Local vs regional road connections
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muon2
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« Reply #475 on: April 22, 2016, 02:47:24 PM »

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.

Perhaps you are right that this cannot go further. I think our operational definitions of arbitrary are too different. Maybe its a law vs science thing. For now I will step back to direct connections only for examples, and maybe at a future date we can revisit nicks.
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muon2
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« Reply #476 on: April 24, 2016, 08:15:47 AM »
« Edited: April 24, 2016, 08:34:38 AM by muon2 »

Setting aside nicks for now, I want to look at a particular type of chop that creates an isolated fragment. Here are the current definitions and rules.

Definition: Connecting Path. There is often more than one possible path to connect two nodes. For both local and regional connections the connecting path 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.

Item: A fragment is connected to another fragment in the same political unit if their nodes are locally connected. A fragment is connected to another unit if the connecting path between the other unit and the unit containing the fragment enters the unit in that fragment.

I italicized my language in the definition of fragment that was questioned. These definitions and associated item allowed us to interpret the following chop as one that reduced erosity, creating a tradeoff between chops and erosity.



Here's an example of what I call an isolated fragment that could use my questioned wording.

Definition: Isolated Fragment. An isolated fragment occurs when a chop creates a fragment that has no connections to other units.



This is certainly a chop we'd like to see as it follows the river in this example. We have agreed that Adlai and Clay are not connected since you have to go through Dewey on the most direct path or Bryan on the more circuitous path. So the path through west Adlai between Clay and Dewey is not a connecting path, so west Adlai has no connections by the existing rules. I think the natural connections for west Adlai are to both Clay and Dewey, and this should be the graph.



Unlike other fragments an isolated fragment cannot rely on the location of the prior connecting paths of its original unit. Here's a rule that resolves this situation to get the result I suggest in the graph.

Item: An isolated fragment has a connection with a unit when there is connecting path with that unit.

This treats the isolated fragment as if it were a new unit for the purposes of making a connection. Note that this requires knowledge of the node of the fragment since it now is treated as if it it were an independent unit. Without a node in the isolated fragment there is no way to define new paths to be used as connections to the isolated fragment. That takes us back to the question of if and how to define a node in a fragment.
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Torie
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« Reply #477 on: April 24, 2016, 12:10:55 PM »
« Edited: April 24, 2016, 12:22:45 PM by 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. Smiley

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.

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muon2
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« Reply #478 on: April 24, 2016, 02:45:09 PM »

Actually if I've written my definition correctly, then the fragment you would like to use is an isolated fragment, in that it has no connections to other units, at most a local connection to other fragments in the chopped unit. That leads to rules that favor your preferred chop.

Definition: Isolated County. An isolated county is a county or equivalent that has no regional connections. Example: Pitkin county, CO.
  
Item: An isolated county is connected to a unit if there is a local connection to the unit.

Item: An isolated county fragment that has no regional connections to adjacent units in other counties in the same district is connected to a unit or fragment across county lines if there is a local connection to the unit.

The underlined narrowly defines the connections for your preferred chops. Without the underlined it would treat all isolated fragments the same whether or not there is a regional link to the rest of the district. Without the underlined it is simpler and either way it accommodates your preference. Any thoughts?

Oh, and I do like your signature. What's the source?
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Torie
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« Reply #479 on: April 25, 2016, 06:57:31 AM »

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.
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muon2
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« Reply #480 on: April 25, 2016, 07:28:42 AM »

It's true that isolated counties are very few in number (I'm only certain of one). But completeness requires that I address it. It turns out that the mechanism that makes most sense to address isolated counties also works for isolated fragments without regional connections even in ordinary counties.

So as you see there are two types of isolated fragments. One type has no possible regional connections and must use local connections. The other type can make regional connections using state highways that were not part of the connecting path to the unit containing the fragment. The tricky part is that if the fragment is adjacent to two counties, but there is only a regional connection to the county not in the district, it still isn't connected to its district. Not good.

Using regional connections where available requires the judge to recognize where the district extends into other counties. This tangles chops and connectivity more than is minimally necessary, but the tangle may be desirable. Human brains handle the tangle much better than computers.

