Chops and Erosity - Great Lakes Style

[jimrtex]

Here's how I would write that into a scoring rule for MI.

Definition: Urban County Cluster (UCC). A UCC is a geographic unit within an MSA. It is made up of those counties in the MSA such that each county has either 25,000 population or 40% of its population in an urbanized area. the geographic subunit of a UCC are its counties.

Urban County Cluster (UCC). A UCC is one or more counties within a metropolitan statistical area (MSA).  A county is included in a UCC if at least 40% of the population of the county is in urbanized areas; or if at least 25,000 persons live in urbanized areas.

Changed to recognize that urbanized areas may be plural.  Also MSA also stands for micropolitan statistical area.

Definition: Subunit. The geographic subunit of a county are the census-defined county subdivisions. Except for Detroit, the geographic subunit of county subdivisions are the vote tabulation districts (VTD). The geographic subunit of Detroit is city-defined neighborhood cluster, the subunit of the neighborhood cluster is the neighborhood, and the subunit of the neighborhood is the VTD.

In Michigan aren't townships the subunits of counties?

I think when expressed this way, it tends lose focus on whole counties as an ideal.  See the Ohio Constitution and how in practice there are an extremely unnecessary number of county cuts.

Definition: Chop. A single chop is the division of a geographic unit between two districts. A second chop divides the unit between three districts. In general the number of chops is equal to the number of districts in that unit less one.

Definition: Minimum Number of Districts (MND).  The minimum number of districts to cover a geographic unit is the number of districts that could be wholly contained in the unit, rounded up to the next whole number.   ie MND = ceil (population_of_unit / quota).  For geographic units with a population less than the quota, MND is one.

I think that there should be a distinction made between excessive divisions, and necessary divisions, even if they are mathematically equivalent for arithmetic comparison.

Definition: Microchop. A microchop is a chop where a district has less than 0.5% of the quota in a geographic unit.
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I don't understand why microchops are treated separately from mesochops.  You have violated the integrity of the political subdivision.  Why not increase the maximum deviation to 1% and do away with microchops.

Definition: Macrochop. A macrochop is a chop where the remainder of a geographic unit after subtracting the population of the largest district in the unit exceeds 5% of the quota.

Is this true for counties that could have more than one whole districts (eg Wayne).

What is the reason for distinguishing macrochops?

[jimrtex]

So I took some time this morning to put together the complete county connection map for MI. As usual this represents all the regional connections defined by a path between seats of county government that follows state and federal numbered highways. When there is more than one path between two counties, the path is defined by the one that takes the shortest time according to Mapquest.

Technically, I-75 jogs into Emmet county for a brief part just south of the Mackinac bridge, so it can't be on a path between Mackinac and Cheboygan. But I-75 also can't be on a path between Mackinac and Cheboygan since the south end of the bridge is in Cheboygan. There is ferry service across the strait and in mild winters it can run all year, but usually it doesn't. So that leaves no possible link, so the map shows the best alternative which is Mackinac to Cheboygan.

It is possible to travel directly (ie not in a circuitous fashion, nor substantially through any other counties) between Mackinac and either of the two LP counties.

It is a similar situation to Whitman-Asotin, and Snohomish-Chelan, and distinguishable from Franlin-Columbia.

[jimrtex]

Oh, I was mixing up cuts and chops. And you treat a multi-county UCC as one county for this purpose, right?  Anyway, as I think I mentioned before, within UCC's smaller unit chops should count, whether or not you have a macro chop into a UCC. So I was focused on erosity measures within a UCC, which I thought was what we were discussing. And outside UCC's, I am still not persuaded why some state highways should count, and not others, and what to do if there are no state highways between adjacent counties. Is that deemed a chop when two counties with no state highway between them are in the same CD? Or do payed county highways count to avoid a chop?  None of this may obtain to WI or MI perhaps (although some state highways are poorly labeled and hard to find on Dave's matting utility.

There are various mathematical formula that are used to measure compactness of districts. 

One of them compares the perimeter of a district (the length of its outer boundary) with the circumference of a circle with the same area as the district.  It is a measure of the convoluted-ness of the boundary, which may indicate gerrymandering.

