Chops and Erosity - Great Lakes Style

[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.

[muon2]

To move the discussion to some practical examples, below are 4 plans for Illinois. How do they score?

All the plans have the same boundary between IL 17 and 18 (see first image). All the plans have a macro-chop between IL-01 and 6, with no subunit chop, and an I chop into DuPage with a subunit chop from the west. The area closer in to Chicago is the same in all maps.

Plan A has two micros between IL 13, 14 and 15, an I- chop in Waukegan, and I-chops in Kendall and DeKalb with no subunit chops.

Let me begin the erosity discussion with the 6 downstate CDs. This has the advantage of letting us focus on regional links between counties, and I'll repost my state map for reference.



I will break the discussion down by segment between districts. Usually it's just a matter of counting severed links.

CD 17-18: erosity 7
CD 15-18: erosity 5
CD 16-18: erosity 2
CD 15-17: erosity 7
CD 15-16: erosity 3

CD 14-15: erosity 8; the microchop in Mason intercepts the only state highway between Menard and Mason. The microchop has two links, one to Menard and one to the rest of Mason. The remaining piece has 5 links, with the Menard link lost but replaced by the microchop link, 3 of which are cut by the boundary.

CD 13-14: erosity 8; like the previous segment the microchop in Mercer intercepts the link to Henry, but creates a link to the rest of Mercer.

CD 11-13: erosity 1; note the chop penalty for splitting the Rockford UCC only allowed the counties to be treated separately. They just act like any other county for the purposes of erosity. I also note that none of the other 2-county UCCs had more than one link along one segment, since if it did it would only count as one severed link (UCCs as supercounties).

CD 6-16: erosity 3.
CD 12-14: erosity 0.
CD 14-16: erosity 6; these segments involve the chop of Kendall into two quasicounties. The southern part has the links to LaSalle, Grundy, and Will, and to the north. The northern part has the link to Kane, the link to the south, and a potential new link to Will which does not figure on this segment, so I'll defer this discussion to my next comment.

CD 12-13: erosity 2 (or 3 or 4); the chop of DeKalb creates two quasicounties. The northern part including the county offices in Sycamore maintains its links to Ogle, McHenry, Kane, and adds a link to the southern part of DeKalb; two of those links are severed on this segment. The southern part definitely has links to Lee, LaSalle, and the northern part.

In the south the assumption is that links must connect to the most populous subunit, which is Sandwich. Local links are presumed within the county, and no prior regional link is lost (but perhaps not severed). In the original model (see the AL discussion) only primary regional links went into a chop that was not due to a macrochop. That would mean the southern part of DeKalb wold have links to LaSalle (on segment 13-14), Lee (not severed), and the northern part of DeKalb (already counted).

The original model is easy to implement since regular chops create no new links other than those between the fragments in the county. The potential problem is that one can shape chops to to advantageously intercept those primary links and get a reduction in erosity, when it wasn't really deserved. For example, in this plan, you could run the chop up to put Franklin, South Grove, and Malta townships from the NW in CD 13, and put Pierce and Squaw Grove from the SE in CD 12. This eliminates a severed link from the Sycamore fragment to Ogle and reduces erosity by 1. Try it and see if that is a move mappers should be driven to make.

If you don't like that, the solution is to let the new quasicounties reestablish links just as if they were counties in their own right. That tends to increase erosity around chops. In this case Sandwich has a link to Kendall on US 34, but technically no other highway route from any county can get to Sandwich. Yet since links can't go away, there's an assumption that there's a local connection to Sandwich from the north. That opens up the possibility of another link from the southern part of DeKalb to Kane along US 30.

As you can see protecting against chop/microchop games in erosity can make the system a lot more complicated. I'd love to keep it simple, if the cost in gaming isn't too high. Hence my score varying from 2 to 4 for this segment. The total so far from the downstate segments is EROSITY = 52 (or 54).

[traininthedistance]

So, I unfortunately checked out of this discussion for awhile and it seems to have gotten sufficiently weedy that doing so was a mistake.  And it has also sufficiently moved on from Michigan.  

But!  Despite that, I have a map that I'd be curious to see scored.  