One thing may help me understand the scope of your local-connected chop preference. It clearly is in play for simple chops. Is it necessary for macrochops, too? That is do you want to grab a town in a macrochopped county that is not regionally connected to the adjacent county? nb We excluded this in the Detroit metro with no complaints, and I don't recall it popping up anywhere else, unlike your simple chop usage.
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Torie
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« Reply #481 on: April 25, 2016, 07:34:43 AM »
« Edited: April 25, 2016, 07:37:44 AM by 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.
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muon2
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« Reply #482 on: April 25, 2016, 08:13:01 AM »

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.
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Torie
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« Reply #483 on: April 25, 2016, 08:28:56 AM »
« Edited: April 25, 2016, 08:33:22 AM by 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.
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muon2
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« Reply #484 on: April 25, 2016, 08:46:30 AM »
« Edited: April 25, 2016, 08:56:32 AM by muon2 »

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.

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.
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Torie
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« Reply #485 on: April 25, 2016, 09:04:23 AM »


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.
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muon2
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« Reply #486 on: April 25, 2016, 09:18:50 AM »


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.

I thought I was restating your comment about fragments that did or did not have state highway connections to the node. In my following example I thought echoed the type of precluded chop you said was OK, and I just extended it to a macrochop.

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.

I can't using scoring preference on connections. All parts of each district must be connected to be a valid plan. Scoring takes place after a plan is deemed valid. Established connections are the basis for measuring erosity, and they are the only basis for measuring erosity. I won't say a connection is OK for a validity check and then vanishes for erosity scoring.
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Torie
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« Reply #487 on: April 25, 2016, 09:27:21 AM »

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.
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muon2
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« Reply #488 on: April 25, 2016, 09:48:54 AM »

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.

I intend my second comment to say something quite a bit more than a disdain for preferences that are not part of a scoring rubric. It goes to the fundamental linkage between connections and erosity in my model. The connections used to test for a valid plan are one and the same as the connections used to measure erosity. That has always been the case. A plan with internally disconnected districts is invalid on its face, just as is a plan with discontiguous districts. 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.
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Torie
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« Reply #489 on: April 25, 2016, 10:03:43 AM »

"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.
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Torie
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« Reply #490 on: April 25, 2016, 02:29:25 PM »

Actually if I've written my definition correctly, then the fragment you would like to use is an isolated fragment, in that it has no connections to other units, at most a local connection to other fragments in the chopped unit. That leads to rules that favor your preferred chop.

Definition: Isolated County. An isolated county is a county or equivalent that has no regional connections. Example: Pitkin county, CO.
  
Item: An isolated county is connected to a unit if there is a local connection to the unit.

Item: An isolated county fragment that has no regional connections to adjacent units in other counties in the same district is connected to a unit or fragment across county lines if there is a local connection to the unit.

The underlined narrowly defines the connections for your preferred chops. Without the underlined it would treat all isolated fragments the same whether or not there is a regional link to the rest of the district. Without the underlined it is simpler and either way it accommodates your preference. Any thoughts?

Oh, and I do like your signature. What's the source?

The map came from here. I found the page doing a search for "new york topographic maps".
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muon2
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« Reply #491 on: April 25, 2016, 04:57:28 PM »

"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.

The model is predicated on the ability to transform a map of connected areas to a graph of nodes and links. I included many of those equivalent graphs with my artificial maps. From the graph one can test that a plan has fully connected districts. The same graph then provides the cut set of links to measure erosity. Thus my obsession with the definition of connections.

Graph theory is a well-developed and still active area in discrete mathematics. It has found its way in research in both hard sciences and social sciences, and is critical to computer networks and algorithm development. I take advantage of some of its results in this model.
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Torie
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« Reply #492 on: April 25, 2016, 05:25:11 PM »

"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.

The model is predicated on the ability to transform a map of connected areas to a graph of nodes and links. I included many of those equivalent graphs with my artificial maps. From the graph one can test that a plan has fully connected districts. The same graph then provides the cut set of links to measure erosity. Thus my obsession with the definition of connections.

Graph theory is a well-developed and still active area in discrete mathematics. It has found its way in research in both hard sciences and social sciences, and is critical to computer networks and algorithm development. I take advantage of some of its results in this model.

