Chops and Erosity - Great Lakes Style

[Torie]

I thought I did clean up the Detroit lines, but my issue here, is that I don't see in the text of your rules anything about intra county chops where there is no macrochop into the county or UCC, so internal units don't matter. And I interpret your text as treating a UCC as one county, so not only intra county subdivisions, but counties themselves within the UCC, don't matter. As to chop count you can draw the lines anyway you want, and only have to worry about erosity. Perhaps I am misinterpreting your text. Remember that I am a lawyer, so I am a text driven kind of guy!

I am still concerned about multiple chops into one county not being penalized. It seems unfair to the county or UCC taking the hit.

My focus here on this exercise of course, is not playing the game here on Atlas, but fashioning something with more universal application that will withstand all the nit picking. I have no doubt that is why you are spending so much time on this as well, no?

[muon2]

I thought I did clean up the Detroit lines, but my issue here, is that I don't see in the text of your rules anything about intra county chops where there is no macrochop into the county or UCC, so internal units don't matter. And I interpret your text as treating a UCC as one county, so not only intra county subdivisions, but counties themselves within the UCC, don't matter. As to chop count you can draw the lines anyway you want, and only have to worry about erosity. Perhaps I am misinterpreting your text. Remember that I am a lawyer, so I am a text driven kind of guy!

I am still concerned about multiple chops into one county not being penalized. It seems unfair to the county or UCC taking the hit.

My focus here on this exercise of course, is not playing the game here on Atlas, but fashioning something with more universal application that will withstand all the nit picking. I have no doubt that is why you are spending so much time on this as well, no?

I suspect that part of the lack of clarity is due to my transfer of test from the VA effort here. In VA there are no state-defined subunits, so there was little point in putting in a general statement. Obviously MI not only has well-defined subdivisions, but it has explicit statutory use of those in redistricting. I would expect a general statement for all such states with statutory divisions, but I wasn't working on it when we switched to MI. My intent would be something along the line of requiring that in a chop of a unit, no more than one subunit may be chopped by a district, much like current MI law.

Multiple chops in a county are penalized, just no more than multiple counties chopped.

[muon2]

Here's a rather crude example of erosity measure taken from Torie's initial CD-10. The brown lines indicate the townships invoked by the macrochops of Oakland and Macomb. The blue line segments indicate connections between geographic units that span the district border. There are 37 such segments. If some parts are hard to read I can only suggest viewing it with a tool that has a zoom.



Since St Clair is not chopped there is only one regional connection to each of Sanilac and Lapeer counties. Lapeer is chopped but not macrochopped so it stays with regional connections to St Clair and Genesee, bu the chop creates two units with a local connection between them. The regional connection between St Clair and Lapeer is internal to CD 10 and the regional connection between Lapeer and Genesee is in CD 5 so neither create erosity. Without the Lapeer chop there would be connections to both Oakland and Lapeer, so this is an example of a well-placed chop that helps reduce the erosity.

In a macrochopped county, the townships and cities become the units of interest. In Oakland, Holly and Groveland each establish separate connections to Genesee, as well as to the townships to their south. The chop in Holly creates an internal connection between the two parts, but the connection to the south is to the Holly part in CD 11, so it doesn't effect erosity.

It's interesting to note that half the connections contributing to erosity here are in the Troy peninsula, but to my eye that is a fairly erose feature, so I would expect it to generate a lot of points. I found that all the contiguous units were also locally connected. That's probably not surprising in a flat area that is highly developed.

I mentioned before that the Lenox microchop is another example of erosity reduction. Without it the erosity would count connections to both Richmond township and Richmond city. With it there is just the link between the two pieces in Lenox.

[Torie]

Thanks for the comment and review. I suspect however that failure to penalize county chops within a UCC, equally applies to VA. That is a policy decision, but to ignore intra UCC county lines will be problematic, and controversial, in the public square. If ignored in MI, the array in the Detroit UCC would be different in all probability, particularly the lines of MI-09 and CD-10 and CD-11 where they intersect.