But it has certain negative features:

(1) It includes the external boundary of the state since this is part of the boundary of the district.  In Michigan you will have a district that include the upper peninsula.   Even if you have a straight east-west boundary across the lower peninsula, it will score poorly.  And you can make that boundary across the lower peninsula more irregular, with little increased penalty.

(2) It penalizes use of boundaries that follow natural boundaries, such as rivers.  In Ohio, one rules exploit was to create a district along the Ohio River, producing one district with a bad score, but permitting the other districts to have lower score.  It in effect plastered over the rough surface to produce a smooth internal surface.

(3) It has little penalty in districts that mix urban areas with intricate boundaries combined with rural areas.  For example, you could have a quite complex boundary in Cuyahoga County.  Its score would improve if you added Medina County, and improve even more if you added Wayne County.  The same thing can happen in the Detroit area.

You can eliminate the first two problems by ignoring external boundaries and using a simplified measure of the boundary.  Muon prefers a count of highway cuts, while I would use a straight line measurement between boundary nodes (a boundary node is where three (or more) counties meet, as well as the where a boundary between counties meets an external land boundary.

For example, the border between Genesee and Oakland would be measured as a straight line between the Livingston-Genesee-Oakland junction, and the Lapeer-Genessee-Oakland junction.

The above approaches work when you have whole county districts.

Both my method and Muon's method can be extended to chopped counties.  Consider a north-south split of Clinton County.  As long as the boundary followed township boundaries, it does not really matter whether the boundary within Clinton is straight across, or jogs up a township and back, particularly if the jog is for purposes of population equality.

Both Muon and I would treat the two parts of Clinton as the equivalent to counties for measuring erosity.   If Shiawasee were in a 3rd district, then Muon would check for a highway connection between Shiawassee and the two parts of Clinton.  If there is no highway, then Muon would in essence say that the boundary does not disrupt communication and therefore does not disrupt community of interest.

I would simply measure the two segments of the boundary between Shiawasee and Clinton.

In addition, Muon would count a cut between the two parts of Clinton, while I would measure the distance across Clinton.

A third approach would be to ignore the split of Clinton County for purposes of measuring erosity.  Instead Clinton County would be treated as being in the district in which the majority of the population resided.

But the above still does not address the problem within areas of concentrated population such as the Detroit area.  For the most part, it will be impossible to create whole-county districts.  At most, you might control excessive division of counties, and block double (or multiple spanning) where two or more districts include territory from a pair of counties.  It may be impractical to not have a district crossing the Macomb-Oakland boundary, but it is unnecessary to have two or more.

My preferred approach would be to treat the districts in a large UCC as a single unit when measuring erosity.   One could still check for excessive county chopping within the UCC.

After the statewide plan were adopted, then a plan for the 6 Detroit districts could be created, using townships and cities as the building blocks.  A limitation of this decomposition, is that it may require premature definition of the outer boundary of the area.  For example, your decision to go from Oakland and Macomb into Lapeer may have been based on how you were arranging the Detroit area districts.  It might be produce a better Detroit-area plan by going into Monroe. Livingston, or Washtenaw to pick up the extra population.   But I am willing to risk that for the simplification that decomposition provides.

If there were a statewide redistricting commission, then there could be regional redistricting commissions as well.  There might also be local redistricting commissions.  For example, a Clinton County commission could refine the boundary within the county.  Even though they may think the division of the county between two districts sucks, they can still determine a least suck-iest division.

[jimrtex]

Oh, I was mixing up cuts and chops. And you treat a multi-county UCC as one county for this purpose, right?  Anyway, as I think I mentioned before, within UCC's smaller unit chops should count, whether or not you have a macro chop into a UCC. So I was focused on erosity measures within a UCC, which I thought was what we were discussing. And outside UCC's, I am still not persuaded why some state highways should count, and not others, and what to do if there are no state highways between adjacent counties. Is that deemed a chop when two counties with no state highway between them are in the same CD? Or do payed county highways count to avoid a chop?  None of this may obtain to WI or MI perhaps (although some state highways are poorly labeled and hard to find on Dave's matting utility.

Let's back up a moment and start with the simple model, identify shortcomings, and propose solutions. For example, let me take your first question about UCCs.

