections. So I don't like option A.

Option D creates more links than initially exist to other counties. We've restricted that to macrochops so that simple chops are not overly punished in the erosity score.

That leaves two options, and of those option C has been the preferred interpretation for cases like this. If you're still with me and think I've missed a reason to go a different way in interpretation, please weigh in.

[Torie]

OK, after 3 cups of coffee, I have finished wading through this nightmare, and think I understand it, although not really your 4 options. What you and Jimrtex have apparently been doing is what I have never done, because to me it doesn't make any sense, so I never considered it.

So let's step back from all of this a bit. Why is it necessary to create two subunits with this chop? Why is it necessary to create Leroy as a node?  Is seems to me that you have the Chatam node, and two highway cuts, one to Butler (with the highway cut at Millry), and one to Wagarville. End of story. So what is the policy reason to create another subunit, and another node. What does it accomplish? What mischief is it designed to stamp out?

Obviously the idea that you can eliminate highway cuts with creative chops that would otherwise exist is ludicrous, as you suggest. But before having to torture my brain with any of this further, we need to get past the the issue of whether or not we need to create another subunit with its own node out of thin air by virtue of a chop of a subunit. The only time I see the need to create a pseudo node is where a subunit not chopped is node-less because the node is parked in another subunit.

[muon2]

What you say is reasonable. I would say it is the practical effect of the theory of nodes and links as a way to find erosity. The idea is that every plan uses geographic units that are linked together. If it's IA then it is nothing more than nodes of counties linked to each other because chops don't come into play.

When a county is macrochopped then the county is replaced by its subunits. Those are represented by nodes and links that connect to each other and the remaining county network. As with an unchopped state I can go back to the initial principle of counting severed links in this extended network to get the erosity. In the MI thread we treated Kent and the big Detroit UCC counties in this way.

For a simple chop we don't decompose the county into its subunits, though we may cognizant of them by limiting how many can be chopped. For erosity purposes a simple chop decomposes a county into two subunits. These subunits must be represented by nodes and links just like every piece of geography in a plan. Hence one needs to establish the rules for how the subunits formed by a simple chop connect to the rest of the plan. My four choices outline ways to do that.

Besides the reasoning I supplied with choice C there is a practical benefit that I alluded to at the start of this post. It allows the user to just take the original node and cut it with the existing links assigned to separate pieces. One never actually has to find the other node. The links to other counties remain exactly what they were. The result is the type of network map that I showed for your AL plan.



I agree that the intermediate step is long winded, but I felt a need to justify the choice in the context of the model rather than just provide an ansatz. I also need to create an underlying rationale for the Pike twp connection.



In the above map I'm assuming a Stark macrochop and I've shaded Pike twp, including East Sparta, in green and Tuscarawas county in blue. Both Pike and East Sparta are subunits so I've placed stars at the location of their nodes at the respective town halls. Note that East Sparta bordered Tuscarawas in 2010 according to the lines above.

The path along OH-800 has exactly the same problem that the connecting path to Choctaw did in the AL map. But here I don't have the case of a chop of a subunit. I do have the case of a muni carved from a township much like a chop would split the township. So my solution to the connection issue for Pike is to do exactly what I would do if East Sparta was a chop of Pike. Assign the connection to Tuscarawas to Pike and not to East Sparta.

[Torie]

1. "Ansatz?"  You expected me to know what the heck that meant? Really? I looked it up, and I still don't know what the heck it means. Whatever. I thought it might be a typo of "ersatz," but no.

2. So cutting to the chase, a divided subunit, does not create another node, and we just just count road cuts where the road crosses a CD line, right? So what I have been doing, I can keep dong, right?

3. I think I agree that if a state highway crosses a county line into a subunit, and then en route to the node of that subunit, travels through another subunit, that does not matter. It would only matter anyway, if the subunit were chopped somehow in a way that cut the road north of North Sparta but not before. If the choice is between picking the closest node, or the node of the subunit where the road first enters, the latter makes more sense, and is easier to apply. So are we on board with that, and have I accurately stated what is in play here?