Salient points:

* No munis chopped besides Detroit; one subunit within Detroit is chopped.  Both Detroit districts are within 51-53% BVAP.
* No microchops anywhere.  I've never really cottoned to them, TBH.  A chop is a chop is a chop.  I do wonder if using them on the 1-4 border might sufficiently decrease erosity to be worth it.
* The Detroit metro lines are, I think, pretty damn clean.
* One macrochop is saved outside of the Detroit area at the expense of some more erosity in the southwest– the standard (but high-inequality) "pretty" district 6 is sacrificed and a GR-burbs-to Benton Harbor thing put in its place for the sake of one fewer chop and nicer lines in Central MI.
*It's even possible to lower the county chops by sending the Flint-based district into Livingston rather than the Thumb– but doing so will increase inequality and create a UCC chop, so let's leave that thought for another map.

The one thing I don't like about this map is the split of Saginaw, I mean, something needs to be chopped and the actual Tri-Cities are all together, at least, but it's still a little sad.  But, hot damn, that District 8.

[muon2]

So, I unfortunately checked out of this discussion for awhile and it seems to have gotten sufficiently weedy that doing so was a mistake.  And it has also sufficiently moved on from Michigan.  

But!  Despite that, I have a map that I'd be curious to see scored.  









Salient points:

* No munis chopped besides Detroit; one subunit within Detroit is chopped.  Both Detroit districts are within 51-53% BVAP.
* No microchops anywhere.  I've never really cottoned to them, TBH.  A chop is a chop is a chop.  I do wonder if using them on the 1-4 border might sufficiently decrease erosity to be worth it.
* The Detroit metro lines are, I think, pretty damn clean.
* One macrochop is saved outside of the Detroit area at the expense of some more erosity in the southwest– the standard (but high-inequality) "pretty" district 6 is sacrificed and a GR-burbs-to Benton Harbor thing put in its place for the sake of one fewer chop and nicer lines in Central MI.
*It's even possible to lower the county chops by sending the Flint-based district into Livingston rather than the Thumb– but doing so will increase inequality and create a UCC chop, so let's leave that thought for another map.

The one thing I don't like about this map is the split of Shiawassee, I mean, something needs to be chopped and the actual Tri-Cities are all together, at least, but it's still a little sad.  But, hot damn, that District 8.

I'm waiting on Torie to get me his deviations for his IL plan A so I can make sure I'm looking at the same thing he did (I tried to construct it from the images and the deviations were outside the permitted range). In the meantime, I can probably look at yours this weekend. It's an interesting plan, and it will be interesting to see how those macrochops affect the erosity.

You may not have seen my reply on the microchop question. I used their existence to relegate inequality to a tiebreaker, since there were some serious games that could otherwise occur. However, moving inequality to a tiebreaker puts "clean" states like IA and WV in a bind, since they don't need any chops at all, and they become a one-dimensional measure of erosity with no flexibility. Originally the inequality score was to be at the same level as chop and erosity scores (they were calibrated to be that way) and not a tiebreaker. If microchops are nothing special, I'm prone to restore inequality's place and have a three-variable Pareto test.

[Torie]

Sorry, I have been distracted by a host of matters, and have not had time to pursue the matter of discussing fashioning a practicable redistricting metrics regime. But to move matters along, and accede to your request, below is a  partial response.

Yes, plan A requires a macro-chop of York Township, so under the Muon2 metrics, it is a fail.



Here are the minority percentages in the two African American CD’s (the figures for the Hispanic CD are above).



Plan D (which I suspect will score the highest, is below. I moved the lines between IL-01 and IL-07 to cut rid of the Worth Township chop by IL-01 (that can be done with all of the plans). The IL-02 figures are also displayed, so I think Mike deemed an Hispanic VAP score of 59.6% some magic number, and I guess when moving stuff around a bit, I picked up 30 Hispanic basis points over Plan A, and got there.






The rejiggering of the line between IL-14 and IL-16 might have potential it seems. Call it Plan E.  

[muon2]

Thanks for all the extra info, but I'm going nuts trying to duplicate the Torie A map. The districts outside of Chicago should be straightforward, and I've even gone to a spreadsheet to add counties and townships, but I'm not getting things to add up. Here's the comparison for CDs 10-18.

