Local vs regional road connections

[muon2]

Here's a situation involving two chops into a county creating two isolated fragments. As before consider that all contiguous counties are locally connected, the black lines represent state highways, and the connecting path is based on the shortest distance.



As a side note, if the node for Dawes were in the western part of that county, then the Dawes-West Agnew path would be the connecting path and the fragment would not be isolated. It also would not be connected to Calhoun in that case and the district would be disallowed as in option A.

I don't follow this at all. Given where you put the state highways, and the chops, I don't see the relevance in this example of where the D node is.

In the map above there are two paths between Dawes and Agnew. Given the location of the Dawes node, the eastern path is the connecting path since it's shorter. The chops shown put that path going into the central Agnew fragment. That leaves west Agnew with no connecting paths so it is isolated.

Suppose the Dawes node were relocated to a point near its western border with Calhoun. In that case the western path between Dawes and Agnew would be the connecting path. It enters Agnew in the west Agnew fragment, so west Agnew would not be isolated. It would have a regional connection to Dawes. Thus I could not consider the local connection to Calhoun and the west district would be disallowed.

The situation as interpreted by option A is the same as if the Dawes node were in the west rather than at the shown location. That is why I brought it up.

Does this clarify or muddy my initial comment?

[Torie]

Yes, it does clarify. We are now focusing on the connections between D and the west fragment of A. I don't consider that fragment "isolated" from D. It has a state highway link, albeit not direct. To me the shortest route metric deals with erosity measuring highway cuts, not isolation. So where the D node is would affect whether or not there is a highway cut.

[muon2]

Yes, it does clarify. We are now focusing on the connections between D and the west fragment of A. I don't consider that fragment "isolated" from D. It has a state highway link, albeit not direct. To me the shortest route metric deals with erosity measuring highway cuts, not isolation. So where the D node is would affect whether or not there is a highway cut.

But we already concluded that it could. Here's a simple chop of Agnew that we've discussed before.



We agreed that the only highway that counts between counties is the one with the shortest path between nodes that doesn't cross into another county (setting aside nick paths). That shortest path highway is the connecting path. It is cut and counts for erosity if it crosses the county line between districts. In the above map the shortest path from Agnew to Dawes is the eastern path and it goes between the two districts. It is cut and counts for erosity.

Now consider if the Dawes node was in the west end of Dawes. That would make the western path the shortest path between Agnew and Dawes. It enters Agnew (the chopped county) in the same district as Dawes so there is no cut link between Agnew and Dawes.

Policywise this makes some sense. The shape of the chop is well-fitted to the notch corner of the western district and really doesn't change the geometric shape much. If the Dawes node is in the west the chop fits better with the population/government centers (with the nodes as proxies) than it does if the node is in the east of Dawes. There is a more obvious cut between centers with the Dawes node in the east.

[Torie]

The agreement was for whole county connections, not chops. I see the policy issue for erosity evaluation, but not for a total ban based on lack of connectivity.

[muon2]

The agreement was for whole county connections, not chops. I see the policy issue for erosity evaluation, but not for a total ban based on lack of connectivity.

We agreed that when there is a chopped county, each connection from the whole county to its neighbors would be assigned to only one fragment of the chopped county. The assignment is based on which fragment the connecting path first enters. Your only expressed concern with my definition was on the subject of pseudonodes, which we have been hashing out separately.

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

Definition: Fragment. A fragment is a contiguous unit entirely within a district formed by the chop of a political unit. For a fragment that does not contain the node of the whole political unit, the node is that of the most populous subunit in the fragment. Fragments are connected to other fragments in the same political unit if their nodes are locally connected. A fragment is connected to another county or fragment in another county if the connecting path between the counties enters the county in that fragment.

[Torie]

Well, irrespective to what I agreed to (perhaps not understanding the implications at the time), I still don't see the policy reason for a flat ban. The fragment does not purport to have anything to do with a node connection. It is connected to the other subunit by a state highway. Perhaps it is not that important an issue, particularly in as much as the map would be docked on erosity, but that is my view until I understand a policy reason to the contrary. The computer can be programed differently when evaluating highway cuts versus connectivity.

[muon2]

Well, irrespective to what I agreed to (perhaps not understanding the implications at the time), I still don't see the policy reason for a flat ban. The fragment does not purport to have anything to do with a node connection. It is connected to the other subunit by a state highway. Perhaps it is not that important an issue, particularly in as much as the map would be docked on erosity, but that is my view until I understand a policy reason to the contrary. The computer can be programed differently when evaluating highway cuts versus connectivity.

Let me pose a different mechanism that may be what you seek.

Definition: Local Connection. There is a local connection between two subunits within a county if there is a continuous path of public roads and ferries that allow one to travel between the two nodes without entering any other unit. Roads along the border of two units are considered to be in both units on either side of the border.

Definition: Regional Connection. There is regional connection between two counties or subunits in different counties if there is a continuous path of all season numbered state or federal highways or regularly scheduled ferries that allow one to travel between the two nodes without entering any other county. If the node is not on a numbered highway, then the connection is measured from the point of the nearest numbered highway in the county to the node.