How can Macomb and Oakland be deemed "macro-chopped" if the Detroit UCC is treated as but one county for chop purposes?

[muon2]

Thanks for the comment and review. I suspect however that failure to penalize county chops within a UCC, equally applies to VA. That is a policy decision, but to ignore intra UCC county lines will be problematic, and controversial, in the public square. If ignored in MI, the array in the Detroit UCC would be different in all probability, particularly the lines of MI-09 and CD-10 and CD-11 where they intersect.

How can Macomb and Oakland be deemed "macro-chopped" if the Detroit UCC is treated as but one county for chop purposes?

The Detroit UCC was macrochopped, so it was replaced by its constituent counties (this must happen in any UCC larger than 105% of a CD). Then some of the constituent counties were macrochopped, specifically the three that must be macrochopped. Those then are replaced by townships and cities. Note that any large UCC will have to consider the internal county lines and the public square worry is abated. (nb. all the VA UCCs were large in this sense, or are one county plus an IC.)

The only time county lines might not come into play is for a small UCC like Lansing. There one could have a situation where a chop into the rural part of a county counts the same as a chop of a whole county. It was exactly this scenario in the Lansing area in our 2013 discussions that led to the idea that a splitting of a whole county off of a small UCC is just as undesirable as a chop into a county. This system preserves that sensibility.

[Torie]

The Detroit UCC was macrochopped by going out into Lapeer?  Is it clear in the text that chops out, are the same as chops in, for penalty purposes, when it comes to UCC's? If below the 105% threshold, than is it open season to chop within the UCC without penalty per the text?

[muon2]

The Detroit UCC was macrochopped by going out into Lapeer?  Is it clear in the text that chops out, are the same as chops in, for penalty purposes, when it comes to UCC's? If below the 105% threshold, than is it open season to chop within the UCC without penalty per the text?

No, the chop out kept you at the minimum score for the Det UCC. A chop in would add. The text say count the number of districts in the unit and subtract one, that's the chop count.

If a unit is within 105% of the quota then it is possible to chop (with penalty) but not macrochop. If a unit is under 10% of the quota it is not possible to macrochop, but chops are still possible. The math in the text implies that under 10% you may only have chops (and microchops) within a unit, from 10% to 105% you may have chops and possibly a macrochop depending on the division within the unit, and above 105% you must have chops that form a macrochop. Chops that are not micro always count towards the penalty. Macrochops simply flag those units that must be inspected at a higher granularity for chops within chops.

States like MI can have a rule that a district in unit not macrochopped shall not have move than one subunit chopped between the same two districts. The rule could also be that if two districts chop two or more subunits in a unit then the chop becomes a macrochop. The first form of the rule is a bar and second form is not a bar, but creates a penalty.

[Torie]

The above text is almost impenetrable. What exactly happens that causes a penalty with lines within a UCC when a macrochop is in play, that would not happen absent a macrochop?  Exactly how is the penalty free leash shortened?  Where in the text are you penalized for chopping counties within a UCC?

Perhaps the text in your second paragraph is a badly needed fix for multi county UCC's. Sensitivity to county chops within a UCC and subunits of counties should always be in play, whether or not the 105% threshold is breached. If not, then you draw within UCC's solely based on erosity and the VRA, and in that case maybe the highest scoring map would have one of the black UCC's picking up blacks in both Macomb and Oakland, and not going to Pontiac (assuming that Detroit UCC was within the 105% test). And microchops should count, so you can't do multiple microchops. The map below does two chops, one in Troy and the other in West Bloomfield (a microchop), in order to lose a highway cut (a state highway ends, so it pays to get the CD to take it in all to the end). One should not be rewarded for the West Bloomfield microchop. It's just ludicrous. And with more microchops elsewhere, the Troy chop could be made micro as well.