The simple model says all counties are equal and fewer chops are better. The problem is that there's nothing to dissuade mappers from taking whole urban counties and fingering their districts out to a bunch of rural ones, nor to demote a plan that takes a mid-sized urban area like Lansing and splits it right along the county line. The solution was to define the UCC and add to the chop count when the UCC is split.

Now comes implementation in the chop scoring. The next step simple model would count each county chop and count each multi-county UCC chop then add them together. The modeler now asks if there are problems that are undesirable.

Consider that the implementation has to deal with the following situations: a whole county chop of Clinton from Lansing, a small chop of Clinton, and a small chop of a smaller metro one-county UCC like Calhoun. In the simple UCC application the small chop of Clinton would count twice and the other two examples would only each count once. It seems strange to double count a small chop in Clinton, but not Calhoun. But it also would be strange to double count a chop in Calhoun. It looks like the simple UCC model still is weak.

An alternative would be to treat excessive UCC chops as a separate metric from county chops.

Then the divisions of the Lansing and Battle Creek UCCs are equally bad.

The challenge then is to define what excessive means.

The minimum number of districts in a UCC is ceil(population/quota).  But treating this as a maximum may be problematic when the population is near to an integer multiple of a quota.

So perhaps ceil(population/quota + wiggle), where wiggle is either a constant such as 0.2, or a function of the population.   My sense is that it should not be linear with the population.

For example, if wiggle = 0.2 * (population/quota), we' are saying it is OK to split a UCC with between 0.83 and 1.00 quotas into two districts; but between 1.67 and 2.0 quotas into three districts, which seems excessive.  So maybe something like 0.2 * sqrt(population/quota)

2 if pop >= 0.82 quotas
3 if pop >= 1.74 quotas
4 if pop >= 2.67 quotas
5 if pop >= 3.62 quotas
6 if pop >= 4.57 quotas
7 if pop >= 5.53 quotas
8 if pop >= 6.49 quotas

The computation can be hidden from those submitting plans.   For Michigan, the rule is:

(i) Don't split the Lansing UCC;
(ii) Split the Grand Rapids UCC between two districts.
(iii) Split the Detroit UCC among 6 or 7 districts.
(iva) Don't chop single-county UCCs.
(ivb) Single-county UCC chops count as county chops.

(iva and ivb are alternative rules).

[jimrtex]

The finagling over chopping townships versus munis brings up another point--in quite a lot of states, town boundaries don't make a lot of sense, and there are no significant townships.

Exactly. That was what I was driving towards in the VA exercise. I took many of the larger counties and independent cities and found suitable subunits. My macrochop rule would not affect counties under 70K, and most large units have planning areas, or other recognized subunits. The same exercise would have to apply to the states that don't have county subdivisions established by the state for use by the Census.

Which is why I favor commissions beginning in the 0 year or earlier.  If it happens after the census numbers are available, definition of community of interest becomes too self-serving.

[jimrtex]

I'd like to roll back part of the discussion, so I can see where there is agreement and where questions need to be resolved.

At the level of someone looking at the two MI plans and not knowing any detail did the non-political scores seem reasonable relative to each other?
train: Inequality 10, chop 17, erosity 129
Torie: Inequality 10, chop 19, erosity 108

Let's set aside microchops, since they did not come into play for the MI maps. Perhaps they will return if a need arises.

Much of the detailed discussion was on macrochops and their effect on chops and erosity. My goals for them were the following:
=A measure for erosity that treats small scale erosity in urban areas the same way as large scale erosity in rural areas.
=A measure that could be coded in a straightforward way into software like DRA and doesn't change for different maps, for example the links between counties form a table that is known well in advance of the Census data, and the Kent links also become a table in software.
=A mechanism to determine if subunits should have subunits considered within them (in MI that means Detroit, but other states aren't as clean as MI - see IL).

A big part of the macrochop mechanism is the threshold to trigger it. Here are the features I was seeking.
=A threshold to determine what areas are sufficiently urban to warrant special treatment.
=A threshold that favors smaller chops over bigger chops.
=A threshold that doesn't particularly favor placing chops in small counties over large counties.

How about a process that uses decomposition and iteration?  This avoids the issue of mixed chop sizes.

Round 1, Whole State division into regions.