CD	Torie	muon2
10	+2608	+2746
11	-2529	-2529
12	+3021	+3021
13	+149	-3116
14	-3104	+161
15	-3387	-3387
16	+872	+872
17	+77	+75
18	+1190	+1796

I added the three whole counties and four townships for CD 10+11 and my numbers match the Census, so I suspect you have a stray small precinct missing in your CD 10. Our totals for CD 13+14 are the same and I've double checked my township chops, so I suspect you have a microchop lurking in either Henry or LaSalle counties (both have small-sized precincts right on the county line). If my suspicion is correct you can rid that plan of both the invisible microchop and the Mercer chop. CD 17 is just weird since you have 2 extra people, but I added all the counties by hand and still get +75. CD 18 is even weirder since it's a fairly large discrepancy, and I've added all my counties by hand to check my map. Could there be a precinct (like from 7 with a similar color) grabbing something in 18?

You may want to run the DRA contiguity check on your plans. It may not matter as much on A, but as I get to your more finely tuned plans, I suspect it will become relevant.

EDIT: I think I will have an easier time assessing IL plans if there are separate screenshots for the north and south halves of Chicago/Cook with town lines on. The resolution is so poor otherwise, I can't make out where some chop lines go.

[muon2]

So, I unfortunately checked out of this discussion for awhile and it seems to have gotten sufficiently weedy that doing so was a mistake.  And it has also sufficiently moved on from Michigan.  

But!  Despite that, I have a map that I'd be curious to see scored.  






Salient points:

* No munis chopped besides Detroit; one subunit within Detroit is chopped.  Both Detroit districts are within 51-53% BVAP.

* No microchops anywhere.  I've never really cottoned to them, TBH.  A chop is a chop is a chop.  I do wonder if using them on the 1-4 border might sufficiently decrease erosity to be worth it.

* One macrochop is saved outside of the Detroit area at the expense of some more erosity in the southwest– the standard (but high-inequality) "pretty" district 6 is sacrificed and a GR-burbs-to Benton Harbor thing put in its place for the sake of one fewer chop and nicer lines in Central MI.

I see a GR precinct next to Wyoming that is in CD-3. If I put it in CD-2 with the rest of GR CD-3 goes outside the deviation limit. Let me know if you want the (micro)chop of GR or if you have a revised Kent for scoring.

Your chop of Lapeer (35,666) is just barely over the threshold for a macrochop (35,298). That's going to run up the erosity score, so let me know if you want a revision there, too.

[traininthedistance]

I see a GR precinct next to Wyoming that is in CD-3. If I put it in CD-2 with the rest of GR CD-3 goes outside the deviation limit. Let me know if you want the (micro)chop of GR or if you have a revised Kent for scoring.

Your chop of Lapeer (35,666) is just barely over the threshold for a macrochop (35,298). That's going to run up the erosity score, so let me know if you want a revision there, too.

Kent is easily revised; I'll have it up soon.

I'm clearly following this discussion even worse than I thought I was if that threshold in Lapeer actually makes a difference.  Ugh.  I figured it was just a chop already, didn't realize you could get rewarded for making it just a tiny bit smaller.  This one's going to take possibly some time, because any fix will likely increase inequality, as well as other erosity thresholds (by having the Lapeer part of 10 touch Sanilac, or at least more townships within the District 5 part of Lapeer, which if I'm following correctly both will bump the score up?)

[muon2]

Here's a post from the earlier thread on MI chops (linked in the OP) that touches on issues in train's map. The first map shows some arrangements using the same CD 2, 3, and 8 as in train's map. The macrochop of Jackson is avoided using east-west strips. The macrochop of Saginaw is avoided by linking Bay to the thumb as train was perhaps thinking.

The second map answers train's query about erosity between CD 1 and CD 4. In train's plan the segment between those two has an erosity of 10 and CD 1 has a deviation of -530. In the second map below the segment has an erosity of 9 and CD 1 has a deviation of only -49. It would be interesting to see if microchops could do better than that.

Here are two revised regional plans that could represent improvements. The first is an improvement of my original 8 region plan. It shifts Sanilac and Lapeer and a couple other areas up north. Lapeer is shifted to improve compactness. The average deviation is 0.951% which should equate to a shift of 3.80%. I can get that down to 0.896% (3.58% shift) by readjusting the boundary of the northern district producing a less compact shape for the red region.



