Local vs regional road connections

[Torie]

Somehow, I knew that is what you would say. This lacunae of yours never entered my synapses before somehow. We shall see how it goes. It's barely possible that a gratuitous chop could cause a map to enter the pareto optimal frontier, by shedding two cuts in exchange for one chop. Hopefully, in real life, that situation will not arise.

[Torie]

And here I thought I had been so consistent with this use of chops to reduce erosity for the better part of three years. I know it came up in our recent discussion of NC maps. Perhaps it was a case of non liquet rather than a lacuna? Either way it should be clear now, I hope.

You taught me something. I had to look that up. A gap in the law versus no law. I am not quite sure what the distinction is. Maybe the connotation of non liquet is that it's more novel, and applicable law is farther away, as opposed to where there are precedents, but precisely where the line is drawn at the margins has not been legally resolved.

[Torie]

Going back to the topic at hand, how do you thing gutting the Albany metro area that way comports with the common sense rule? How do you think the commentators would react to such a gutting being the cat's meow map? Isn't the common sense approach, that you start with the core metro county, and branch out to its burbs first?

I am not in the mood right now to go to the mat with you over this, but I find the map disturbing. It is something for us to seriously think about, as to whether there is some workable fix for this. Now please don't go all stubborn on my here! Just think about it, in some dark room and muse about it for awhile. Thanks my friend.

[Torie]

The Albany pack plan would be eliminated on the chop score.

Vis a vis which other map?


One thing we did in the MI exercise at train's suggestion was sum the CHOP and INEQUALITY scores, instead of using INEQUALITY as a tie breaker. I suspect the Albany pack plan has lower INEQUALITY by virtue of the chops, I know I pushed 3 of my CDs right to the 0.5% limit. That might be a method to keep the Albany pack plan in the hunt.

That is just an accident is it not, as opposed to something systemic favoring pack plans? Accidents should not drive policy.

[Torie]

The Albany pack plan would be eliminated on the chop score.

Vis a vis which other map?


My plan in that post.

One thing we did in the MI exercise at train's suggestion was sum the CHOP and INEQUALITY scores, instead of using INEQUALITY as a tie breaker. I suspect the Albany pack plan has lower INEQUALITY by virtue of the chops, I know I pushed 3 of my CDs right to the 0.5% limit. That might be a method to keep the Albany pack plan in the hunt.

That is just an accident is it not, as opposed to something systemic favoring pack plans? Accidents should not drive policy.

Not entirely an accident. More chops, including macrochops, tend to reduce inequality. A plan that chops one county and one subunit for every CD above the first should be able to get perfect equality.

I see. If based on experimentation, that actually proves to be the case, I will be more open to the suggestion. It is a rather important policy consideration in my view. But I don't have that much problem with 3 out of the 4 counties being in one CD, avoiding a chop, with the core county one of the three (which is your map). That is a reasonable tradeoff. It's the shredding of a group of counties in a metro area (as I defined that term), that concerns me.

[Torie]

Yes, I see. You are feeling quite proud of yourself this morning aren't you. 

We shall see whether we need to raise the salience of inequality to get the kind of maps of which I approve.   We seem to have dodge the bullet in NY, after temporary panic, and maybe we have enough to so dodge elsewhere.

[Torie]

My edits are in red. None of this should come as a surprise to you. I am quite firm in my opinion on the bridge chop issue. I am unaware of any argument to the contrary that I find of much merit thus far. I thought we did away with pseudo nodes for fragments, except for computer mapping purposes.
Where is the language that a fragment can create but one highway cut that we worked through?

Definition: Node. A node is a reference point for a geographic unit. For a political unit the node is the primary place of government for that unit.

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, unless such highway in such other county is a qualifying nick cut. 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.

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.

Definition: There is a bridge chop if two counties wholly or partially within one district are connected sole by an intervening county that contains a fragment.

Definition: There is a  nick cut if a highway between the nodes of two counties enters another county without traveling through the node of such other county and its distance in such other county is one third of less of the distance of the length of the county measured from the two on its boundary that are farthest apart. The nick cut is a qualifying nick cut if there is also a local connection between the two counties connected by the highway with a nick cut.

Item: Each unit or fragment in a district must be 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.

Item: Two whole units in a district cannot be connected solely by way of a fragment (bridge chop). is disfavored.

Definition: Cut link. A cut link is a connection between nodes in different districts.

Definition: Erosity. The erosity of a district is the set of cut links to nodes in that district.

