Chops and Erosity - Great Lakes Style

[traininthedistance]

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'd have to think on it some more; I admit to some frisson of satisfaction when I can get those deviances pretty low, and 0.5% isn't that low to my eyes, but I'm open to being convinced that it should be strictly secondary to those other factors.

Anyway, I'm an idiot and there's a strictly better 1/4 anyway, both on erosity and inequality:

MI train 2015A3


1 is +428, 4 is +155.

Now I'm done for the day.

[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.

These regions chop multi county UCC's.

How so? Detroit (6), GR (2) and Lansing (1) are maintained here. The maps are from the thread where the concept of UCCs were developed.

[Torie]

That green county to the north (Sanilac?) is in the Detroit UCC? If so, that's weird.

[muon2]

That green county to the north (Sanilac?) is in the Detroit UCC? If so, that's weird.

No it's not in the UCC, but it was grouped with Detroit to add the needed population. The Detroit UCC by itself is short of 6 CDs (5.96). You can deal with it by chopping into a county like Lapeer, or by adding a whole county like Sanilac and chopping away from that. The group with Sanilac is closer to 6 than the group without, so if one is trying to minimize total chop size for the entire map, as was the case in that exercise, the Sanilac group works better.

[Torie]

That green county to the north (Sanilac?) is in the Detroit UCC? If so, that's weird.

No it's not in the UCC, but it was grouped with Detroit to add the needed population. The Detroit UCC by itself is short of 6 CDs (5.96). You can deal with it by chopping into a county like Lapeer, or by adding a whole county like Sanilac and chopping away from that. The group with Sanilac is closer to 6 than the group without, so if one is trying to minimize total chop size for the entire map, as was the case in that exercise, the Sanilac group works better.

As you know, I am less interested in chop size, subject to the metrics as to which we agree to a fair extent, and more interested in what is pleasing to the eye. Jutting that far north, unless perhaps it scores a micro-chop, is not something that I would incentivize. I know you depreciate my "artistic" eye, but I am reasonably confident, the public shares it perhaps more than you do, at least where it does not eliminate or reduce to micro-chops, the prevalence of chops - both counties, and subunits. I was amazed how sensitive gerrymanderers were to subunit chops. I suspect part of it, is that it makes ballot preparation, far more inconvenient, when local elections are held simultaneously with federal elections. If local elections are held in odd years (as in NY), it is less of an issue.

I am sure that you can easily guess which of my Illinois plans I like the best, right?

[Torie]

The PVI-08 for MI is D+4.7, so the expected delegation is 8.3D to 5.7R and the difference is 2.6 which rounds to 3. The political ratings for the districts are CD 1: r, CD 2: d, CD 3: R, CD 4: e, CD 5: D, CD 6: e, CD 7: D, CD 8: d, CD 9: d, CD 10: r, CD 11: R, CD 12: d, CD 13: D, CD 14: D. That's 2R, 2r, 2e, 4d, 4D (UC for uncompetitive, lc for competitive).

SKEW: 1 ( 8[D+d] - 4[R+r] - 3[state] )
POLARIZATION: 18 ( 6[r+d] + 2*6[R+D] )

The population range is +2887 - (-2555) = 5442. This is between 4801 and 5600.
INEQUALITY: 10


How does a PVI of 4.7 translate into 8.3 to 5.7 again?

What do D versus d versus e mean exactly? I see that you go the "halvies" route for the polarization formula (by doubling D and R), but scorn it for chops.

For equality, perhaps rather than take the extremes, one might add all of the population deviations, and then divide by the number of CD's to get a score. That way one will be incentivized for every CD to get the range down, even if one is stuck with relatively extreme numbers in two CD's given other constraints. I tried to equalize where I could without causing a chop in my Illinois maps.

In my Illinois maps, is the Chicago UCC deemed "macro-chopped" if Boone is not in it at all (a whole county chop, and where it is in it, say in my plan F, does IL-12 cause a Macro-chop, or does a macrochop only occur where there is a chop into a UCC, rather than a chop out?  I think you said my MI map macro-chopped the Detroit UCC, when there was only a chop out into Lapeer, which I find confusing.

I wonder how my Michigan map scores vis a vis Trains, using my cleaned up Oakland County lines, and Muon2's Orchard Lake fix.

[muon2]

The PVI-08 for MI is D+4.7, so the expected delegation is 8.3D to 5.7R and the difference is 2.6 which rounds to 3. The political ratings for the districts are CD 1: r, CD 2: d, CD 3: R, CD 4: e, CD 5: D, CD 6: e, CD 7: D, CD 8: d, CD 9: d, CD 10: r, CD 11: R, CD 12: d, CD 13: D, CD 14: D. That's 2R, 2r, 2e, 4d, 4D (UC for uncompetitive, lc for competitive).

SKEW: 1 ( 8[D+d] - 4[R+r] - 3[state] )
POLARIZATION: 18 ( 6[r+d] + 2*6[R+D] )

The population range is +2887 - (-2555) = 5442. This is between 4801 and 5600.
INEQUALITY: 10


How does a PVI of 4.7 translate into 8.3 to 5.7 again?