(a) Identify whole-county regions that have a population approximately equal to an integer number of districts (say 5% x sqrt(N)).   Counties in a region must be connected.
(b) Each UCC must be contained within one region.
(c) More regions (ie more single-district regions) is better.
(d) If local equality can be improved by shifting a single county without breaking connectivity it must be shifted.
(e) Inequality can be measured
    (i) total deviation; or
    (ii) total shift count, the population that would have to be moved in the minimal number of
         shifts (number regions - 1) to bring all regions to either full equality or 0.5% equality.
(f) Erosity can be measured using simplified boundaries.  Distance is measured node to node, where a node is either a junction of three or more county boundaries, or two county boundaries and the external boundary of the state (states trimmed to the Great Lakes or ocean).

Round 2) Refinement of inter-region boundaries.

(a) Each pair of districts is treated independently.
(b) Shift direction identifies which side of the boundary the chop occurs on.
(c)  Adjustment must be identified shift population from Round 1, +/- 0.25% of quota.
(d) Chop must be within one county, but any county on the boundary that is connected to the other district may be chopped.
(e) No MCDs may be cut.  If shifting a MCD improves equality without breaking contiguity it must be shifted.
(f)  Erosity is measured by simplified internal distance.  Distance along county lines is excluded.
(g) If necessary to split an MCD, then this would be a separate process.  It is preferable to split a county that does not require an MCD split, with one that does.

Round 3) Definition of districts in multi-district regions.

(a) Large cities (eg Chicago and Detroit) may be treated as counties.  Isolated areas of the remnant county may be treated as part of the city-county, or as separate counties.  For example, Hamtramck, Highland Park, and the Grosse Pointe's could be considered part of the Detroit unit, rather than the Wayne unit.   On the other hand, Chicago might divide the remnant of Cook County into two units.
(b) Larger MCDs (say greater than 10% of a quota) shall be split into subunits.
(c) Districts will be defined using subunits (smaller MCDs, and subunits of larger MCDs).
(d) Between districts, at most one MCD may be divided, even if the division uses subunits.
(e) Districts may not multi-span counties (eg only one district may cross the Oakland-Macomb boundary, one between Oakland-Wayne, one between Macomb-Wayne).  The treatment of Detroit and Wayne as separate units does not make an exception (eg Oakland-Wayne and Oakland-Detroit).
(f) Erosity is measured  by internal simplified distance.  Distance along county lines does not count.
(g) District populations should be within 0.5% of quota.   If this is not possible, then subunits would be split in a 4th round.

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Within a UCC, chops up to a threshold are free. 

A cut along county lines within a UCC is still a chop.  A UCC chop does not count as a county chop.

(a) Cutting Clinton is a chop of the Lansing UCC, but not a chop of Clinton.
(b) Cutting along the southern boundary of Clinton is a chop of the Lansing UCC.
(c) Cutting Calhoun is a chop of the Battle Creek UCC, but not a chop of Calhoun.
(d) Cutting a non-UCC county counts as chop of that county.

Chops such as (a), (b), and (d) will tend to be favored because they are smaller.

[jimrtex]

I like this as an algorithm to design a plan, but I tried something similar a year or so ago and had difficulty turning it in to a metric to judge plans. At a minimum it requires the mapper to submit their regions with their plan, and that has the downside of potentially disqualifying plans that were designed without regions. My sense is that isn't as good for public participation.

The intent is that the whole process be done in a stepwise fashion.  All participants would submit a regional plan.

If someone skipped that step, they could still produce a regional map.  This is how I comprehend Torie's map.



Presumably, he is going to need a large transfer from the Lansing region to the Grand Rapids region.  That may cause his plan to not advance.

But if it did, I'm pretty indifferent to whether the population is moved from northern Clinton, western Clinton, western Eaton, or perhaps even Calhoun.  If we have complete plans, then we are faced with variants that cause the whole number of plans to explode.

I think it is better in terms of public participation to start out with simple plans.

[jimrtex]

It is less than a macro-chop Jimtex (however defined), and just why absent a macrochop, should UCC's be sacred cows, since the number of votes detached is a relatively trivial percentage? Also the Clinton chop is of rural areas, so they are probably pleased to be detached from the Green, egghead/intellectual, quasi Marxist, gay loving, God-less, cultural cesspool, and bureaucratic, public employee (government and public universities) tax loving parasitical types to boot, that Lansing is all about, in favor of being moved into the culture of the more traditional and steady practical Dutch heavy, into practical money making, and growing the economic pie rather than shrinking it, folks in the Grand Rapids UCC.

