Local vs regional road connections

[muon2]

There are some open questions here. I used a brute force approach that created a link to an unincorporated SD if there was a connection to population in the SD. That ignored the idea of the node for the SD. I did that here to illustrate that this division of the subunits, typically put the SD node inside a muni subunit. The Monroe SD offices are in the city of Monroe, so any path to the SD node forces one through the city technically invalidating the path. That doesn't make much sense so I've looked at links to the largest population VTDs within those unincorporated subunits.

That brings up a second issue. The Woods Creek part of the Monroe SD is contiguous but disconnected from the rest of the SD, but only because the city is a separate subunit. In this illustration I allowed connections to it independent of the rest of the SD. It gets more complicated since the Maltby area is contiguous but disconnected as well, even keeping the city of Monroe in the SD for connection purposes. I show a link from the Northshore SD to the west of Maltby, but maybe it shouldn't exist since one can't get from Northshore SD to the Monroe SD offices without going through part of the Snohomish SD.

To define a connection one must say what points are connected. The only connection from Woods Creek to High Rock within the Monroe school district passes through the city of Monroe. Nominally that seems ok since the school district board meets in Monroe city. So linking the Sultan SD to the Monroe SD is actually tracing a path that starts and ends in cities that are separate subunits from the rest of the school district. It requires a rule such as

Connections are defined based on paths between the nodes (seats of government) associated with the subunits. When the node for an unincorporated area is in a separate subunit based on an incorporated muni, the path between nodes can include those associated munis and still be considered to be within the unincorporated subunit.

That allows the Sultan SD to connect to the Monroe CD on either the north of south side of the river since roads are available on both sides. However, there are no roads, state highway or local, that connect between Maltby and High Rock that stay within the borders of the Monroe SD. That means there is no path that connects the node for the Northside SD in Bothell city to the node in the Monroe SD in Monroe city that stays in those two school districts. So should the link from Northside to Monroe near Maltby be eliminated?

[muon2]

There is a presumption that a geographic unit (county or subunit) is all internally connected when it is whole even if individual areas are not. Camano Is is part of Island county even though it's connected to Snohomish not the rest of Island. All of our maps that have a whole CD in Snohomish would be invalid if this were not true. I visualize it as the whole of Island carrying Camano with it when Island is linked to a district.

By the same token all of Monroe SD is presumed to be internally connected, even though there are actually four separate disconnected but contiguous pieces.

Let me repeat here the definitions of nodes and connections.

A political unit can be represented by a node that is the political center of that unit. For a county the node is the county office where the elected officials meet. For a city or town the node is the city or town hall. For a precinct the node is the polling place. Units are connected based on the path that connects their nodes.

Two units are locally connected if there is a continuous path of public roads that allow one to travel between the two nodes without entering any other unit. Local connections can include seasonal public roads. A local connection path can be traced over water without a bridge if there is a publicly available ferry that provides part of the connection. Units smaller than a county must be locally connected within a district.

There is often more than one possible path to connect to nodes. For both local and regional connections the connection between two units is considered to be based on the path that takes the shortest time as determined by generally available mapping software.


Erosity measures severed connections, not cut highways.

For a school district the node is the district office. I would introduce a clarifying rule here. If the node is in a different subunit, then tracing a path through the subunit that includes the node does not invalidate the path as a connection. This would be a useful rule in VA, too, with independent cities that host county offices.

When a subunit is chopped (but not macrochopped) then each part of the chop functions as a new subunit for determining connections. If the piece of the subunit has the node of the subunit then that becomes the node of the chopped piece. If a piece of the subunit doesn't have the original node then the node is defined as the most populous place in that piece (which could be a village or a precinct). That's how we've done it in other states (like MI).

[muon2]

So on to the particulars ...



In this example Sultan SD is connected to Monroe SD by way of US-2. When Monroe SD is chopped as shown the connection along US-2 is severed. The remainder is still connected to Sultan SD by way of Ben Howard rd which runs along the south bank of the Skykomish river from Sultan to Monroe.

My concern is whether or not there should be a connection that I show going west from Maltby. If all of Monroe SD were together then there would not be a connection there because to get from Monroe SD offices to points west of Maltby one most go through the Snohomish SD along WA 522.