What do D versus d versus e mean exactly? I see that you go the "halvies" route for the polarization formula (by doubling D and R), but scorn it for chops.

For equality, perhaps rather than take the extremes, one might add all of the population deviations, and then divide by the number of CD's to get a score. That way one will be incentivized for every CD to get the range down, even if one is stuck with relatively extreme numbers in two CD's given other constraints. I tried to equalize where I could without causing a chop in my Illinois maps.

I wonder how my Michigan map scores vis a vis Trains, using my cleaned up Oakland County lines, and Muon2's Orchard Lake fix.

The definitions and formulas were spelled out for the VA commission, so I'll just link it.

I can use either the average deviation or the range, it's just a questions of making the appropriate graph and there are states that look at both measures. SCOTUS has generally considered the range when looking at population equality choosing to address the greatest discrepancy between districts, so I defer to them. I would note that if one uses the average deviation, it invites creating an outlier district while balancing it with a bunch of districts close to the quota.

I was hoping you would ask about your MI. If you could gather the plan and amendments in one post I'll tackle it.

[Torie]

MI Torie 2015A

[Torie]

The PVI-08 for MI is D+4.7, so the expected delegation is 8.3D to 5.7R and the difference is 2.6 which rounds to 3. The political ratings for the districts are CD 1: r, CD 2: d, CD 3: R, CD 4: e, CD 5: D, CD 6: e, CD 7: D, CD 8: d, CD 9: d, CD 10: r, CD 11: R, CD 12: d, CD 13: D, CD 14: D. That's 2R, 2r, 2e, 4d, 4D (UC for uncompetitive, lc for competitive).

SKEW: 1 ( 8[D+d] - 4[R+r] - 3[state] )
POLARIZATION: 18 ( 6[r+d] + 2*6[R+D] )

The population range is +2887 - (-2555) = 5442. This is between 4801 and 5600.
INEQUALITY: 10


How does a PVI of 4.7 translate into 8.3 to 5.7 again?

What do D versus d versus e mean exactly? I see that you go the "halvies" route for the polarization formula (by doubling D and R), but scorn it for chops.

For equality, perhaps rather than take the extremes, one might add all of the population deviations, and then divide by the number of CD's to get a score. That way one will be incentivized for every CD to get the range down, even if one is stuck with relatively extreme numbers in two CD's given other constraints. I tried to equalize where I could without causing a chop in my Illinois maps.

I wonder how my Michigan map scores vis a vis Trains, using my cleaned up Oakland County lines, and Muon2's Orchard Lake fix.

The definitions and formulas were spelled out for the VA commission, so I'll just link it.

I can use either the average deviation or the range, it's just a questions of making the appropriate graph and there are states that look at both measures. SCOTUS has generally considered the range when looking at population equality choosing to address the greatest discrepancy between districts, so I defer to them. I would note that if one uses the average deviation, it invites creating an outlier district while balancing it with a bunch of districts close to the quota.

I was hoping you would ask about your MI. If you could gather the plan and amendments in one post I'll tackle it.

"Item 4: SKEW measures the partisan fairness of a plan. Find the PVI for the state as a fraction (or divide the percent by 100) and multiply that by 4 times the number of districts. Count 0 for each highly competitive district, +1 for each competitive or uncompetitive Democratic district, and -1 for each competitive or uncompetitive Republican district. Take the total for all districts in the state and subtract the expected state delegation difference (0 for VA). Express a negative number as a positive number in favor of the Republicans. That positive number is the SKEW score, and lower numbers are closer to the ideal partisan fairness."

OK, it works, but only a math geek could understand the mechanics. It just won't work for lawyers. Here is what lawyers want (including in particular an example, where the math is walked through step by step, with numbers plugged in rather than x's and y's and such).


Item 4: SKEW measures the partisan fairness of a plan. Take the PVI percentage for the state, and multiply that percentage by 2, and add 50%. That product of that percentage sum and the number of districts in the state, less the balance of the remaining districts in the state, rounded to the nearest whole number, is the difference in the number of districts that the party that the PVI favors (“Majority Party”) would be expected to hold as compared to other parties (“Expected Majority Party Delegation Difference”). Count 0 for each highly competitive district, +1 for each competitive or uncompetitive Majority Party district, and -1 for each competitive or uncompetitive non Majority Party district ("Partisan District(s)"). Subtract the sum of such Partisan District numbers from the Expected Majority Party Delegation Difference. Express a negative number as a positive number. That positive number is the SKEW score, and lower numbers are closer to the ideal partisan fairness.

As an example of the application of the above formula, if the PVI of a state were 4.7% in favor of the Majority Party, and a state had a delegation of 14, with 7 Majority Party Partisan Districts, 6 non Majority Party Partisan Districts, and one highly competitive district, the Expected Majority Party Delegation Difference would be 3  (8.4 Majority Party districts ((4.7% x 2) + 50%) x 14 = (9.4% + 50%) x 14 = 59.4% x 14 = 8.316, less 5.684 non Majority Party districts (8.316-5.684 = 2.632), rounded to the nearest whole number = 3. If the state plan had 7 Partisan District Majority Party districts, 6 Partisan District non Majority Party districts, and 1 highly competitive district, its SKEW would be 2 (3 – (7-6 – (0 x 1)) = 3 - 1 = 2).