[muon2]

The above text is almost impenetrable. What exactly happens that causes a penalty with lines within a UCC when a macrochop is in play, that would not happen absent a macrochop?  Exactly how is the penalty free leash shortened?  Where in the text are you penalized for chopping counties within a UCC?

In the flow chart, a macrochop does not add a point to the score, only chops add to the score. There must be one or more chops to trigger a macrochop, so one cannot escape the penalty for chops. Note that a macrochop is a statement about the whole unit (UCC, county, etc) not about individual districts in the unit. What a macrochop does is determine that the plan must be assessed at the next finer level of geography as well as at the coarser level that triggered the macrochop.

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The second paragraph is a restatement of the numbers in the flow chart. The rule is the flow chart, and the second paragraph is an example derived from the rule.

As I said earlier, the rule is written for all states and not all have statutory subdivisions like MI, VA being one of them. Certain groups of states may have additional rules to recognize the more important status those subdivisions have. That would include a special rule to recognize towns instead of counties as the primary unit in New England states. It would include special rules for the statutory subdivisions in many of the Midwest and Northeastern states. I mention two such versions of a rule in my previous post.

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State highways are not particularly relevant at the township level, since there aren't enough to establish connectivity. If there is one it might be the preferred connection, but it isn't a guarantee. A state highway on the border of a unit counts in both units for establishing a path for a connection. In your example, I see no reward for the microchop, it looks to me like it increases erosity by one. On your other point I'm still assessing my suggestion that the sum of microchops in a unit be considered as a potential chop, which would address the case you raise when turning Troy into a microchop.

[Torie]

Well we can quibble about the highway cuts. Rochester Road seems to quit being a state highway at the south end (the color changes), but maybe not, and I don't see a highway cut with my microchop into West Bloomfield.

I don't get the bit about one or more chops to create a microchop (we are talking about looking at internal chops give a microchop, versus not doing so), but putting that aside, what I was saying, was that with no macrochop, I don't see language about worrying about intra UCC chops, because you don't get to that level of "granularity" as you put it absent a microchop. What can you get away with absent a macrochop, that you can't if there is one? What exactly turns on the categorization, in practical terms?

"State highways are not particularly relevant at the township level, since there aren't enough to establish connectivity. If there is one it might be the preferred connection, but it isn't a guarantee. A state highway on the border of a unit counts in both units for establishing a path for a connection. In your example, I see no reward for the microchop, it looks to me like it increases erosity by one. On your other point I'm still assessing my suggestion that the sum of microchops in a unit be considered as a potential chop, which would address the case you raise when turning Troy into a microchop."

The above is also opaque. I thought highway cuts between CD's were relevant. I assumed highways along borders are not deemed cut. Yes, there are not tons of highways within individual townships But in cities, there seem to be in Oakland County), which is why you are free up to a point to chop away at some townships. How is this relevant to anything we are talking about?  The issue is chop count versus erosity, and whether it is desirable to encourage penalty free chops to reduce highway cuts.

We are not communicating well today.

[muon2]

Let me roll back to the basic description of erosity as a cut set from a graph. One starts with the identified units in the state and determines which are connected. For example here's one I did for RI a year ago.



The units here are towns so the links in blue are based on local connections.

Here's the AL one from 2013. Connections are based on state highways since it's a county level map.



The map defines the connections at the top level (the UCC concept was not fleshed out), but some measure is needed to determine when should connections at a lower level be used. That is the job of the macrochop. So some plans will need different areas expanded in more detail based on the chops they create.

The erosity comes by overlaying the district boundaries on the connection map, like this one I put together in 2013 for AL. The erosity in the early simple version in just a matter of counting all the lines intersected by the boundaries - that's called the cut set.