The rule I cited above says that if a chopped piece doesn't have the original node then the node is defined by that largest place in the chopped piece. Maltby is the largest Census Defined Place in the Monroe SD so once it is chopped, Maltby becomes the node for that piece. That means the link west of Maltby exists.

But what then of the connection to Sultan? It existed at the time of the chop but then vanishes if I reset the node to Maltby. It doesn't make sense to eliminate that valid connection just because of the form of the chop - that invites gaming the rules. If you can follow all of that, I'm looking for insight from other eyes to see a way out of the paradox.

Actually the easy way out is to chop the Maltby part out to CD 1 and leave the Woods Creek part in CD 8. They are close enough in population for it to work, and the paradox is resolved. I've posed this precisely because the paradox may appear in other settings and not have an easy way out.

[muon2]

Let me back up again and use the subunits of Stark county to illustrate nodes and connections.



The county has 3 types of subunits. Townships are governments marked with their names in sans-serif capitals. Villages are incorporated governments with under 5000 people marked with all capitals in a serif font. Cities are incorporated governments with over 5000 people marked like villages but with solid lines and with a circle after the name. Census defined places (CDP) are labelled with mixed capitals and lower case, and they are not units of government and not county subunits.

Nodes for the subunits are the seats of government - township hall, village hall, city hall. It's wherever  the governing board meets. The node is usually in the subunit, but Nimishillen town hall is in the city limits of Louisville, so it is actually in a different subunit. It's not that unusual if the township office wants to take advantage of city services like water and sewer in an otherwise rural area.

Connections occur between subunits if there is a continuous path of public roads that allow one to travel between the two nodes without entering any other unit. Generally that's pretty clear. There are connections from Pike twp to Bethlehem, Canton, and Sandy twp, as well as to East Sparta village. There isn't a connection from Pike to Tuscarawas county since OH-800 goes through East Sparta between the Pike twp hall and the county line. It's a highway cut at a county line that's not a connection cut.

Nimishillen should logically be connected to the adjacent townships and cities of Louisville and Canton. The definition above would leave Nimishillen only connected to Louisville since Nimishillen's town hall is in Louisville and a path to any other subunit requires going through Louisville. That led me to the clarifying rule: If the node is in a different subunit, then tracing a path through the subunit that includes the node does not invalidate the path as a connection.

Now consider Plain and Canton twps. Their nodes are in the large pieces north and south of Canton respectively. A path between their nodes must go through Canton city or an adjacent township, so Plain and Canton twps are not connected.

There is a presumption that a geographic unit is all internally connected when it is whole even if individual areas are not. Plain has disconnected fragments in the SW and SE corner and Canton has one in the NW corner. These are locally connected to the other twp, but as long as the townships are kept whole those local connections with the fragments don't count. Similarly, Plain is not locally connected to Jackson, but the SW fragment of Plain is connected to Jackson if it is chopped from the rest of Plain.

Once the fragments are chopped from the main part they must be locally connected to the district they are in and have their own node. Suppose Jackson, Perry and Bethlehem twp were in one district and everything to the east was in a different district except for the SW corner of Plain twp. That chops Plain and creates a new node for the SW fragment. The interpretation so far has been that the new fragment has connections to North Canton city (it shows as a village on the map), Canton city and Meyers Lake village. Those connections would be cut in this hypothetical example and contribute to erosity.

If this makes sense I can return to the application in WA.

[muon2]

The Pike township hall is in Pike twp even with its Magnolia address. It's at 7134 East Sparta Ave which is just off of OH-800 about 2 mi north of East Sparta. There's no problem with its location.

I agree that it is odd that neither Pike nor East Sparta is technically connected to Tuscarawas due to the irregular annexation lines of East Sparta. The question probably should be whether East Sparta is connected to Tuscarawas instead of Pike. Personally I would favor Pike since it is otherwise locally connected to Tuscarawas, while East Sparta is not.

A rule clarification could be: A highway that would otherwise qualify for a regional connection except for a muni taken out is not invalidated a connection. I have a similar interpretation for simple chops at the county level where a highway is interrupted by a precinct line.