Just write the program, so that it has forks in the road. I'm not buying into any of this. Sorry!

We may need another phone call soon. When "techies" tell lawyers it can't be done, it raises the blood pressure of the latter. Tongue
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muon2
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« Reply #493 on: April 25, 2016, 06:23:07 PM »
« Edited: April 25, 2016, 06:25:43 PM by muon2 »

"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.

The model is predicated on the ability to transform a map of connected areas to a graph of nodes and links. I included many of those equivalent graphs with my artificial maps. From the graph one can test that a plan has fully connected districts. The same graph then provides the cut set of links to measure erosity. Thus my obsession with the definition of connections.

Graph theory is a well-developed and still active area in discrete mathematics. It has found its way in research in both hard sciences and social sciences, and is critical to computer networks and algorithm development. I take advantage of some of its results in this model.

Just write the program, so that it has forks in the road. I'm not buying into any of this. Sorry!

We may need another phone call soon. When "techies" tell lawyers it can't be done, it raises the blood pressure of the latter. Tongue

This isn't even about the program, but goes well beyond that. There are theoretical papers about using graph theory to attack redistricting. I saw some old ones that got me thinking about this during the last cycle. Now, like me, the mathematicians have figured out that maps can transform into graphs, and have some nice theorems, too. However, they haven't yet figured out how to get erosity from the transformation or balance erosity against chops. I hope that's where we come in.

It's the transformation that's a mathematical certainty, not a techie limitation. Smiley
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jimrtex
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« Reply #494 on: April 25, 2016, 08:14:29 PM »

Actually if I've written my definition correctly, then the fragment you would like to use is an isolated fragment, in that it has no connections to other units, at most a local connection to other fragments in the chopped unit. That leads to rules that favor your preferred chop.

Definition: Isolated County. An isolated county is a county or equivalent that has no regional connections. Example: Pitkin county, CO.
  
Item: An isolated county is connected to a unit if there is a local connection to the unit.

Item: An isolated county fragment that has no regional connections to adjacent units in other counties in the same district is connected to a unit or fragment across county lines if there is a local connection to the unit.

The underlined narrowly defines the connections for your preferred chops. Without the underlined it would treat all isolated fragments the same whether or not there is a regional link to the rest of the district. Without the underlined it is simpler and either way it accommodates your preference. Any thoughts?

Oh, and I do like your signature. What's the source?

The map came from here. I found the page doing a search for "new york topographic maps".

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muon2
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« Reply #495 on: April 30, 2016, 07:33:41 AM »
« Edited: April 30, 2016, 08:04:47 AM by muon2 »

Let me add a higher level of statements above definitions and items. These are principles that guide the rules. Then I'll go back to illustrations of planar graphs and open questions about their definitions and applications.

Principle: Values for parameters that describe a plan are based on simple integer measures.

Principle: Each plan can be represented by a planar graph of nodes and links, where each node corresponds to a discrete area in the plan (unit, subunit, or fragment), and each link corresponds to a connection between nodes.

Principle: Each node must have a link to at least one other node in the graph, a pair of nodes may not have more than one link between them, and links may not cross in the plane (ie the nodes and links form a simple connected planar graph).

Principle: Internal connectivity and the shape of districts (erosity) are determined from the graph that represents the plan.

Principle: The effects of scaling in a map from low density to high density areas are represented by the division of nodes due to district lines (chops) and the creation of new links.

Principle: There are qualitative differences in the division of nodes and their grouping in districts, such as differences that reflect quantitative measures of communities of interest, population equality, and political responsiveness.

Principle: An optimal plan is on the Pareto frontier that balances the shape of the districts against the number and quality of node divisions and their grouping.
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« Reply #496 on: April 30, 2016, 07:58:44 AM »

The use of the term node without explaining what it is, is confusing. Thus my suggestions below in red.


Let me add a higher level of statements above definitions and item. These are principles that guide the rules. Then I'll go back to illustrations of planar graphs and open questions about their definition.

Principle. Each map is divided into governmental jurisdictions, with a specific location in each jurisdiction assigned a node.