This post was just for fun. It has a mild point (the amount of population is small enough to just chill and it really is rural, which is why the population is small), and then I went ballistic, trolling my butt off, and I loved it. Maybe it will earn me my first death point.

You failed to follow instructions.  Given this map,



(1) Create whole-county regions with a population approximately equal to a whole number of districts.
(2) Multi-county UCCs must be contained in a single region.
(3) Create as many regions as possible.

Having done that, the following map can be derived which shows the minimum population shifts to bring the regions into balance.

If your plan advanced, the next phase would be to define where the county chops were to be made.  By trying to do everything at once, you have to try to deal with all the problems of chops and erosity at different levels.   In addition, you would have to try to compare competing plans that differed only at a local level, such as choosing between chopping Clinton or Eaton counties. 



Eaton County is quite remote from East Lansing.   East Lansing is in Clinton County.  A typical couple in northern Clinton is a split commuter couple, with one working for Dow in Midland, and the other for the state government or for Michigan State.  The typical couple in western Eaton is a split commuter couple, with one working for the state government or GM, while the other works for a furniture manufacturer, tulip bulb cultivator, or Zondervan in Grand Rapids.

[jimrtex]

But Osceola can be shifted producing better equality between regions and reducing the stranded population outside UCC to under 10% of the quota (around 64,000).

[jimrtex]

Edit: Missaukee not Manistee

Jimtex, I don't think your "instructions" are part of the game, nor the 10% figure wherever that came from. Also, there is no penalty for the size of an I-chop, so one can play with that to get a higher score in other areas. Sure, your approach is a more efficient process I admit, once you have gathered the data base on a spread sheet, which takes a fair amount of work, including knowing where the counties are (so putting the percentages of each county on a map is probably what one should do first perhaps following your method).

Your first map came in at 11.5%.   The version with Osceola (not Manistee Missaukee) shifted came in at 9.1%.  There was no magic about 10%, it was just to indicate the level of equality one can achieve in a state with more populous counties than Iowa.

I believe that is a mistake to not consider the size of the chops.  To paraphrase Reynolds v Sims, people vote, not chops.   To survive a legal challenge, we are going to going to have to establish that reducing county division was of paramount concern.  Stranding 64,000 persons is better than stranding 81,000 unless there was a significant erosity cost.

A commission in Michigan that wanted public participation would provide an application that might have an interface similar to what I drew.  They would publish their numbers, so interested parties could verify them (as you know governments sometimes make mistakes in this area).  They would publish a standard for describing a plan, so that if some drew map with a spreadsheet and paint, they could submit a plan.

In a real app, you would be able to click on the county and it would be painted.  You might be able to draw areas, etc. but that is hardly needed given the relative small number of counties.  One could hover and see the county name, and switch to a satellite layer with translucent colors.  One could show the actual populations, though that is less practical in my experience.

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It wasn't really "my" map.  I found a map on the Internet, and was using it for example.  You've jumped ahead to the next step.  But your going back and forth about whether it is better to split Eaton or Ingham illustrates a weakness of a single comprehensive stage.  It become exceedingly complex when trying to consider where the boundary should be between Grand Rapids and Lansing, when it is somehow tied to the division of Hamtramck.   If your statewide map had been approved, then there could be a simple focused discussion on where to get 13,647 persons, where all the options might be considered.

The switch of Osceola (not Missaukee) was automatic.  When a single county on a boundary can be switched and improve the equality between the two districts, then it is shifted.  The algorithm is simple.   Determine counties in the more populous district that have less population than the difference.   Choose the one that reduces the difference the most, while not breaking contiguity.

I had noticed that the shift of Missaukee would produce a 3rd district within 0.5% bounds.  I'll submit it as a joint effort.

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I would only use road connectivity to control which counties may be directly connected.  In Michigan this is mainly to force the Lake Michigan crossing at the bridge, and to disqualify a few near corner connections.  Within counties I would be inclined to treat contiguity and connectivity as equivalent, other than corner connections of townships.  An exception might be made for a place like King County, WA, where Lake Washington would either have to be crossed on a bridge, or go around the ends of the lake.