Item: The EROSITY score for a districting plan is the set of all cut links in that plan. EROSITY is also equal to one half the sum of the erosity for the districts in the plan. [I don't understand the one half the sum business.]

[Torie]

Thanks for the math explanation.

Yes, "disfavored" or whatever term is used, will need to be defined. You know what I meant.

[Torie]

I don’t understand the sentence underlined in red. I thought a numbered highway needed to go into the node jurisdiction. If not, is the only requirement is that the numbered highway enter the county in question, and then can use local roads to get to the node thereafter?

The word “any” that I underlined, suggests that there can be more than one regional path between two counties. If that is the case, then the direct red line that I drew representing a regional highway connection node C to node B would not be a nick cut, because part of it also serves as a regional path from node A to node B, albeit a circuitous one and its use of the highway in question for a bit was not built to connect node A to node B (which is the point).  And the second red line from node C to the right does use the shortest direct regional path from A to B (assuming there is always only one qualifying regional path, to wit, the shortest one). Do we really want to exclude that?

My recollection is that I made the test the number of the state highway. I drew two red lines on your map, which represent additional numbered state highways in addition to what you drew (the local politicians are good a pork barreling, so thus the plethora of state highways). If the right red line and the vertical black line for the last bit of the path to node B are the same number, then it is a qualifying nick path. If not, it is not. In the nicked county, or the county where the regional connection is in issue, if we don't have the same number as the state highway at the point where it enters the nicked county, it is not a valid nick path. If the number is the same, then you do.  And by that test, if the path from node C to node D in your second graphic has a different highway number for the final portion in Dewey going north, then you would also not have a valid path there as well.

And how about that rural NC connection issue in the western part of the state, where we had a numbered highway that traversed the whole county as a nick cut without traveling through the node of that “nicked” county. We wanted to exclude that, so we did the distance metric. If that path did not use a highway that served in part as a, or the (depending on the resolution of the above), regional connection from the node of the nicked county to the node of some other adjacent county, then it would count as a regional connection?

So we have quite a bit here to think about.

 

[Torie]

Is this the example from western NC?

And then, at the other extreme from the UCC urban area exception issue,  we have the Clay County "nick cut" link.  State highway 64 as it traverses through Clay County from Cherokee to Macon just misses the county seat of Clay, Hayesville, and there are no other urban areas in Clay County. Yet the "nick" traverses the length of the whole county. That is a no go. That is not a nick. I am not sure what rule to fashion to deal with that. That the length of the nick highway cannot be more than a third of the length of the county measured from the two points thereof that give the longest length? Or something like that? And by measuring the length of the highway for this ratio, the rule would tend to penalize twisty state highway nick cuts that twist and turn over rugged terrain, which is a good thing I would think. An absolute highway distance parameter not based on a ratio might not work too well, given counties vary a lot in size.

My definition handles this case. US-64 is on a path from both Hayesville (Clay) to Murphy (Cherokee) and Hayesville to Franklin (Macon). Either or both disqualify it by definition. So it can't be used as a nick path from Murphy to Franklin.

That is where "a" versus "the" is benign. But in other cases its malignant. You are using "a" as a substitute for a distance metric.

[Torie]

[Torie]

Now I'm confused. I thought the uniform highway number was a different standard than the maximum 1/3 of distance in the cut. At least they were two different proposals when you and jimrtex were debating this over NC.

It must be both the same highway number and fit within the length parameter.

Moving C closer to D does not change the length in A, but it does change the fraction of the path in A. If I put the nodes for C and D on the same numbered highway right at the border with A, the fraction in A would be the majority of the length. Yet if I move C and D farther apart I can eventually get the fraction in A under 33% and it becomes a link. That is counter intuitive to me.


The fraction is the length of the nick as the numerator and the length of the nicked county as the denominator. The length of the road outside the nicked county is irrelevant. If I am missing something, please put up a graphic.

[Torie]

Now I'm confused. I thought the uniform highway number was a different standard than the maximum 1/3 of distance in the cut. At least they were two different proposals when you and jimrtex were debating this over NC.

It must be both the same highway number and fit within the length parameter.

Moving C closer to D does not change the length in A, but it does change the fraction of the path in A. If I put the nodes for C and D on the same numbered highway right at the border with A, the fraction in A would be the majority of the length. Yet if I move C and D farther apart I can eventually get the fraction in A under 33% and it becomes a link. That is counter intuitive to me.


The fraction is the length of the nick as the numerator and the length of the nicked county as the denominator. The length of the road outside the nicked county is irrelevant. If I am missing something, please put up a graphic.