Principle. The node that is assigned to each governmental jurisdiction, is where the seat of government is located, or if one does not exist, a location within a sub-jurisdiction thereof with the greatest population.


Principle: Values for parameters that describe a plan are based on simple integer measures. Does this leave room for the preference mechanic, that I am so resistant to giving up?

Principle: Each plan can be represented by a planar graph of nodes and links, where each node corresponds to a discrete area in the plan (unit, subunit, or fragment), and each link corresponds to a connection between nodes.

Principle: Each node must have a link to at least one other node in the graph, a pair of nodes may not have more than one link between them, and links may not cross in the plane (ie the nodes and links form a simple connected planar graph).

Principle: Internal connectivity and the shape of districts (erosity) are determined from the graph that represents the plan.

Principle: The effects of scaling in a map from low density to high density areas are represented by the division of nodes due to district lines (chops) and the creation of new links.

Principle: There are qualitative differences in the division of nodes and their grouping in districts, such as differences that reflect quantitative measures of communities of interest, population equality, and political responsiveness.

Principle: An optimal plan is on the Pareto frontier that balances the shape of the districts against the number and quality of node divisions and their grouping.

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muon2
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« Reply #497 on: April 30, 2016, 08:21:05 AM »
« Edited: April 30, 2016, 07:06:19 PM by muon2 »

The items you added on nodes I treat as definitions, not principles. In principle I could define every census tract as a unit and each census block in the tract as a subunit. In principle I could use contiguity to define connections. The rules would work mathematically, but would not be satisfying since it would ignore the preference to follow existing political subdivisions and highways between them. That's why the principle uses nodes and links only in their broadest sense - a node represents a discrete area on a map and a link represents a connection between two areas in the map that are represented by nodes.

In principle any binary preference can be represented by a 1 or 0. So the principle of small integer values supports preferences. I think my resistance is that your application of preferences in sequence tends to run against the use of the Pareto frontier since it overly winnows the set of choices. I'd rather use the preferences in sum total (once reduced to binary or other values) as it preserves a larger space for a Pareto test

Thinking about it today, there is a modified version of one of your suggested principles worth stating.

Principle: Each complete map is divided into geographic units based on governmental jurisdictions such that every area in the map falls in a unit. Geographic units of large population may be divided into subunits based on governmental jurisdictions such that every area in the geographic unit falls in a subunit. Units and subunits should be identifiable from Census geography.
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muon2
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« Reply #498 on: April 30, 2016, 09:18:36 PM »

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.



The East Agnew fragment is clearly isolated and has no state highways at all. The clear interpretation is that it uses its local connections, and is linked to Dawes, Elbridge and central Agnew.

The West Agnew fragment is more complicated. The state highway from Dawes to West Agnew is not the connecting path and the path from Calhoun to Agnew enters in central Agnew. It qualifies as isolated.

Option A: If state highway connections have priority in determining links to West Agnew, then there are connections to Dawes and Central Agnew, but none to Calhoun. That makes the Calhoun district disconnected from West Agnew and would be disallowed.

Option B: If as an isolated fragment it goes straight to local connections, then the connection to Calhoun would exist as well. That would make the district internally connected and allowable.

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.

Here's the equivalent graph showing the link in question as a dashed line.

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« Reply #499 on: May 08, 2016, 07:52:18 AM »

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.



The East Agnew fragment is clearly isolated and has no state highways at all. The clear interpretation is that it uses its local connections, and is linked to Dawes, Elbridge and central Agnew.

The West Agnew fragment is more complicated. The state highway from Dawes to West Agnew is not the connecting path and the path from Calhoun to Agnew enters in central Agnew. It qualifies as isolated.

Option A: If state highway connections have priority in determining links to West Agnew, then there are connections to Dawes and Central Agnew, but none to Calhoun. That makes the Calhoun district disconnected from West Agnew and would be disallowed.

Yes, unless there is a local connection to the E node, and no local connection to the A node.

Option B: If as an isolated fragment it goes straight to local connections, then the connection to Calhoun would exist as well. That would make the district internally connected and allowable.

Yes, I would allow local connections to suffice only if the chop takes the entirety of the subunit, and even then, it is not preferred.


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.

Here's the equivalent graph showing the link in question as a dashed line.

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