The problem is that in a dense county like Jefferson AL there is nothing in this original method to prevent some serious gerrymandering nor to measure erosity effectively in the urban area. However, AL doesn't have statutory divisions between the county and VTD available like MI does. If I were repeating my work for AL today, Jefferson would be replaced with some reasonable graph of munis and planning zones that would have its own internal and external connections and the erosity would be recomputed based on that. AL doesn't have townships, but there are sources from Jefferson that would be a reasonable substitute. This is what I was posting for the larger VA counties and ICs on that thread, so when we got to connections and erosity there would be detail in place.

I suspect part of the miscommunication is that I've been working on this continuously for two years and I don't tend to roll back to the beginning every time I start up on a thread. In fact, when I did roll back to the start on the VA thread, I couldn't even get to this point before the participants lost interest. On this thread I've been stuck starting in the middle of the content and trying both to push backwards to go over material from one more years ago and to push forward to the detail able to actually produce a score.

[muon2]

I had hoped in the VA exercise to take everything from the start, go step by step, get a group consensus on what to test, then let mappers with different visions produce plans governed by the rules. Each mapper has different designs that they favor, and having a bunch of mappers would expose weaknesses in a set of rules that I alone might not find.

But some rules can support variations and in VA the independent city is the unique feature that needs special rules. I just couldn't keep the interest up long enough to come to consensus on what rule to test. That meant I never got as far on chops and erosity as I wanted to. Nor of course did I address the township/city structure in MI which is shared by a few states, but needs special handling when it occurs.

[Torie]

One thing led to another, and I ended up drawing this "contest" map for WI, as an exercise to show the Pub gerrymander did not accomplish much, other than make WI-01 lean Pub rather than a tossup from a PVI perspective.

However, it raises an issue. The second map below is an alternative, that does shift about 1.5 PVI points between WI-07, making WI-07 tilt Dem, and WI-03 competitive (lean Dem) per 2008 numbers. (With the trends, WI-07 might be tossup with this map, and WI-03 tilt Dem.)

The chop into Dunn County (like the name ), is necessary, and notice that it gets rid of a highway chop, so this map has one more necessary county chop than the contest map, but one less highway chop. I guess that is OK, but where two maps are tied this way, some might prefer that one county chop racks up more penalty points than one highway chop (and I still think township and city chops should count for something, just less penalized than county chops).

What is even more problematical however, is doing the second "unnecessary" county chop, to lose a highway chop (a "gratuitous" county chop as it were, that need not be done to get within the 0.5% deviation limit in population from the CD quota). In the second map that was done with Sauk County. A map without a gratuitous chop should be favored I think over the map with such a chop. A gratuitous county chop should not be allowed to reduce the highway cut count I guess is my suggestion.

The 0.5% population play does make for an interesting redistricting game I must admit - much more interesting than without it. And there are a lot of games that can be played with it - a lot.



 

[muon2]

WI was one of the original states for which I posted a regional county connection map back in 2012. All of the links are based on state highways between county seats.



The first Torie map in the previous post cuts 11 links on the boundary between CD 3 and CD 7.

The second map cuts 9 links not counting the chop in Dunn. The chop in Dunn has a link between the two parts which is also cut, bringing the total to 10 that is how it would be judged on the one interpretation (used in the AL discussion). If viewed this way it has one more chop and one less erosity and is Pareto equivalent to the first map.

However, depending on how one counts the links, a secondary path between Dunn and Chippewa follows WI-64. If that link becomes active after the chop then the number of cut links rises to 11, the same as in the first. IIRC this interpretation was used in a discussion of MD plans way back when, in part because there was no concept of macrochops. If this view is used, then the second map loses to the first one. It's worth exploring the relative merits of the two interpretations.

I've been putting together a detailed example for MI which I hope will illustrate the counting in a chopped county as well as provide some justification for the crossover to macrochops for large chops.