I don't know what the underlined means. I don't recognize it from a previous proposal. jimrtex had referenced the length of the entire path as a denominator IIRC.

I'd still like to see an example where you feel my proposal creates an untenable result. From my perspective, it would not bother me to have no nick paths, but I'm trying to accommodate those who see a value in them.

The length of the nicked county is the length of the line drawn between the two points on the county's boundary that are farthest apart. That is the denominator. The numerator is the length of the road while in the nicked county. I have used this metric since the NC Clay County discussion. I have described in our discussion here my issues with your approach. My approach focuses on whether the highway is really designed to link the two nodes that happens on the way to nick another county.

[Torie]

If I understand this, you would have either of the red highways become a nick path. I would exclude them, since either of them becomes the connecting path (ie shortest) between A and C. To me that's true even if the highway was explicitly built for a connection from C to B.

Yes, either would be a nick path assuming their length in the nicked county is a third or less of the nicked county's maximum length.

Can I ask if any of the county pairs I listed in NY causes grief? I want to make sure we aren't arguing over something so artificial that it need not control the rules.

There are 50 states. I think my rule hews to the common sense metric. It makes sense. I don't think yours does. It does not focus on whether there are really direct links between nodes (not interrupted by going through another node), and intended to be so. Sure, this will not be a very common occurrence. Neither are Indian Reservations. But it is important.

[Torie]

Isn't taking a ratio of distance in a nicked county, naturally scaling? Yes, to me, common sense, trumps introducing "novelty" to your system. That is never going to change.

[Torie]

Isn't taking a ratio of distance in a nicked county, naturally scaling? Yes, to me, common sense, trumps introducing "novelty" to your system. That is never going to change.

The ratio could be truly scaling if the densities were generally uniform. One problem with many scale-independent measures of compactness is how they are tripped up by urban concentrations. For example one standard test is to compare the area of the smallest circle that encloses a district with the area of the district (Reock measure). That test scales with the size of the district. Yet, if the district has large regular rural areas combined with erose areas in an urban area the district scores well. I am similarly concerned that a nick passing through an urban area misses features that would be irrelevant when in cuts a rural area.

I don't understand how your comment is relevant to my point, and I don't understand your last sentence at all. What does "misses features that would be irrelevant" mean?

Sure an erose elongated county might allow for a longer nick. So what? That is hardly a big deal. The metric works well enough for government work as it were.

[Torie]

As described with my two red lines above, the result as to what is a valid nick, and what is not, appears to be very arbitrary. If a road happens to tie into another road going that goes between two notes, even with a highly circuitous route, with another route more direct, you lose the validity of the nick, and if not, you have one, even if highly circuitous.

[Torie]

As described with my two red lines above, the result as to what is a valid nick, and what is not, appears to be very arbitrary. If a road happens to tie into another road going that goes between two notes, even with a highly circuitous route, with another route more direct, you lose the validity of the nick, and if not, you have one, even if highly circuitous.

Circuitous yes, arbitrary no. We have many circuitous connections defined directly between counties. Among these are ones that jimrtex has complained about, yet they remain for me (and I think you). There's nothing arbitrary about saying that a nick path can't already be on a direct path in the nicked county. It's saying that nick paths arise out of unusual situations where a highway passes through a third county in a truly incidental way.

Conversely using a 1/3 distance standard would be circuitous no, arbitrary yes. It tends to lead to more direct nick cuts so they would be presumably less circuitous. The use of 1/3 is itself arbitrary as it is not based on any comprehensive study of real geography. Look at the work that jimrtex put into UCCs to come up with a cutoff within MSAs that was not arbitrary.

Well I don't agree that the third rule is arbitrary, and most counties are not that erose anyway. I guess we are at a dead end here. What's arbitrary is involving highways that happen to connect in some circuitous way between nodes, to invalidate a direct nick cut, or allowing nick cuts that avoid that that themselves are circuitous and not designed to connect nodes. We just are not going to agree on this one.

[Torie]

I think I agree for scoring as opposed to computer mapping purposes, that having pseudo-nodes for, and only for, isolated fragments, is useful. Bear in mind that I would allow for chopped counties, that mere pavement suffices, albeit it is not preferred as compared to connections which are state highways. Yes, I have no inclination thus far, to concede to your "preference" in exorcising the preference mechanic. I think we need more boxes to work with than are afforded by a rigid hewing to the elegance regime.