[jimrtex]

Here is our collaborative effort with Missaukee rather than Osceola shifted.  The increase in the number shifted is slight, from 9.1% to 9.3%, the number of chops is reduced from 5 to 4, and erosity is reduced.

[jimrtex]

Quick question that I missed the answer to: if, say, you have a large multi-district UCC, and you have the minimum number of districts in it, but more than one of those districts crosses the UCC boundary, does that give you any extra penalty?  What if, say, there's a county that is not part of the UCC but is literally only accessible through the UCC, does that get mulliganed or not?

Spoiler alert: in particular I'm thinking about various ways to draw the Pittsburgh area.  It has to take at least parts of four districts but do three of them need to be entirely within the UCC, especially with non-UCC Greene in the corner mucking things up?

The Pittsburgh UCC requires 4 districts, so Greene can be included.  I'm ambivalent whether you have one district with just a small portion of the UCC, or two districts that are closer to 1/2 and 1/2, or perhaps three districts that extend outside the UCC, if one includes Greene.  I'd probably try to put Greene with a district that comes in from the east.  Fayette is fairly remote from Pittsburgh, in likely gets pulled into the UCC based on settlement along the Monongahela.  Then if could reach Erie, I'd have the other district heading that way.  If I couldn't reach Erie, I'd go east so as to leave as much population north of the UCC to put in the Erie district.

In Virginia, I included Accomack and Northampton with the Hampton Roads UCC, and stripped some of the UCC off the north.  That was based on the region between the James and Potomac being rather short of population, and it also needed some of the excess from the Washington UCC. Conceivably you could cross the Chesapeake, as has been done in the past based on some COI argument, even though there are no longer ferries operating.

[jimrtex]

This is based on what Muon has labelled as Torie 2015 C.  Its main feature is no chops needed for the Grand Rapids region.   Note I required this to be within 0.5% x sqrt(2) of 2 quotas, which is barely.  Otherwise, you have a bit of systemic population bias.



There is an alternate that would move the shift from Flint to Detroit to Flint to Saginaw Bay, reduce the shift northward from Lansing to Saginaw Bay, and increase the shift eastward from Lansing to Detroit.

[jimrtex]

I messed up.  I switched Mecosta, but used the population of Osceola.  Clare and Mason are slightly too large to improve equality with a simple swap.

This is based on the plan named Train 2015 B, with an adjustment.  As originally proposed, it required a double shift to transport the excess population from Saginaw Bay district to Detroit.  But a transfer of Osceola from Saginaw Bay to Lansing, reduces the difference between those two districts, and permits a direct transfer from Lansing to Detroit.  Overall, the shifted population is 6.6% of a quota.

[jimrtex]

This is a plan I created in 2013:

[jimrtex]

Which plan do you like best now, Jimtex?

I am going to present and score several, and then we can compare.  Perhaps you will try to create your own plan.

[jimrtex]

Which plan do you like best now, Jimtex?

I am going to present and score several, and then we can compare.  Perhaps you will try to create your own plan.

I did, and compared it to "yours" above, as modified by me.  

If you are using some scoring system other than Muon2's, except maybe for penalizing microchops, matters however will descend into further chaos than they are now however.  One scoring system at a time should be tested, is my suggestion. Muon2 isn't applying his zoom thing anyway I don't think, which is perhaps the most problematical part of his system until further refined, other than what we discussed about uber penalizing double chops that add up to a microchop of a multi county UCC.

I am proposing a simpler, alternate scoring system.

By focusing on regions containing whole UCC's you get something that is more Iowa-like with 8 regions.

Erosity is measured by the simplified internal border length.  This avoids the whole issue of road connectivity. 

I do use connectivity as a constraint on a limited basis, but only as a substitute for pure contiguity.  For example, Gratiot and Shiawassee are contiguous, while Saginaw and Clinton are not.  I define Gratiot and Shiawassee as not being _connected_, and therefore you can not have a region (or district) that goes directly between Gratior and Shiawassee.  However, if the Gratiot-Shiawassee boundary is part of a region boundary you are charged for it (about 3/4 of a mile).