4. Do you have any idea how tortuous this has been to me? Whatever happened to KISS? Is KISS a thought crime in the physics world?

[muon2]

1. "Ansatz?"  You expected me to know what the heck that meant? Really? I looked it up, and I still don't know what the heck it means. Whatever. I thought it might be a typo of "ersatz," but no.

2. So cutting to the chase, a divided subunit, does not create another node, and we just just count road cuts where the road crosses a CD line, right? So what I have been doing, I can keep dong, right?

3. I think I agree that if a state highway crosses a county line into a subunit, and then en route to the node of that subunit, travels through another subunit, that does not matter. It would only matter anyway, if the subunit were chopped somehow in a way that cut the road north of North Sparta but not before. If the choice is between picking the closest node, or the node of the subunit where the road first enters, the latter makes more sense, and is easier to apply. So are we on board with that, and have I accurately stated what is in play here?

4. Do you have any idea how tortuous this has been to me? Whatever happened to KISS? Is KISS a thought crime in the physics world?

In physics and mathematics an ansatz is an educated guess with no justification, yet it can be demonstrated to get a usable answer. Once one has an ansatz, it's a great tool to use with a class of problems, but it may not survive rigorous scrutiny. I'd like to be able to present a tool - in this case how to count roads in a simply chopped county. I'd also like to show that I'm being completely consistent in my use of network theory where everything has a node and links - hence showing that the AL chop really is based on nodes, even if the practical user doesn't have to think about nodes.

On point 3, I think that we have to be careful on when it applies. It applies when one subunit has been formed out of another leaving a portion of the original behind. It doesn't necessarily apply when the subunits are of the same original type. For example I'm not proposing here that I-77 is automatically connected to Bethlehem twp west of Pike. There are no exits on I-77 that can take one directly into Bethlehem - it's a corner-cutter like those we have considered at the county level. I'd have to look at more examples to decide what to do with I-77 at the subunit level.

[Torie]

Yes, in the back of my mind, I was concerned about the corner cutter issue, as a problem lurking out there, but considering a muni cut out of a township as something special leaves me cold too. That distinction seems artificial to me. So this one will need to be carefully worked though, so that we hew to the common sense metric. The idea here is really about a road entering one subunit, and then going through another to get to the node of the first subunit. At least in this context, it may be just ignoring traversing through the intervening subunit makes the most sense as a universal rule. In that sense, it kind of tracks the nascent nick rule.

[muon2]

Interstates are an inherent challenge because they are limited access and can go miles through a subunit with no exit. Bethlehem twp doesn't actually pose a problem with I-77 since OH-21 provides a regional connection to Tuscarawas.

That brings me to Nimishillen twp and Louisville city. The nodes are shown by stars with Louisvile in white and Nimishillen in blue. The Louisville city within the township. The Nimishillen node is within Louisville city. If I apply the same rule to Nimishillen that I did to Pike, then Nimishillen is connected to the neighboring townships and Louisville is not. I think that's the commonsense result, but now backed by an actual rule.

[Torie]

Interstates are an inherent challenge because they are limited access and can go miles through a subunit with no exit. Bethlehem twp doesn't actually pose a problem with I-77 since OH-21 provides a regional connection to Tuscarawas.

That brings me to Nimishillen twp and Louisville city. The nodes are shown by stars with Louisvile in white and Nimishillen in blue. The Louisville city within the township. The Nimishillen node is within Louisville city. If I apply the same rule to Nimishillen that I did to Pike, then Nimishillen is connected to the neighboring townships and Louisville is not. I think that's the commonsense result, but now backed by an actual rule.