Moving on to more important matters, isn't my signature just gorgeous? It also explains why most of the geography of NY state is essentially empty. And it also shows just why one of the key fights in the Revolutionary War was in that long green vertical zone running from Canada to NYC. It was the equivalent to what the Union did along the Mississippi in the Civil War to slice the Confederacy in two. But what the Unionists succeeded in doing, the British failed, and the rest is history. It was a rather close thing though.

[

[Torie]

I find this a bit confusing because we seem to be dealing with cuts and chops and connectivity all at the same time. Also there are very few isolated counties, so this rule is of very limited application. Most isolated fragments will not be in isolated counties. Having said that, there should be a preference for connecting the isolated fragment to the county that has the regional connection I would think.

[Torie]

Yes, I do want to grab a town that is not regionally connected in a macro-chop if that is the only way to avoiding chopping a town. I prefer to grab a town that is regionally connected, but not at the price of chopping it. So thus my preference regime. If you have a choice between two towns, pick the one with the regional connection, if neither town will be chopped, but pick the town without a regional connection, if the town with a regional connection will be chopped. The same rule should obtain both with ordinary county chops, and with subunit chops in macro chopped counties. I do carve out an exception for pseudo subunits within a subunit via the one bite exception (the Phoenix example).

This I think follows the common sense rule.

[Torie]

Here's what I'd ideally like as a definition and implementation. Setting aside macrochops for now, would it cause a serious problem? The most I see is occasional extra erosity for certain isolated fragments that do have both a regional connection to a county in their district and are locally connected to a different county not in the district.

Definition: Isolated Unit. Counties or fragments may exist that have no regional connection, but are locally connected to other contiguous units. Such counties or fragments are isolated units.
  
Item: An isolated unit is connected to another unit if there is a local connection to the unit.

It is very simple to illustrate and judge. It avoids the need for separate county and fragment definitions. No knowledge of the layout of districts is necessary.

This is an instance where there are no state highways in play. So it sort of states the obvious, other than allowing chops where no state highway is available. It does preclude a fragment creating chop where the CD chops into a county without a state highway connection, but where the fragment has a state highway connection to the node of its county. I think that is OK. I want to allow a chop into a county that takes a whole subunit without a highway connection across the county line (although not preferred), but I'm OK with precluding such a chop where a whole subunit is not taken in, but only a fragment thereof, thereby chopping the subunit. Indeed, you may be too generous. Even if a fragment has no state highway connection to its county node, why allow it, if there is another fragment creating chop available within the county that does have such a regional connection? It would seem to me that the preference regime should obtain here too.

The problem you describe involves a state highway in play. Yes, preferring the state highway, may create extra erosity. If it does, the two maps would be tied, with one winning on chops, and the other on erosity. That's fine with me.

[Torie]

Non-isolated fragments only require local connections within a county. That was defined earlier and is consistent with subunits inside a macrochopped county. It doesn't come into play for non-isolated fragments when there is only one chop (since by definition there is a state highway to the county seat interrupted by the fragment), but when there is more than one chop it may. Think about three fragments in a county where two have only a county road connecting them. They are connected in my initial implementation of fragments.

I don't see how the above is responsive to my comments.

The only place I think my rule precludes one of your locally connected chops is in the following circumstance. There is a large county that is macrochopped between two or more districts. Another district almost entirely outside of the macrochopped county takes a small bite in the form of a town not regionally connected to the rest of the district, but the town does have a state highway connecting it to one of the dominant districts in the macrochopped county. Essentially it would have to have a state highway running parallel to the county border through the town in question, but no fork in the town to cross the border. I think this would be a very rare case, and I'm not sure it's worth a special rule.

I don't follow the "special rule" bit. Any chop creating a fragment without a state highway connection should lose under the preference regime to a map that chops creating a fragment that does have a state highway connection.

[Torie]

I guess a "special rule" means a preference in your mind. Yes, maybe it will be rare as to your example. But if the rule is that a chop using a highway connection is preferred to one that is not, it has a pretty broad application, as opposed to being so limited that it is "special."

Your second comment to me seems to be using a lot of words that basically say that you don't like preferences, as sort of a conclusory statement. It certainly is easy enough to apply a preference regime. You just don't like it based on a rather compelling desire for elegance. On that one, we just disagree. Your approach does not hew to the common sense regime in my judgment.

[Torie]

"In crafting a rule to allow for certain local connections across county lines, the rule must function both for connections that are intact and those that are cut."

Why is that? As I say, for example, I want to allow for chops using local highways, in a way that would not be allowed for determining if whole counties are connected. You yourself carve out exceptions.