The equality measurement is the amount needed to bring the regions into substantial equality.  It in effect is a measure of the total chopped population.  It avoids the whole issue of chop size calculation.

[jimrtex]

This is a connectivity map.



Connectivity is not used as part of an erosity measure, but rather as a more stringent criteria than literal contiguity for placing adjacent counties in the same district.   Connectivity would be defined before any maps were drawn.

To be connected, counties must be contiguous.   In general there must be a direct, non-circuitous way to travel between the counties, particularly considering the distribution of the population.  There is no requirement that the route be entirely in the two counties, but if the route goes through other counties it should not be through population concentrations, or drawn in a way to evade the population concentrations.

Continuity of land use may also be considered.  If the land on both sides of the boundary is crop lands, or urban development, the boundary itself is likely artificial.

The length of the border may be considered.  If the direct distance between the end points of the boundary is greater than 20% of the square root of the land area of the smaller county, the counties should generally be considered connected, unless there is a substantial reason not to, such as a substantial physical barrier.     If the direct distance between the end points of the boundary is less than 20% of the square root of the land area of the smaller county, a justification for connectivity may be needed.  If another county intrudes near the boundary, this may be a consideration.  For example the jog up of the northern boundary of Ottawa County cuts the length of the Muskegon-Kent boundary from 12 to 6 miles, but you have an area that is 12 miles wide to both the east and west of the boundary in the two counties.

On the map, green links are between connected counties.  Orange links are where the boundary is entirely in the Great Lakes.  These counties are not considered to be connected.    The links between Mackinac and Emmet and Cheboygan use the bridge.

The red dots are where four counties have a common junction point, or a near common junction point.  Point contiguity or near-point contiguity is not considered connected.

The yellow links are counties I would consider to be connected, but I could see someone arguing that they are not.  Red links are counties I would not consider to be connected, and would need stronger justification to change.

In general, we should be liberal in the granting of connected status.   It is only intended to restrict the most tenuous instances of literal contiguity.  It is not part of the measurement of erosity, or an indication of community of interest.

[jimrtex]

Somehow I knew that is what you would do.  For erosity, would not a map with juts containing now much area, but a lot of population, garner far less of a penalty, as compared with what makes for the minimum line length of more rural districts large in area, unless you somehow take a ratio of line length to population for subsets of each CD? Your method really emphasizes overall equality in population. That will tend to result I suspect in "uglier" maps. Anyway, it will be interesting to compare what your map looks like that gets the high score with your system vis  a vis Mike's, and get forumite reaction to it. Good luck!

Can you give me a hypothetical example of the bolded part?  I'm not sure what you are saying.

[jimrtex]

Scoring example:



This is a submitted map.  The three multi-county Urban County Clusters (UC), Detroit, Lansing, and Grand Rapids are highlighted in purple.

Each region is comprised of a group of connected counties, and has a population that is approximately equal to that of a whole number of congressional districts of ideal size.  For Michigan, the ideal population (the quota) is 705,974 which is the state's population of 9,883,640 divided by the total number of congressional districts (14). 

The population of each region is shown as the actual population relative to the quota.  For example, the population of the blue region in the Upper Peninsula and northern Lower Peninsula is 701,034, which is 0.993 (99.3%) of the quota.

An urban county cluster must be wholly contained in a region.  There may be multiple UCC in a region.   There are 11 single county UCC in Michigan (not shown).  In this submited plan, the Muskegon UCC is in the same region as the Grand Rapids UCC, and the Jackson UCC is in the same region as the Lansing UCC.

It is within the rules to have multiple larger UCC in a region.  The Detroit and Lansing UCC could be be combined into a single region with a population equal to about 7 districts.  But this would reduce the total number of regions from 8 to 7, and any 8-region plan automatically defeats a 7-region plan.  The Lansing and Grand Rapids UCC could be combined into a single 2-district region.  But this will create a band across the state.  The area south of the band has a population equivalent to 2.4 districts, too large for two regions, but too small for 3 regions.

[jimrtex]

To be connected, counties must be contiguous.   In general there must be a direct, non-circuitous way to travel between the counties, particularly considering the distribution of the population.  There is no requirement that the route be entirely in the two counties, but if the route goes through other counties it should not be through population concentrations, or drawn in a way to evade the population concentrations.