In this second plan I have made some adjustments to jimrtex's most recent regional plan. The erose shape of the Grand Rapids region largely disappears when it is split into two CDs. The average deviation is 1.007% which converts to a 4.03% shift.

[traininthedistance]

Two revised Kents for the price of one.



District 2 is -3124, District 3 is +836.  Very similar to the original, just a touch more inequality.



District 2 is +226, District 3 is -2514.

This one keeps the inequality better under control than the other one, and as a bonus Holland is all together in one district (as it usually isn't because it spans a particularly chop-prone county line), but 2 looks more erose, by the eyeball test at least.

[traininthedistance]

Here's a post from the earlier thread on MI chops (linked in the OP) that touches on issues in train's map. The first map shows some arrangements using the same CD 2, 3, and 8 as in train's map. The macrochop of Jackson is avoided using east-west strips. The macrochop of Saginaw is avoided by linking Bay to the thumb as train was perhaps thinking.

The second map answers train's query about erosity between CD 1 and CD 4. In train's plan the segment between those two has an erosity of 10 and CD 1 has a deviation of -530. In the second map below the segment has an erosity of 9 and CD 1 has a deviation of only -49. It would be interesting to see if microchops could do better than that.

How much worse is the erosity on the southern Michigan strips as compared to my Jackson split?  And it seems like one of those strips is over 0.5% off anyways, so there's still a chop to contend with anyway.

I was playing around with putting most of Sanilac instead of Lapeer into the Detroit area; I feel like local sentiment would prefer Lapeer rather than breaking off a Thumb county but this might be a case where the numbers and local sentiment are in conflict, if you can do it better with Sanilac instead.

[muon2]

I see a GR precinct next to Wyoming that is in CD-3. If I put it in CD-2 with the rest of GR CD-3 goes outside the deviation limit. Let me know if you want the (micro)chop of GR or if you have a revised Kent for scoring.

Your chop of Lapeer (35,666) is just barely over the threshold for a macrochop (35,298). That's going to run up the erosity score, so let me know if you want a revision there, too.

Kent is easily revised; I'll have it up soon.

I'm clearly following this discussion even worse than I thought I was if that threshold in Lapeer actually makes a difference.  Ugh.  I figured it was just a chop already, didn't realize you could get rewarded for making it just a tiny bit smaller.  This one's going to take possibly some time, because any fix will likely increase inequality, as well as other erosity thresholds (by having the Lapeer part of 10 touch Sanilac, or at least more townships within the District 5 part of Lapeer, which if I'm following correctly both will bump the score up?)

There are two state highway paths that connect Sanilac to Lapeer: MI 53 and MI 90. Mapquest say that MI-53 is shorter, so that is the primary link. In a macrochop both links would count. In a simple chop only the primary link counts, though that could be an open question I posed wrt Torie's IL map. If the primary link stays within the district at the county line, then erosity doesn't increase for a simple chop.

[traininthedistance]

There are two state highway paths that connect Sanilac to Lapeer: MI 53 and MI 90. Mapquest say that MI-53 is shorter, so that is the primary link. In a macrochop both links would count. In a simple chop only the primary link counts, though that could be an open question I posed wrt Torie's IL map. If the primary link stays within the district at the county line, then erosity doesn't increase for a simple chop.

Yeah, that doesn't help; the link does in fact change districts at the county line.  (I guess it helps prevent 10 from really touching Tuscola, though?)

EDIT:



I also switched Zilwaukee from 5 to 4 to lower inequality since 5 needs to take on more people.  4 is +1,113; 5 is +243, 10 is -979.

Still a little unclear on the rationale for distinguishing between macrochops and non-macro chops.

[muon2]

Two revised Kents for the price of one.



District 2 is -3124, District 3 is +836.  Very similar to the original, just a touch more inequality.



District 2 is +226, District 3 is -2514.

This one keeps the inequality better under control than the other one, and as a bonus Holland is all together in one district (as it usually isn't because it spans a particularly chop-prone county line), but 2 looks more erose, by the eyeball test at least.

I posted the Kent connection map earlier in the thread. Yellow lines are links with state highways, blue lines are links without state highways.

Based on our analysis of Torie's chops of Kent, the best measure of erosity for macrochops is to use all both types of links between units within a county, and to only use highway links between counties. The links severed by the border between districts is the erosity.