Well the map above is an example of a subunit node that is in a foreign subunit. So the issue is whether you erase the subunit in which the the node from another subunit is in, or create a pseudo node in the subunit in which no node is located. What exactly is your dividing line, between a subunit that is second class, versus a regular one, other than well, it is obvious that one subunit was carved out from another?  Tell me why it raises problem to just create a pseudo node for the nodeless subunit (where that subunit is not rendered nodeless by a chop, where me via some simple mechanics, and you via something deep into the weeds, get to the same place apparently)?

[jimrtex]

OK, after 3 cups of coffee, I have finished wading through this nightmare, and think I understand it, although not really your 4 options. What you and Jimrtex have apparently been doing is what I have never done, because to me it doesn't make any sense, so I never considered it.

So let's step back from all of this a bit. Why is it necessary to create two subunits with this chop? Why is it necessary to create Leroy as a node?  Is seems to me that you have the Chatam node, and two highway cuts, one to Butler (with the highway cut at Millry), and one to Wagarville. End of story. So what is the policy reason to create another subunit, and another node. What does it accomplish? What mischief is it designed to stamp out?

Obviously the idea that you can eliminate highway cuts with creative chops that would otherwise exist is ludicrous, as you suggest. But before having to torture my brain with any of this further, we need to get past the the issue of whether or not we need to create another subunit with its own node out of thin air by virtue of a chop of a subunit. The only time I see the need to create a pseudo node is where a subunit not chopped is node-less because the node is parked in another subunit.

My approach is totally different from that of Muon2.

I think it is too complicated to try to score a plan globally on a statewide basis, particularly for legislative districts. So instead I would attempt to draw a map based on first-level units, typically counties, that has pretty good equality. Each region in this map would have a population of a roughly integer number of units. In many cases, the regions would have a population equal to a district, and could be used directly for legislative plans. For congressional maps, they might need some touch-up. Compactness would be measured based on perimeter length.

The process would be repeated for division of the multi-seat regions and any touch-up using secondary units.

[muon2]

Interstates are an inherent challenge because they are limited access and can go miles through a subunit with no exit. Bethlehem twp doesn't actually pose a problem with I-77 since OH-21 provides a regional connection to Tuscarawas.

That brings me to Nimishillen twp and Louisville city. The nodes are shown by stars with Louisvile in white and Nimishillen in blue. The Louisville city within the township. The Nimishillen node is within Louisville city. If I apply the same rule to Nimishillen that I did to Pike, then Nimishillen is connected to the neighboring townships and Louisville is not. I think that's the commonsense result, but now backed by an actual rule.

Well the map above is an example of a subunit node that is in a foreign subunit. So the issue is whether you erase the subunit in which the the node from another subunit is in, or create a pseudo node in the subunit in which no node is located. What exactly is your dividing line, between a subunit that is second class, versus a regular one, other than well, it is obvious that one subunit was carved out from another?  Tell me why it raises problem to just create a pseudo node for the nodeless subunit (where that subunit is not rendered nodeless by a chop, where me via some simple mechanics, and you via something deep into the weeds, get to the same place apparently)?

Is there a functional difference between a pseudo-node and the actual node? If the result is the same either way, it is far easier to describe the process in terms of actual locations that are easily defined. Then I apply the rule that allows crossing the cut out subunit, even if you start within it, and the result should be the common sense result that Nimishillen is connected to the four adjacent townships.

[Torie]

"Is there a functional difference between a pseudo-node and the actual node? If the result is the same either way, it is far easier to describe the process in terms of actual locations that are easily defined. Then I apply the rule that allows crossing the cut out subunit, even if you start within it, and the result should be the common sense result that Nimishillen is connected to the four adjacent townships."

So this only applies when a subunit node is located in a foreign node? Is that the general rule? The functional difference, is that the subunit without a node located within it, has a node in a different location than the pseudo-node would be located in. And then the question, is would that result in any map distortions, and/or anomalies, that would otherwise be avoided by following the usual practice of each subunit having a node, as opposed to where it does not, essentially combining the two subunits for erosity measurement purposes. Have I stated what is in play here correctly?