Can this be defined in a way that a person sitting at a computer with a program such as MapQuest could determine whether such a connection exists? As I read this it has a substantial subjective component, and two groups working on the connectivity map could reasonably come up with two different plans.

The organizers would define the connectivity map.  Presumably if they provided an app, this could be a displayable layer.  Any scoring would verify connectivity.

The Census Bureau has a county contiguity file for the United States, which can be trimmed to an individual state (eg the census file includes the contiguity between Monroe, MI and Lucas, OH). 

From census files the land boundary (direct) distance and areas can be obtained.  The substantiality of each border can be calculated.  I have used the border distance divided by the square root of the area of the smaller county.  We can imagine that the counties are wood blocks that have been glued together.  If there is longer surface the bond will be tighter.  Shorter, and we might be able to break them apart.  The size of block is an indication of the leverage that may be applied.

Where we can twist the blocks apart, we might use pegs or reinforcing rods.  This is the equivalent to roads connecting the counties.  Some of the reinforcing rods might be outside the boundary of the junction, but they can be seen as reinforcing the connectivity, particularly if they are not through the populated areas.

I used the primary/secondary road shapefile from the census bureau, as well as the urban areas shapefile.

If the organizer were a public commission, they could prepare a preliminary definition of connectivity, which would be reviewed by the government of each county.

[jimrtex]

Somehow I knew that is what you would do.  For erosity, would not a map with juts containing now much area, but a lot of population, garner far less of a penalty, as compared with what makes for the minimum line length of more rural districts large in area, unless you somehow take a ratio of line length to population for subsets of each CD? Your method really emphasizes overall equality in population. That will tend to result I suspect in "uglier" maps. Anyway, it will be interesting to compare what your map looks like that gets the high score with your system vis  a vis Mike's, and get forumite reaction to it. Good luck!

Can you give me a hypothetical example of the bolded part?  I'm not sure what you are saying.

Think of a long thin tendril that is not very big, but contains a lot of people. Picture it being in Manhattan or something. The overall effect on the line length is trivial. The psephological impact might be large.

Definition of districts within multi-region CDs would be at a second phase.

In New York the initial phase would define 6 regions, a 19-district region for the NY UCC, and 2-district regions for Buffalo, Rochester, and Albany-Schenectady, and 2 single-district regions.

[jimrtex]

The submitted map can be represented as a graph, with the vertices representing the regions, and the links representing the boundary between the regions.   Since we will making our population shifts/chops along these boundaries, we can eliminate any links where there are not connected counties.  There were none in this example, but in Michigan they might occur if four regions met at the junction of four counties.  In that case, the diagonally opposite regions would not be linked.

[jimrtex]

B) This is perhaps a more lonely crusade, but I increasingly feel there ought to be some recognition for Combined Statistical Areas, where the Census delimits separate metros but the facts on the ground veer towards a common regional identity.  If we're getting rewarded for splitting Saginaw/Bay City/Midland (or Cleveland/Akron/Canton, or Dayton/Springfield, or any similar assemblage of nearby mid-sized cities that are functionally the same region, and nigh-universally felt as such), then IMO something's gone wrong.

The risk with using CSA is either overconstraining or underconstraining.

Is it desirable to have a district starting in Lenawee coming in to Wayne County if it can avoid a crossing of the Wayne-Macomb border (underconstraint).

Not only do we have Saginaw/Bay City/Midland, there is Kalamazoo-Battle Creek which is 4 counties.  Lansing drags in Shiawassee.   Mount Pleasant-Alma forces Gratiot and Isabella to stick together.  Muskegon gets added to Grand Rapids.   Genesee  and Washtenaw get added to Detroit.

We haven't said that there can't be some subjective judgment that would keep Saginaw, Bay City, and Midland together.  But it must be something that works quantitatively as well.

[jimrtex]

To get to 48% Cleveland has to be split. OH recognizes city wards as a subunit of municipalities. The OH constitution explicitly states that "such district shall be formed by combining the areas of governmental units giving preference in the order named to counties, townships, municipalities, and city wards." [emphasis added]

The proposed constitutional amendment will remove city wards.