By that measure the segment on the first map has an erosity of 12, 11 within Kent and one for the Ottawa-Allegan link. The second map has an erosity of 15, 14 within Kent and one for the Muskegon-Ottawa link.

[muon2]

Still a little unclear on the rationale for distinguishing between macrochops and non-macro chops.

There needs to be a transition from rural erosity to urban erosity. If only county links are used then rural districts come out fine but urban districts have unusually low erosities. There are example of this earlier in the thread.

The solution is to use county subdivisions in districts that go into dense areas. One could just define that to be use subdivisions for UCC counties when they are chopped. That has the drawback that it will strongly encourage chops to go in the smaller non-UCC counties. So instead I use a threshold test, if the sum of the chops is over 5% of the quota then it's a macrochop. In this case one adds all the smaller fragments to get the sum. The 5% threshold corresponds to the substantial inequality threshold for local districts and showed up in the population shift diagrams we used in 2013 (see the thread in the OP). It targets chops that must happen in the largest counties and elsewhere encourages smaller chops where possible. It also treats smaller chops the same in counties regardless of size.

[muon2]

District 2 is +226, District 3 is -2514.

This one keeps the inequality better under control than the other one, and as a bonus Holland is all together in one district (as it usually isn't because it spans a particularly chop-prone county line), but 2 looks more erose, by the eyeball test at least.

I posted the Kent connection map earlier in the thread. Yellow lines are links with state highways, blue lines are links without state highways.

Based on our analysis of Torie's chops of Kent, the best measure of erosity for macrochops is to use all both types of links between units within a county, and to only use highway links between counties. The links severed by the border between districts is the erosity.

By that measure the segment on the first map has an erosity of 12, 11 within Kent and one for the Ottawa-Allegan link. The second map has an erosity of 15, 14 within Kent and one for the Muskegon-Ottawa link.

On that second map if you put Walker and Grandville with Gaines, Byron and Alpine twps in CD 3 the erosity plummets to 9 (including the Muskegon-Allegan link). The deviations are better, too, -2308 and +20. We long ago decided that chops are based on the number of districts in a county, not the number of fragments, so the chop count doesn't go up for this version.

[muon2]

How much worse is the erosity on the southern Michigan strips as compared to my Jackson split?  And it seems like one of those strips is over 0.5% off anyways, so there's still a chop to contend with anyway.

In your map the CD 6-7 segment has an erosity of 9, 8 in Jackson and 1 for Hillsdale-Lenawee. The CD 7-8 segment has an erosity of 2 along the Jackson border. The CD 6-8 segment has an erosity of 4 for the usual county links. That's a total of 15.

If CD 6 runs from Kalamazoo to Monroe along the southern border and CD 7 goes from Battle Creek to Ann Arbor, a chop of Monroe including Milan and its surrounding twp puts the two CDs deviations at -1871 and -1951. The Monroe chop adds a link between the two pieces, but the highway link between Washtenaw and Monroe is no longer servered, so the CD 6-7 segment has and erosity of 7. The CD 7-8 segment has an erosity of 5, and there is no CD 6-8 segment. The total erosity is reduced to 12 by avoiding the macrochop.

If microchops don't count as chops, and thus don't create a bridge county, you can do the same as above but shift Litchfield and its surrounding twp in Hillsdale. That eliminates the chop and reduces erosity. A microchop in Kalamazoo could also eliminate the chop, but has one higher erosity than the Hillsdale one, since it can't go at the primary link without exceeding 0.5%. For this purpose, I assume that to qualify as a microchop, it must not chop county subdivisions.

[traininthedistance]

How much worse is the erosity on the southern Michigan strips as compared to my Jackson split?  And it seems like one of those strips is over 0.5% off anyways, so there's still a chop to contend with anyway.

In your map the CD 6-7 segment has an erosity of 9, 8 in Jackson and 1 for Hillsdale-Lenawee. The CD 7-8 segment has an erosity of 2 along the Jackson border. The CD 6-8 segment has an erosity of 4 for the usual county links. That's a total of 15.