Until I complained, you created a pseudo-node with Leroy, so it is not as if the very concept of a pseudo-node causes for you a reflexive negative reaction in the way that say the words "Trump/Cruz" causes with me.

[muon2]

I think we are on the same page. I used a pseudo-node when there was no political unit in play as in the county chop that lacked the county seat. I could use a pseudo-node when the node resides in a different subunit, but prefer the actual location if other rules give the same connection result either way. I might be convinced to use a pseudo-node for the captured node, but I should see more examples.

Here's my last area of complication from Stark (it's the county that keeps on giving). I've colored the following subunits and marked their nodes with stars.

Canton city (white star)
Canton township (green)
Plain township (dark blue)
North Canton city (light blue, actual location slightly north of image)
Meyers Lake village (red)



Here are some thoughts and questions for this area. Suppose Canton city and twp are in one district and North Canton city, Meyers Lake village and Plain twp are in a different district.

North Canton and Canton city are locally connected so there is a link cut because they are in different districts.

If a township is kept whole the parts are presumed to be connected to the node. Contiguity requires that the fragments of Plain that are wholly enclosed are kept with Canton city, and this chops Plain twp. That leaves three separate fragments of Plain twp. Do they create three cut links to Canton with attendant erosity (that's the way I was treating it in the King county examples)? If not, would it change if the Fairhope fragment were shifted to the Canton district, leaving two fragments with cut links to Canton?

Meyers Lake isn't contiguous to Canton city, but it is to parts of both Canton twp and Plain twp. There are local roads from Meyers Lake to both those township fragments, too. The paths from Meyers Lake to either township goes through Canton city. It seems clear that Meyers Lake should be connected to both, so there will be a cut link to add to erosity.

Then there's the question of whether the Plain twp fragment creates a cut link to the Canton twp fragment in the area immediately east of Meyers Lake.

Alternate thoughts?

[Torie]

"I used a pseudo-node when there was no political unit in play as in the county chop that lacked the county seat."

Which I didn't like, but you assured me didn't matter as to the result, but I would be more comfortable if it died, and only apply where the entirety of the a subunit has no node.

I will deal with the balance of your post tomorrow.

[Torie]

As a general rule, we want to create an incentive to unite the township fragments. Areas that are surrounded by another area should be ignored. They can go in either CD. Some states laws I think allow a CD to not be contiguous if the lack of contiguity involves uniting a split township or city or whatever. So if by the surrounded area, you mean the bit of Plain Township that seems surrounded on all sides of Canton City to the northeast of Hills and Dales, that should be ignored.

Thus, if Plain Township is all in one CD separate from Canton City, we just have one highway cut between Canton City and Plain Township, with a second, but one one additional cut, between Canton Township and Plain Township, ignoring that Canton township is fragmented by Meyers Lake.

If Fairhope is in the Canton City CD, chopping Plain Township, I think that should create another cut if the township to the east is in another CD, and there is a road cut involved. If the township to the east is in the Canton City CD, then no highway cut is involved, obviously. So, putting Fairhope in either CD is a freebie, unless it involves another highway cut to the township to the east, because that township is in another CD. The idea is that the fragments don't create highway cuts arising from Canton City biting into Plain Township, or Meyers Lake creating a Canton Township fragment, but the fragments could create another highway cut vis a vis adjacent townships.

I hope this makes sense. Below are images in relevant part of the highway cut results, with the black lines being cuts, and the red lines not counting as cuts. I didn't focus on where the nodes were for this exercise. The concept behind the red lines is to avoid being punished for getting a subunit's fragments together.

[muon2]

I think I follow, with one exception. In the left figure with the Plain chop there is a red link between Plain twp and Canton twp near Meyers Lake. I would have thought that it would switch to black when Plain was chopped. If you wouldn't switch it, why, and is there any circumstance where you would have a black link between Plain twp and Canton twp?