I agree with your sense that a plan should be rewarded that keeps the disconnected parts of a township together. On the erosity side there is already some reward as I illustrated with be example. If more reward is needed, then it dividing such a disconnected unit can count towards the chop score.

[muon2]

The Pike township hall is in Pike twp even with its Magnolia address. It's at 7134 East Sparta Ave which is just off of OH-800 about 2 mi north of East Sparta. There's no problem with its location.

I agree that it is odd that neither Pike nor East Sparta is technically connected to Tuscarawas due to the irregular annexation lines of East Sparta. The question probably should be whether East Sparta is connected to Tuscarawas instead of Pike. Personally I would favor Pike since it is otherwise locally connected to Tuscarawas, while East Sparta is not.

East Sparta is but a village, so its existence is irrelevant it should seem to me. That still leaves hanging I think all of my points about highways, that I don't think you addressed.


Villages are incorporated munis less than 5000 persons, as opposed to cities which are over 5000. They both count much as cities and towns do in WA.


A rule clarification could be: A highway that would otherwise qualify for a regional connection except for a muni taken out is not invalidated a connection. I have a similar interpretation for simple chops at the county level where a highway is interrupted by a precinct line.

Is this going beyond the concept of where a muni is part of the subunit, but stands as its own subunit, ala Monroe and the school district issue? Presumably absent that, the subunit would have its own node, and each stands on its own. I don't know what interrupted by a precinct line means. If you mean the situation of where a precinct line would need to be changed, to avoid a highway cut, I don't think one needs a rule for that. Otherwise, are not precinct lines qua precinct lines wholly irrelevant?

This is independent of and precedential to anything related to Monroe. The issue is due to munis that evolve from an underlying set of townships that cover a county. The solution will have extend at the county level to VA independent cities which sometimes host a county seat and can cause similar issues at that level.

We have had cases where a simple chop placed the connecting highway on the border but the chop crossed the highway in such a way that the highway couldn't be on a path to either part of chop without crossing through the other. That would cause a connection that existed before the chop to vanish after the chop - not a good result. We have ruled that as long as both parts of the chop are otherwise connected to their districts the highway connection adheres to the district on the border.


I agree with your sense that a plan should be rewarded that keeps the disconnected parts of a township together. On the erosity side there is already some reward as I illustrated with be example. If more reward is needed, then it dividing such a disconnected unit can count towards the chop score.

There is currently no reward for keeping the fragments together where otherwise disconnected by an intervening city. But dividing the fragments, is better than chopping a subunit that is not fragmented. So you need an intermediate zone, to wit something on the order of a preference. Many, many roads led to preference resolutions, if one wants to hew to the common sense rule. There is no escape in my opinion.

There is a reward in that keeping the fragments together prevent them from contributing to erosity.

Once the fragments are chopped from the main part they must be locally connected to the district they are in and have their own node. Suppose Jackson, Perry and Bethlehem twp were in one district and everything to the east was in a different district except for the SW corner of Plain twp. That chops Plain and creates a new node for the SW fragment. The interpretation so far has been that the new fragment has connections to North Canton city (it shows as a village on the map), Canton city and Meyers Lake village. Those connections would be cut in this hypothetical example and contribute to erosity.

In this case chopping that one fragment adds 3 to erosity. The question is whether that is enough penalty.

I have thought a lot about the preference issue. My sense is that it applies best when no more than one preference choice is applicable - that is it forms a yes-no decision. If the only tie breaker were existence or non-existence of a chopped fragmented township (like Plain in my example) then it could function.

Real plans might have multiple such chopped townships. If we start counting the number of fragmented townships that are chopped, it's really just another score where the non-existence equals 0. At that point it either should add a third Pareto axis or it should modify one of the existing axes. If it should be a factor, I favor the latter solution where it modifies the CHOP score.

The UCC factors began as a preference, but the data indicated it functioned more efficiently as a modifier to CHOP. I suggest that any of these preferences could be modeled the same way. Or are you suggesting that we should revisit that decision about UCCs and return them to a preference?

[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.

[muon2]

Well the colors are certainly getting festive.


The Pike township hall is in Pike twp even with its Magnolia address. It's at 7134 East Sparta Ave which is just off of OH-800 about 2 mi north of East Sparta. There's no problem with its location.