If CD 6 runs from Kalamazoo to Monroe along the southern border and CD 7 goes from Battle Creek to Ann Arbor, a chop of Monroe including Milan and its surrounding twp puts the two CDs deviations at -1871 and -1951. The Monroe chop adds a link between the two pieces, but the highway link between Washtenaw and Monroe is no longer servered, so the CD 6-7 segment has and erosity of 7. The CD 7-8 segment has an erosity of 5, and there is no CD 6-8 segment. The total erosity is reduced to 12 by avoiding the macrochop.

If microchops don't count as chops, and thus don't create a bridge county, you can do the same as above but shift Litchfield and its surrounding twp in Hillsdale. That eliminates the chop and reduces erosity. A microchop in Kalamazoo could also eliminate the chop, but has one higher erosity than the Hillsdale one, since it can't go at the primary link without exceeding 0.5%. For this purpose, I assume that to qualify as a microchop, it must not chop county subdivisions.

Several questions:

1) How are you getting 2 from the bolded part?  Wouldn't it just be 1, for Jackson-Ingham?
2) Wouldn't the modified 6-7 segment have an erosity of at least 8? (Barry-Kalamazoo, Kalamazoo-Calhoun, Calhoun-Branch, Calhoun-Hillsdale, Hillsdale-Jackson, Jackson-Lenawee, Lenawee-Washtenaw, Washtenaw-Monroe)?  I guess, also, with the Monroe chop, that doesn't add any further erosity somehow?  Even though it's over 0.5% of a district?  But only since it's going along a particular road (that is not even necessarily the only state route conning those two counties, which is apparently why a Kalamazoo microchop of Ross Twp. is somehow worse?)

Even putting all that aside, I guess we've stumbled upon a situation where the rules are actually preferring more elongated shapes that "feel" more erose to the non-initiated.  Interesting.

For the record, I feel very strongly that microchops should count as chops.

[traininthedistance]

Huh, I wonder how this split of 6/7 would fare:



There are 16,067 people in the CD-7 portion of Jackson, which I guess helps because it's not a macro chop anymore?  

Also, not having a 7/8 border, or the line right along Jackson City (since you get penalized for having lines right along small cities/boroughs, even when the line is reasonably straight) should help with chop counts in comparison to my first map.

[muon2]

How much worse is the erosity on the southern Michigan strips as compared to my Jackson split?  And it seems like one of those strips is over 0.5% off anyways, so there's still a chop to contend with anyway.

In your map the CD 6-7 segment has an erosity of 9, 8 in Jackson and 1 for Hillsdale-Lenawee. The CD 7-8 segment has an erosity of 2 along the Jackson border. The CD 6-8 segment has an erosity of 4 for the usual county links. That's a total of 15.

If CD 6 runs from Kalamazoo to Monroe along the southern border and CD 7 goes from Battle Creek to Ann Arbor, a chop of Monroe including Milan and its surrounding twp puts the two CDs deviations at -1871 and -1951. The Monroe chop adds a link between the two pieces, but the highway link between Washtenaw and Monroe is no longer servered, so the CD 6-7 segment has and erosity of 7. The CD 7-8 segment has an erosity of 5, and there is no CD 6-8 segment. The total erosity is reduced to 12 by avoiding the macrochop.

If microchops don't count as chops, and thus don't create a bridge county, you can do the same as above but shift Litchfield and its surrounding twp in Hillsdale. That eliminates the chop and reduces erosity. A microchop in Kalamazoo could also eliminate the chop, but has one higher erosity than the Hillsdale one, since it can't go at the primary link without exceeding 0.5%. For this purpose, I assume that to qualify as a microchop, it must not chop county subdivisions.

Several questions:

1) How are you getting 2 from the bolded part?  Wouldn't it just be 1, for Jackson-Ingham?

When a county is the subject of a macrochop it is replaced by the subunits of the county, which act as if they were counties in their own right. They have links to other counties which can be severed to increase erosity, and those links must be established by numbered state or federal highways if the link crosses a county line, but can be a local road if the link is is between two units in the same county. The Kent count followed this interpretation.

Since Jackson got macrochopped it is treated for erosity as if each township were a county with links. There are two Jackson townships with highway links to Ingham so each has a link now. Both are cut by the CD 7-8 segment, so the erosity is 2.