[Torie]

For cut counts, you only count state highways connecting county seats unless there is a macro-chop, and then you count all state highways involved with the "macro-chopped" county (btw, Dunn is intermediate chopped rather than macro-chopped isn't it, or has that distinction been lost even though a UCC is involved (somehow I am under the impression that macrochoops only pop up with UCC's)? That is a new one for me. It strikes me as way too complicated. If one wants to draw a distinction between macro [intermediate] and micro chops (that too is problematical for me given you have the 0.5% population variance leeway), simpler is just to count micro-chops at one half point each (maybe .5 points for county microchops and .25 points for town and city microchops, and ban gratuitous ones to game reducing the highway cuts. By the time you are done Mike constructing this labyrinth, only a physicist will understand your metric. At this juncture, I doubt anyone on the Forum really does.

Do you ban traveling chops by the way?  That was an issue vis a vis whether WI-05 could go into Ozaukee County or not via chopping through Washington County (doing a microchop of both Washington County and Germantown). Alternatively, WI-04 could take in all of Ozaukee, WI-05 micro-chopping into Washington County, with no chop of Erin Township, but with an  intermediate chop of the City of Milwaukee. Which of these maps chop wise scores highest in your universe, my original map, the traveling chop map, or the City of Milwaukee chopped map?

[muon2]

As an example of the relationship between chops and erosity, consider CDs 2 and 3 in following plans. In all of the plans the two CDs together are made up of 10 whole counties and exceed the quota for 2 CDs by 1161. All three plans place a chop in Kent county and have 2 CDs for the Grand Rapids UCC, which is the minimum possible.

Suppose in a crowdsourcing exercise to produce a map Plan A is submitted. The deviation in CD 2 is +1854 and CD 3 is -693, an average deviation of 1274, a range of 2547 or 0.36% of the quota.



The county connections for the plan are in the next image. There are blue dots for the 10 count seats, orange lines to show the links internal to CDs 2 and 3, and yellow lines to show the links to counties in other CDs. Those yellow lines contribute to the erosity. A red line shows the link between the two parts of Kent, and since it is split between CD 2 and 3 it is cut as well and adds to the erosity. Using the red and yellow cut links, CD 2 has an erosity of 7 and CD 3 has an erosity of 13.

The path used to form the link between Ottawa (Grand Haven) and Kent (Grand Rapids) follows I-96 roughly where the yellow line is between them. Holland is the largest city in Ottawa, and if it is considered as the node for Ottawa the connection would be along I-196 at Grandville. A longer path than either of those exists that follows MI-6 near the southwestern corner. If the two parts of the Kent chop were treated as if they were individual counties for connection purposes then there would be a link that connects the CD 3 part of Kent to Ottawa along MI-6, and that is shown in pink. If it is counted then the erosity of both CDs increases by 1.



End part 1 of 3

[muon2]

Chops and Erosity, part 2 of 3

Since this exercise assumes a public process to produce a map. Someone observes that the population inequality can be reduced without changing anything other than the choice of cities and townships to include in the chop. This results in plan B where CD 2 is +172 and CD 3 is +989, an average deviation of 581, a range of 817 or 0.12% of the quota. It has a significantly lower inequality, but the CDs have the same set of cut regional county links, so at the county scale the erosity is the same. Using inequality as a tie breaker plan B would knock plan A out of consideration.



Another mapper also makes some changes to the Kent chop and comes up with plan C. Here CD 2 is -588 and CD 3 is +1749, an average deviation of 1169, a range of 2337 or 0.33% of the quota. The CD boundaries involve the same cut links as in plan A and B so it would be tied in chops and erosity. The deviations are slightly better than plan A but probably not enough to have a different inequality score overall. The internal boundary of the chop is clearly less erose than either plan A or B. However, since inequality would be the only tie breaker plan C would fall to plan B.



It seems that there should be some consideration for the lower erosity visible in plan C. Even conventional compactness measures might not see much difference between B and C since they would be dominated by the large perimeter of the whole counties and would lack sensitivity to the smaller changes in Kent. The best way to give consideration to the shape within Kent is to zoom in on that county and apply a similar technique to the on used between counties.