[Torie]

I think I follow, with one exception. In the left figure with the Plain chop there is a red link between Plain twp and Canton twp near Meyers Lake. I would have thought that it would switch to black when Plain was chopped. If you wouldn't switch it, why, and is there any circumstance where you would have a black link between Plain twp and Canton twp?

The red line I guess should really be between Meyers Lake and Canton, and that involves rewarding keeping Canton township whole, which causes potentially for there to be a highway cut from Meyers to Canton townships absent the reward. But I am not sure what happens, or should happen, where the road from the node in Meyers travels through Canton township on the way to Canton City. The node of Canton township lies elsewhere, and if that Canton township salient there were part of Canton City, there would be a highway cut. What happens where there is this intervening salient of Canton township without a node? Does that "cleanse" the highway cut in all events?

I guess for this exercise each fragment should be deemed to have a node where the fragmented township is chopped, but not where there is no chop. In that event, if Canton township is chopped, there is deemed a node in that tiny bit next to Meyers Lake creating a chop between it and Canton City, but if not chopped, there is no highway cut between Meyers Lake and Canton township.

Does that make sense?

Below is the graphic. I put up the question mark, because there is not Canton township node between Meyers and Canton township node. So if no chop of Canton township, I guess no highway cuts at all around Meyers. But if it is chopped, does that generate a highway cut not only from Canton Township to Canton City, but also from Meyers to Canton township to the south? Having two highway cuts generated by the chop of Canton township there, seems a bit much. But maybe that is necessary to make the rule work in general, even if a bit much in this instance, since the rule is that when a fragmented subunit is chopped, each fragment generates its own node. So I guess maybe there is no escape.

[muon2]

Do these then make sense as general rules?

A fragmented geographic unit is one where the unit consists of two or more discontiguous parts. All parts of a fragmented unit are considered connected if the entire district is kept wholly within a district, and the unit has a single node. If a fragmented unit is chopped, each discontiguous fragment is treated as a separate geographic unit with its own node.

If a fragment of a unit is entirely surrounded by a unit, and the population of the surrounded fragment is not needed to bring the population range of the districts within the required tolerance, then inclusion of the surrounded fragment with the surrounding unit does not count as a chop of the fragmented unit.

I added the provision about population to limit the ability to game the system by utilizing large surrounded fragments to balance population without a chop penalty. For small fragments it allows plans to maintain strict contiguity by including the surrounded fragments with the surrounding unit.

If there is no connecting path from a geographic unit to any other unit, then a connection exists from that geographic unit to each contiguous unit if there is a local connection to any part of the contiguous unit.

This would provide for connecting links from Meyers Lake to both Canton and Plain twps, and either could be cut, regardless of the status of chops in either township.

[Torie]

Before I parse the text, are you in agreement with my basic concept?

[muon2]

Before I parse the text, are you in agreement with my basic concept?

I think so, though I have generalized some of the specific conclusions. I'm also offering a way out of the Meyers Lake issue that generally comports with your map, but may not specifically be the result you intend depending on how I parse the question mark in your example.

[Torie]

Before I parse the text, are you in agreement with my basic concept?

I think so, though I have generalized some of the specific conclusions. I'm also offering a way out of the Meyers Lake issue that generally comports with your map, but may not specifically be the result you intend depending on how I parse the question mark in your example.

"Generalized" leaves me a bit nervous. Are we uncertain as to whether there are other imbedded effects in what is generalized? How do you propose to parse the question mark? It would seem to be another cut, if one views the Canton township fragment as having its own node when copped somewhere. The other cut is to Canton City, a separate subunit. You get two cuts because two separate subunits are in play.

[muon2]

I propose to parse the question mark as a cut link. Meyers Lake is equally connected to both Plain and Canton twp. I think there should be a cut if a district line separates Meyers Lake from either of those twps.

At some point the rules have to be general in nature. I've tried to extract the general principle you applied to the specific case here. If there is a defect, I'm hoping you will point it out. If there is an unintended consequence elsewhere that we don't now anticipate, I think we should deal with it as it arises.