It can seem strange to count so much on a short straight line. However, macrochops are designed to handle the urbanized areas like the boundaries in the Detroit UCC or along the Ottawa-Kent line. By macrochopping Jackson, the strong road links from Ingham lead to an extra count. Keep in mind that this method of measuring erosity is building in a sense of communities of interest due to transportation links, and that has happened here.

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There is no way to travel on state highways from Hillsdale to Jackson without crossing into another county, so there is no link between them.

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A simple chop of the county replaces the county with quasicounties consisting of one for each contiguous fragment from a whole district in the county. The connections to each fragment are based on the primary links to the underlying county and a local link between fragments.

In this case Monroe starts with three links to Wayne, Wastenaw, and Lenawee. The chop creates Monroe/Milan with links to Washtenaw and Monroe/main and Monroe/main with links to Wayne, Lenawee and Monroe/Milan. The CD 6-7 segment only cuts the link between the two Monroes. Even if Monroe were macrochopped the only highway link is through Milan and there wouldn't be a link from Monroe/main to Washtenaw.

The primary link from Calhoun to Kalamazoo is along I-94, which enters Kzoo at Charleston twp. The fragment that has Charleston twp has the link. If Kzoo was macrochopped then there would be a link from Calhoun to Ross twp, but not in this case. There's always a local link between fragments within a county, so that link would exist whether the chop was Ross or Charleston+Galesburg. But with a Ross chop, the link to Calhoun would remain with Kzoo/main and it would be severed. It goes back to CoI and priority among links.

I did pose the idea that any highway link might be used for the quasicounties, but that opens up other issues that I discussed at greater length for the IL maps. I think it may be enough to penalize the plan for the small chop and not also erosity.

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This has been noted by others as well. It is primarily due to the fact that the external boundary of the state doesn't count so long districts on the perimeter fare ok. One could count the perimeter, but all plans have it in common and the meaning of links to other states isn't well defined (think of lakes vs land in MI). The other reason is the effect of the macrochop to discourage large chops or place them carefully if one must have them. If you look at my analysis of Kent chops at the beginning of the thread, you'll see why I am motivated to use them.

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As I responded to Torie, I can be persuaded to go in that direction, but then the inequality score should have the same weight in decision making as chop and erosity scoes.

[muon2]

Huh, I wonder how this split of 6/7 would fare:



There are 16,067 people in the CD-7 portion of Jackson, which I guess helps because it's not a macro chop anymore?  

Also, not having a 7/8 border, or the line right along Jackson City (since you get penalized for having lines right along small cities/boroughs, even when the line is reasonably straight) should help with chop counts in comparison to my first map.

It would fare much better. The one chop creates just two quasicounties (see answers above). The erosity of the 6/7 segment is down to 4: Branch-St Joseph, Branch-Calhoun, Hillsdale-Calhoun, and Jackson/Brooklyn-Jackson/main. If microchops give no benefit, then this would be superior to any version using the strips.

edit: I just noticed that US 127 goes right down the township line as it crosses from Jackson to Lenawee, which means it could go to either (or both) fragments. Even if that raises erosity to 5 it's still less erose than the other versions.

[Torie]

Thanks for all the extra info, but I'm going nuts trying to duplicate the Torie A map. The districts outside of Chicago should be straightforward, and I've even gone to a spreadsheet to add counties and townships, but I'm not getting things to add up. Here's the comparison for CDs 10-18.

CD	Torie	muon2
10	+2608	+2746
11	-2529	-2529
12	+3021	+3021
13	+149	-3116
14	-3104	+161
15	-3387	-3387
16	+872	+872
17	+77	+75
18	+1190	+1796

I added the three whole counties and four townships for CD 10+11 and my numbers match the Census, so I suspect you have a stray small precinct missing in your CD 10. Our totals for CD 13+14 are the same and I've double checked my township chops, so I suspect you have a microchop lurking in either Henry or LaSalle counties (both have small-sized precincts right on the county line). If my suspicion is correct you can rid that plan of both the invisible microchop and the Mercer chop. CD 17 is just weird since you have 2 extra people, but I added all the counties by hand and still get +75. CD 18 is even weirder since it's a fairly large discrepancy, and I've added all my counties by hand to check my map. Could there be a precinct (like from 7 with a similar color) grabbing something in 18?

You may want to run the DRA contiguity check on your plans. It may not matter as much on A, but as I get to your more finely tuned plans, I suspect it will become relevant.