An important question is whether to zoom in on all chops to consider erosity. There is already an increase in counted links created by the chop, and that counts towards erosity. Population deviations within 5% of the quota are considered substantially equal by SCOTUS, so it is reasonable to consider chops that partition off less than 5% of the quota small enough to incur only such erosity changes that are due to the link between pieces. Adding the effect of secondary highway links, like the pink line in part 1 would work to penalize chops that were added solely to cover only primary links to reduce erosity.

Removing larger chops would result in districts that were substantially unequal. Such chops will most frequently occur in high-population counties that have areas of high density. Zooming in on only those counties where the chop is substantial provides a mechanism to consider the erosity in those high-density population areas where the boundary will be small compared to county-based boundaries.

This becomes the definition of a macrochop. This is not the opposite of a microchop which functions in all ways like a regular chop in regards to erosity. A macrochop sets a point at which it is worthwhile to zoom into a map to see detail that is relevant to scoring.

End part 2 of 3

[Torie]

I see what you are doing now, and how a chop (other than a micro one?), creates a quasi county that then has independent highways connecting it to adjacent county seats. And apparently state highways to don't go to the county seat of an adjacent county, or quasi county, don't count. Not sure that is good policy, to exclude some state highways that way, and it adds complexity, but at least now I understand the highway cut issue.

Nelsville is the county seat of Clark County in Wisconsin, not Greenwood, but either way apparently Hwy 29 through northern Clark is not a highway cut  because it does not connect from the Clark county seat to an adjacent county, county seat. That is an example as to why, beyond complexity, picking and choosing state highways to count as cut is problematical, because the WI-03 Clark County jut is an erose feature, and thus the cut of Hwy 29 is a good proxy to pick that erose feature up. Your highway cut metric seems more focused on connectivity between county seats, rather than connectivity in general (hwy 29 does connect to county seats in adjacent counties, so the population around it is connected to those counties, even though Clark's county seat is not in play), and trying to get the best possible proxy for erose shapes. This would be particularly a problem with the county seat is not the largest town or city in a county.

I guess I am thinking now discriminating between different types of state highways is a big mistake. they all should count, although I do kind of like your idea that each portion of  a chopped county counts as a separate county for highway chop purposes. Whether that should obtain if the chop is a microchop is however an issue to ponder.

I have a headache!

[muon2]

Chops and Erosity part 3 of 3.

A zoom into Kent replaces counties with cities and townships, and seats of county government with the town hall or city hall. In the map below the halls (nodes) are marked roughly with blue dots and the lines indicate the connections (links) between them. Villages are shown on the map, but they are not considered subunits of the county for redistricting purposes.

Yellow lines indicate connections where the path between units uses a state highway at the boundary, and blue lines are connections made solely with local roads. Yellow lines generally include local roads to get from the hall to the nearest state highway, so what matters is the status of the road as it crosses the town or city line.



One thing to note is that there are a number of nodes that are only connected locally. This includes the cities of Cedar Springs, Rockford, and East Grand Rapids, and the townships of Spencer, Vergennes, and Bowne. These units are considered to be connected by local links, so cutting those links would also count towards erosity. For other local links, scoring can either count them or not, so the calculation will be made both ways.

Here's a zoom into plan A. The chop cuts 8 yellow lines (including the Byron Twp to Ottawa link), and 3 blue lines to locally connected units for a total of 11 cut links. If all local cuts were counted the total would rise to 19.



Here's a zoom into plan B. The chop cuts 9 yellow links (including two to Ottawa), and 5 required blue links for a total of 14 cut links. If all local cuts were counted the total would rise to 20.



Here's a zoom into plan C. The chop cuts 8 yellow links (including one to Ottawa), and 2 required blue links for a total of 10 cut links. If all local cuts were counted the total would rise to only 12.