I agree that it is odd that neither Pike nor East Sparta is technically connected to Tuscarawas due to the irregular annexation lines of East Sparta. The question probably should be whether East Sparta is connected to Tuscarawas instead of Pike. Personally I would favor Pike since it is otherwise locally connected to Tuscarawas, while East Sparta is not.

East Sparta is but a village, so its existence is irrelevant it should seem to me. That still leaves hanging I think all of my points about highways, that I don't think you addressed.


Villages are incorporated munis less than 5000 persons, as opposed to cities which are over 5000. They both count much as cities and towns do in WA.


A rule clarification could be: A highway that would otherwise qualify for a regional connection except for a muni taken out is not invalidated a connection. I have a similar interpretation for simple chops at the county level where a highway is interrupted by a precinct line.

Is this going beyond the concept of where a muni is part of the subunit, but stands as its own subunit, ala Monroe and the school district issue? Presumably absent that, the subunit would have its own node, and each stands on its own. I don't know what interrupted by a precinct line means. If you mean the situation of where a precinct line would need to be changed, to avoid a highway cut, I don't think one needs a rule for that. Otherwise, are not precinct lines qua precinct lines wholly irrelevant?

This independent of and precedential to anything related to Monroe. The issue is due to munis that evolve from an underlying set of townships that cover a county. The solution will have extend at the county level to VA independent cities which sometimes host a county seat and can cause similar issues at that level.

What's the problem with just creating another node where the subunit node is parked elsewhere, and calling it a day?

We have had cases where a simple chop placed the connecting highway on the border but the chop crossed the highway in such a way that the highway couldn't be on a path to either part of chop without crossing through the other. That would cause a connection that existed before the chop to vanish after the chop - not a good result. We have ruled that as long as both parts of the chop are otherwise connected to their districts the highway connection adheres to the district on the border.

Sorry to be so obtuse, but can you do a pictogram or something of what your are talking about? I knew I was drowning when you starting talking about disappearing chops.

There are two separate issues at play here. The first was left out of the post, but you responded to it (I think).

The question of a relocated node could only apply to Nimishillen, not to Pike. The Pike town hall is in its proper township and not in a muni. The Nimishillen town hall is within Louisville.

For Nimishillen is there a reason that my proposal doesn't work?

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The problem in Pike is a regional connection to Tuscarawas county that is interrupted by a muni (East Sparta) that is not itself regionally connected to Tuscarawas.

My notes from a year ago include this passage, so I know it was based on a map I scored on a thread. I'll have to see if I can find it to provide a visual.

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My proposal to deal with Pike is based on that older rule, but instead of a district chopping a county it is the muni chopping the township.

[muon2]

Here's an example that involved the highway interruption rule at the county level. The scoring predates the recognition of macrochops so ignore the scoring as it affects Tuscaloosa county.

Now let me analyze Torie's plan. It has four chops (Walker, Tuscaloosa, Autauga and Washington), and also has the UCC and MCC chop shared by my plan. When I overlay it on the graph it has an erosity of 50 including the addition of the 4 chops to the cut set.

I've recreated the map and enlarged the chop in Washington county to illustrate the rule.



Before the chop Washington used Chatom, the county seat, as the node. It was connected to Mobile to the south via AL-17 and US-45.

Regional connections involve paths that cross county lines, and require a continuous path of numbered state and federal highways between nodes. Using Chatom, Washington was connected to Mobile to the south via AL-17 and US-45. It was connected to Clarke to the east via AL-56 and US-43. It was connected to Choctaw to the north via AL-17. The graph above has links representing those connections.

After the chop nodes are defined for each piece of the chop. As the county seat Chatom remains the node of the blue district piece. Leroy is the largest place in the green piece and becomes the node of green district piece. There is a local connection between the two pieces in Washington since one can go between the nodes on local public roads - in this case AL-56 and US-43.

Regional connections involve paths that cross county lines, and apply to the pieces formed by the chop when connecting to the neighboring counties. Two connections based on continuous state and US highways are clear. After the chop the blue piece is connected only to Mobile. The green piece is connected from Leroy to Clarke via US-43.

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.

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.