EDIT: I think I will have an easier time assessing IL plans if there are separate screenshots for the north and south halves of Chicago/Cook with town lines on. The resolution is so poor otherwise, I can't make out where some chop lines go.

Sorry I was so sloppy. Hopefully these puppies prove better scrubbed.

[Torie]

Here's a post from the earlier thread on MI chops (linked in the OP) that touches on issues in train's map. The first map shows some arrangements using the same CD 2, 3, and 8 as in train's map. The macrochop of Jackson is avoided using east-west strips. The macrochop of Saginaw is avoided by linking Bay to the thumb as train was perhaps thinking.

The second map answers train's query about erosity between CD 1 and CD 4. In train's plan the segment between those two has an erosity of 10 and CD 1 has a deviation of -530. In the second map below the segment has an erosity of 9 and CD 1 has a deviation of only -49. It would be interesting to see if microchops could do better than that.

Here are two revised regional plans that could represent improvements. The first is an improvement of my original 8 region plan. It shifts Sanilac and Lapeer and a couple other areas up north. Lapeer is shifted to improve compactness. The average deviation is 0.951% which should equate to a shift of 3.80%. I can get that down to 0.896% (3.58% shift) by readjusting the boundary of the northern district producing a less compact shape for the red region.



In this second plan I have made some adjustments to jimrtex's most recent regional plan. The erose shape of the Grand Rapids region largely disappears when it is split into two CDs. The average deviation is 1.007% which converts to a 4.03% shift.

These regions chop multi county UCC's.

[traininthedistance]

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As I responded to Torie, I can be persuaded to go in that direction, but then the inequality score should have the same weight in decision making as chop and erosity scoes.

I've always tended to have a lower tolerance for inequality than folks like jimrtex, so that would certainly get my vote.  The three-pronged Pareto test you mentioned seems at first blush to be an approach I'd strongly approve of.

Thanks for all the other explanations; think I've got it straight now (well, I still need to take a closer look at Illinois regarding the Kalamazoo point, but that's a minor point and I trust I can figure it out without any more help).

...

Taking all these tweaks and suggestions into account... here's Draft 2, new and improved:

MI train 2015A2








You'll note that I also found a super-low-inequality configuration for 1 and 4 (not necessarily the lowest-erosity, mind, but lower than what I had before), and shuffled a precinct or two in Detroit to lower inequality between 13 and 14.  I suspect that one can lower inequality in Oakland at the expense of erosity, but this is enough maps for today.  Alternate Oaklands and 1/4 borders might be in the offing for tomorrow, though.

[Torie]

Since a 0.5% variance is legal, in my view the "elbow room" afforded thereby should be used to reduce chops and erosity, including micro-chops. Thus I strongly dissent using it as a factor, except as a tie breaker. Such small population variations really do not raise any material public policy issue in my mind, except if done to make worse maps, rather than better perhaps.  And even then, competitiveness/reflection of state partisan balances, should be used as a tie breaker first (relegating population inequality to being only in play if maps are tied first on chops and erosity, and then further tied on political balance), as I am sure Train would agree.

I know Mike disagrees, but I tend to think counting microchops as a half point penalty (at least for counties), and not having it affect the erosity score, might make for better maps, and is more straight forward and easier to apply than the highway regime, that is a bear. I think this issue needs more map examples to see the real impact on maps, and whether the Muon2 approach is really worth such complexity, because it does produce better maps, and serves to discourage microchops adequately vis a vis no county chops at all. I think I do favor tentatively the quasi county approach for erosity counts for I-chops.  For macro-chops, I am concerned the penalty might be excessive if suddenly all the subdivisions get tested for highway chops. On the other hand, some incentive is needed to make macrochops clean ones, and just the quasi county concept is probably not enough, at least for densely populated areas.

Putting aside the impact of macro-chops on subunits, in all events regarding chops of subunits, 1) there should be but one chop, 2) an I-chop should count as a half point penalty, and 3) a micro-chop of a subunit should be a tie breaker, applied first, prior to reaching the further tie breakers of political balance/competitiveness, and then population equality. That is my sense of it. The public does not like subunit chops. If this metric is applied, the variation below of my Plan F would get a higher score, because the chop of Dundee is reduced to a micro-chop.