Counting the chops in Kent would keep plan C in the mix with a lower erosity than plan B or A. Since all three plans have the same chop count, but differ in erosity, the inequality doesn't come into play. Plan C is the lone surviving plan of the three.

[muon2]

I see what you are doing now, and how a chop (other than a micro one?), creates a quasi county that then has independent highways connecting it to adjacent county seats. And apparently state highways to don't go to the county seat of an adjacent county, or quasi county, don't count. Not sure that is good policy, to exclude some state highways that way, and it adds complexity, but at least now I understand the highway cut issue.

Microchops also create quasi-counties. They are chops in all respects, except that they don't add to the chop count (unless the total of all microchops in a county exceeds the 0.5% threshold).

The regional connection rule is that one must be able to trace a path from one node to another on numbered state or federal highways without crossing into a third county. Highways on a border count in both counties. For counties, I used the address of the seat of county government and the point on a state highway nearest it as the node. A case can be made to use the seat of government of the largest city in a county, if that is not the county seat.

[Torie]

I see what you are doing now, and how a chop (other than a micro one?), creates a quasi county that then has independent highways connecting it to adjacent county seats. And apparently state highways to don't go to the county seat of an adjacent county, or quasi county, don't count. Not sure that is good policy, to exclude some state highways that way, and it adds complexity, but at least now I understand the highway cut issue.

Microchops also create quasi-counties. They are chops in all respects, except that they don't add to the chop count (unless the total of all microchops in a county exceeds the 0.5% threshold).

The regional connection rule is that one must be able to trace a path from one node to another on numbered state or federal highways without crossing into a third county. Highways on a border count in both counties. For counties, I used the address of the seat of county government and the point on a state highway nearest it as the node. A case can be made to use the seat of government of the largest city in a county, if that is not the county seat.

So Hwy 29 counts as two cuts, because it goes from one node to another, just not to nodes in adjacent counties? I still think I prefer counting all highway cuts, but in the end it comes down to what is the best proxy for erosity.

We will just have to disagree on whether microchops are penalized. I won't support that. It creates an incentive to have one microchop per county (or more up to 0.5% as you say), so that there are no bigger chops, making a mess of a map. The public square won't stand for it.

[muon2]

I see what you are doing now, and how a chop (other than a micro one?), creates a quasi county that then has independent highways connecting it to adjacent county seats. And apparently state highways to don't go to the county seat of an adjacent county, or quasi county, don't count. Not sure that is good policy, to exclude some state highways that way, and it adds complexity, but at least now I understand the highway cut issue.

Microchops also create quasi-counties. They are chops in all respects, except that they don't add to the chop count (unless the total of all microchops in a county exceeds the 0.5% threshold).

The regional connection rule is that one must be able to trace a path from one node to another on numbered state or federal highways without crossing into a third county. Highways on a border count in both counties. For counties, I used the address of the seat of county government and the point on a state highway nearest it as the node. A case can be made to use the seat of government of the largest city in a county, if that is not the county seat.

So Hwy 29 counts as two cuts, because it goes from one node to another, just not to nodes in adjacent counties? I still think I prefer counting all highway cuts, but in the end it comes down to what is the best proxy for erosity.

We will just have to disagree on whether microchops are penalized. I won't support that. It creates an incentive to have one microchop per county (or more up to 0.5% as you say), so that there are no bigger chops, making a mess of a map. The public square won't stand for it.

I still contend your microchop fear is a non issue. Those microchops are quasi-counties, too, so they tend to increase erosity. If they didn't one would place enough of them to drive the inequality to near zero and drive out competing maps with the inequality tie breaker. When I've tried that I usually find that my erosity rises and I'm left with a Pareto equivalent, but not superior plan.

The original driver for microchops was your concern about sufficient flexibility, since we saw areas of states where the constraints otherwise left few choices. Flexibility cuts both ways, and a set of rules that are too inflexible may not sit well with other parts of the public than the ones who would disfavor microchops.