[muon2]

I will ask again, when we talk about regional connections, is this the issue of whether subunits can be connected at all, or an erosity measurement issue?

Local connections are those defined by any roads and apply in all cases between subunits for connections within a county.

Regional connections are those defined by numbered state highways and only apply to cases with connections that cross county lines.

In this context I'm talking about erosity. I recognize that you have raised the issue about whether a plan can connect subunits across a county line with only a local connection. I personally like the consistency of having connections mean the same for both uses, but I think that's a different discussion than the issue I'm trying to clear up here (thinking of both Stark and eventually Snohomish). I'm happy to return to that issue once the use of connections for erosity is set.

[muon2]

I will ask again, when we talk about regional connections, is this the issue of whether subunits can be connected at all, or an erosity measurement issue?

Local connections are those defined by any roads and apply in all cases between subunits for connections within a county.

Regional connections are those defined by numbered state highways and only apply to cases with connections that cross county lines.

In this context I'm talking about erosity. I recognize that you have raised the issue about whether a plan can connect subunits across a county line with only a local connection. I personally like the consistency of having connections mean the same for both uses, but I think that's a different discussion than the issue I'm trying to clear up here (thinking of both Stark and eventually Snohomish). I'm happy to return to that issue once the use of connections for erosity is set.

Thanks. I am just trying to avoid confusion. If we are talking about separate things, we get into even more trouble. Again my loadstar is common sense for all of this. We need to do our best to try to hew to that, and avoid a situation, where the rules force something that just seems silly. Once we get past that, we can think about elegance and politics and clarity and all the rest.

So in that context, is the AL example helpful? The key point there was how to treat the regional connection that exists between Washington and Choctaw when there are no chops. There were four choices:

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 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.

In the 2013 case I used interpretation C for the scoring rule. This kept the number of regional connections unchanged when a (simple) chop took place.

[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.

[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.

[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.

[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.

[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.

[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.

[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?

[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?

[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.

[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.

[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.

[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.

OK. Do you agree with my vertical red line (to wit, no cut)?

I think that's what my general rule would do. There's no chop, so there's only a single node for each twp (treating them as fragmented geographic units). There's no path between the nodes of the whole twps so there's no connection between them to cut. Tell me if you think the rule would work out differently as written.

[muon2]

Thanks.

I'll be on the lookout for a situation that takes undue advantage of a surrounded fragment. In the meantime think about the situation where a township has two sizable fragments of roughly equal population, one of which is wholly surrounded by a city but the other sits on the perimeter of the same city. Those two parts both get their services from the same unit of government, the township, and form a clear community of interest based on that township. Shouldn't there be an incentive to keep the two parts in the same district? Compare that to the case where the same two fragments aren't fully surrounded and there is an incentive to keep them whole.

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

I interlineated to make this text clearer to me, assuming that was your intent. I made an inference as to what your intent was, and if I am correct in my inferences, I am in agreement, subject to my friendly amendments.

I indicated the one change I would make to your friendly amendment. The Meyers Lake situation arises because there is no path to the subunit node, not the lack of a path to the imputed node of a fragment.

[muon2]

Thanks.

I'll be on the lookout for a situation that takes undue advantage of a surrounded fragment. In the meantime think about the situation where a township has two sizable fragments of roughly equal population, one of which is wholly surrounded by a city but the other sits on the perimeter of the same city. Those two parts both get their services from the same unit of government, the township, and form a clear community of interest based on that township. Shouldn't there be an incentive to keep the two parts in the same district?

In lieu of keeping the subunit that surrounds the surrounded fragment whole? I don't think so. On the other hand, I do see, that if the choice after keeping the subunit whole which surrounds the fragment, is between taking in the remaining fragment, or some other subunit, there should be an incentive to add the balance of the fragmented subunit. So just thinking off the top of my head, maybe we say that the fragment that is not surrounded is deemed to have no node if all fragments are within one CD or something, so one can avoid a road cut by taking it in as opposed to some other subunit. Putting aside the mechanics of getting there, that to me is the common sense result. Agreed?

I will think about the plausibility of the mechanics. I don't want to get too far away from the basic definition of the node as a specific geographic point defined by the government in question.

While you were writing this I added to my quoted post that you may or may not have seen.