Item: Each unit or fragment in a district must be locally connected to every other unit or fragment in the district. The connection may either be direct or by way of other units in the district.

Definition: Link. A link is a representation of a connecting path between nodes. A link is based on a local connection if the nodes are in the same county. A link is based on a regional connection if nodes are in different counties.

Definition: Component. A component of a district is a set of nodes in the district such that any two nodes are connected to each other by a sequence of links in the district, and that set is connected to no other nodes in the district by a sequence of links in the district.

Item: It is preferred to have only one component for each district. Each component in a district in excess of one increases the erosity by one.

The first underlined change allows isolated fragments to be appended onto districts as you would like. The new underlined item says that isolated fragments are in different components. The cost for extra components is a penalty in erosity reflecting the preference to have regionally-connected districts when possible. Note that this opens the door to allowing locally, but not regionally, connected counties to form a district with an erosity penalty, and obviates the need for a nick path definition.

[Torie]

Definition: Component. A component of a district is a set of nodes in the district such that any two nodes are connected to each other by a sequence of links in the district, and that set is connected to no other nodes in the district by a sequence of links in the district.

I don't understand what the bold means; in particular "that set is connected to no other nodes ..."

Item: It is preferred to have only one component for each district. Each component in a district in excess of one increases the erosity by one.

The first underlined change allows isolated fragments to be appended onto districts as you would like. The new underlined item says that isolated fragments are in different components. The cost for extra components is a penalty in erosity reflecting the preference to have regionally-connected districts when possible. Note that this opens the door to allowing locally, but not regionally, connected counties to form a district with an erosity penalty, and obviates the need for a nick path definition.

Where a whole county is appended via a qualifying nick path, I don't think any penalty should obtain. I wish to distinguish between fragments and whole counties. There is a good policy reason for this, as we saw in the Charlotte metro area.

[muon2]

Definition: Component. A component of a district is a set of nodes in the district such that any two nodes are connected to each other by a sequence of links in the district, and that set is connected to no other nodes in the district by a sequence of links in the district.

I don't understand what the bold means; in particular "that set is connected to no other nodes ..."

It just means that the set of nodes that are linked is complete and is missing no other linked node in the district. The form of the definition is intentionally mathy. Connected components are a concept from graph theory and having disjoint components (ie missing links) in a district can be interpreted as equivalent to extra cut links at the boundary.

Item: It is preferred to have only one component for each district. Each component in a district in excess of one increases the erosity by one.

The first underlined change allows isolated fragments to be appended onto districts as you would like. The new underlined item says that isolated fragments are in different components. The cost for extra components is a penalty in erosity reflecting the preference to have regionally-connected districts when possible. Note that this opens the door to allowing locally, but not regionally, connected counties to form a district with an erosity penalty, and obviates the need for a nick path definition.

Where a whole county is appended via a qualifying nick path, I don't think any penalty should obtain. I wish to distinguish between fragments and whole counties. There is a good policy reason for this, as we saw in the Charlotte metro area.

Please recall that my preference is to exclude nicks entirely. I'm willing to concede your ability to include isolated fragments, and I think giving me some preference to avoid nicks is a reasonable trade. I was not as sold on the need to give equal weight to some of the Charlotte arrangements. This formulation also greatly simplifies the rules by creating a general rule to replace a large number of exception rules (nicks, isolation for fragments and units, subunit connections, etc.), and that is a good thing as far as selling the system.

If you'd rather we can return to haggling over each of the exceptions. We haven't been very productive with that process IMO.

[Torie]

Well I don't think bargaining is really appropriate here. I opined as to what I think is best based on policy considerations. We can just leave this one on the disagreement table. Maybe over time, it will go away, or maybe not. I feel more strongly about the nick exception, than banning highway connected fragments that don't use the most direct route, which in the end will not ver very important, if at all, but I still take exception to that one too.

[muon2]

Well I don't think bargaining is really appropriate here. I opined as to what I think is best based on policy considerations. We can just leave this one on the disagreement table. Maybe over time, it will go away, or maybe not. I feel more strongly about the nick exception, than banning highway connected fragments that don't use the most direct route, which in the end will not ver very important, if at all, but I still take exception to that one too.

I'm not sure where we go from here. We seem to disagree on the fundamental nature of connections and what should be counted towards erosity. We seem to disagree on the importance of a cleaner system of general rules versus one that includes a longer list of exceptions to handle with special rules. We seem to disagree on what features the public will see as critical and which ones are acceptable artifacts of a neutral system. Hmm ...

[Torie]

Just move on. Presumably you find some value in bouncing ideas off of me. In the end, a paper can lay out the options, and where people may disagree. In defending what you prefer, your challenge will be not to lapse into jargon, or abstract grand unified theories, but rather persuade folks that it is common sense, and where it isn't, it is not far off, and not worth the additional complexity. What I am receptive to, is public policy and common sense arguments of course. That is what will change my mind.

The issue we are arguing about as I say is of very marginal importance, and very deep in the weeds.