[muon2]

Nelsville is the county seat of Clark County in Wisconsin, not Greenwood, but either way apparently Hwy 29 through northern Clark is not a highway cut  because it does not connect from the Clark county seat to an adjacent county, county seat. That is an example as to why, beyond complexity, picking and choosing state highways to count as cut is problematical, because the WI-03 Clark County jut is an erose feature, and thus the cut of Hwy 29 is a good proxy to pick that erose feature up. Your highway cut metric seems more focused on connectivity between county seats, rather than connectivity in general (hwy 29 does connect to county seats in adjacent counties, so the population around it is connected to those counties, even though Clark's county seat is not in play), and trying to get the best possible proxy for erose shapes. This would be particularly a problem with the county seat is not the largest town or city in a county.

I'm not sure I follow your concern here. My map of WI has hwy-29 connected to US-10 by way of hwy-73 which is entirely in Clark for that stretch. Both Greenwood and Neillsville are on hwy-73 so any path that connects to one of them connects to the other. You can't use hwy-29 to connect Chippewa to Taylor since that would go through Clark, but hwy-64 provides a direct path so hwy-29 is not an issue.

[Torie]

WI was one of the original states for which I posted a regional county connection map back in 2012. All of the links are based on state highways between county seats.



The first Torie map in the previous post cuts 11 links on the boundary between CD 3 and CD 7.

The second map cuts 9 links not counting the chop in Dunn. The chop in Dunn has a link between the two parts which is also cut, bringing the total to 10 that is how it would be judged on the one interpretation (used in the AL discussion). If viewed this way it has one more chop and one less erosity and is Pareto equivalent to the first map.

However, depending on how one counts the links, a secondary path between Dunn and Chippewa follows WI-64. If that link becomes active after the chop then the number of cut links rises to 11, the same as in the first. IIRC this interpretation was used in a discussion of MD plans way back when, in part because there was no concept of macrochops. If this view is used, then the second map loses to the first one. It's worth exploring the relative merits of the two interpretations.

I've been putting together a detailed example for MI which I hope will illustrate the counting in a chopped county as well as provide some justification for the crossover to macrochops for large chops.

You seem to have highways in Clark that I just don't see at all. I guess any paved road will do to get to the adjacent county, even if not a state highway, is that right?  In a microchop area with no state highways, do you just use any paved road for the quasi county? (I do see now that highway 73 does apparently wind through Clark, just not a yellow line or labeled.)

[Torie]

Nelsville is the county seat of Clark County in Wisconsin, not Greenwood, but either way apparently Hwy 29 through northern Clark is not a highway cut  because it does not connect from the Clark county seat to an adjacent county, county seat. That is an example as to why, beyond complexity, picking and choosing state highways to count as cut is problematical, because the WI-03 Clark County jut is an erose feature, and thus the cut of Hwy 29 is a good proxy to pick that erose feature up. Your highway cut metric seems more focused on connectivity between county seats, rather than connectivity in general (hwy 29 does connect to county seats in adjacent counties, so the population around it is connected to those counties, even though Clark's county seat is not in play), and trying to get the best possible proxy for erose shapes. This would be particularly a problem with the county seat is not the largest town or city in a county.

I'm not sure I follow your concern here. My map of WI has hwy-29 connected to US-10 by way of hwy-73 which is entirely in Clark for that stretch. Both Greenwood and Neillsville are on hwy-73 so any path that connects to one of them connects to the other. You can't use hwy-29 to connect Chippewa to Taylor since that would go through Clark, but hwy-64 provides a direct path so hwy-29 is not an issue.

Oh, I see, highway 73 is not an orange line, but still a state highway. Assuming Hwy 29 has nothing to do with the county seat, is cutting it still a chop because it connects the county seats of Marathon and Chippewa, two non adjacent counties?