I guestion treating non competitive and competitive CD's the same (they aren't, which is why we distinguish between the two). I would count a half point of something for competitive districts, rather than a whole point. Your formula gives no bonus at all for putting CD's in play. Not good in my view.

[Torie]

Off topic here, but what does the dictum about minorities being able to elect candidates of their choice really mean? Suppose in a majority Asian CD, a majority of Asians vote for white candidates? If a CD has less than a majority minority VAP score, it's OK if a minority candidate is still elected. But suppose that enough vote for the other party, so that a minority candidate is not elected? It seems then you have to up to 50% minority VAP (or CVAP). Suppose a majority of Asians vote for white candidates? Do you focus on the color of the candidates, or partisan preferences? If most Asians are Democrats, but vote for white Democrats in large numbers, how can you tell what their preference is? It seems that the concept folks well, where you have minority block voting for their own race, but as you erode down from there, things tend to fall apart, and their is confusion/conflation between the two metrics of partisan preference and a candidate's race.

[muon2]

The PVI-08 for MI is D+4.7, so the expected delegation is 8.3D to 5.7R and the difference is 2.6 which rounds to 3. The political ratings for the districts are CD 1: r, CD 2: d, CD 3: R, CD 4: e, CD 5: D, CD 6: e, CD 7: D, CD 8: d, CD 9: d, CD 10: r, CD 11: R, CD 12: d, CD 13: D, CD 14: D. That's 2R, 2r, 2e, 4d, 4D (UC for uncompetitive, lc for competitive).

SKEW: 1 ( 8[D+d] - 4[R+r] - 3[state] )
POLARIZATION: 18 ( 6[r+d] + 2*6[R+D] )

The population range is +2887 - (-2555) = 5442. This is between 4801 and 5600.
INEQUALITY: 10


How does a PVI of 4.7 translate into 8.3 to 5.7 again?

What do D versus d versus e mean exactly? I see that you go the "halvies" route for the polarization formula (by doubling D and R), but scorn it for chops.

For equality, perhaps rather than take the extremes, one might add all of the population deviations, and then divide by the number of CD's to get a score. That way one will be incentivized for every CD to get the range down, even if one is stuck with relatively extreme numbers in two CD's given other constraints. I tried to equalize where I could without causing a chop in my Illinois maps.

I wonder how my Michigan map scores vis a vis Trains, using my cleaned up Oakland County lines, and Muon2's Orchard Lake fix.

The definitions and formulas were spelled out for the VA commission, so I'll just link it.

I can use either the average deviation or the range, it's just a questions of making the appropriate graph and there are states that look at both measures. SCOTUS has generally considered the range when looking at population equality choosing to address the greatest discrepancy between districts, so I defer to them. I would note that if one uses the average deviation, it invites creating an outlier district while balancing it with a bunch of districts close to the quota.

I was hoping you would ask about your MI. If you could gather the plan and amendments in one post I'll tackle it.

"Item 4: SKEW measures the partisan fairness of a plan. Find the PVI for the state as a fraction (or divide the percent by 100) and multiply that by 4 times the number of districts. Count 0 for each highly competitive district, +1 for each competitive or uncompetitive Democratic district, and -1 for each competitive or uncompetitive Republican district. Take the total for all districts in the state and subtract the expected state delegation difference (0 for VA). Express a negative number as a positive number in favor of the Republicans. That positive number is the SKEW score, and lower numbers are closer to the ideal partisan fairness."

OK, it works, but only a math geek could understand the mechanics. It just won't work for lawyers. Here is what lawyers want (including in particular an example, where the math is walked through step by step, with numbers plugged in rather than x's and y's and such).


Item 4: SKEW measures the partisan fairness of a plan. Take the PVI percentage for the state, and multiply that percentage by 2, and add 50%. That product of that percentage sum and the number of districts in the state, rounded to the nearest whole figure, less the balance of the remaining districts in the state, is the difference in the number of districts that the party that the PVI favors (“Majority Party”) would be expected to hold as compared to other parties (“Expected Majority Party Delegation Difference”). Count 0 for each highly competitive district, +1 for each competitive or uncompetitive Majority Party district, and -1 for each competitive or uncompetitive non Majority Party district ("Partisan District(s)"). Subtract the sum of such Partisan District numbers from the Expected Majority Party Delegation Difference. Express a negative number as a positive number. That positive number is the SKEW score, and lower numbers are closer to the ideal partisan fairness.

As an example of the application of the above formula, if the PVI of a state were 4.7% in favor of the Majority Party, and a state had a delegation of 14, with 7 Majority Party Partisan Districts, 6 non Majority Party Partisan Districts, and one highly competitive district, the Expected Majority Party Delegation Difference would be 2  (8.4 Majority Party districts ((4.7% x 2) + 50%) x 14 = (9.4% + 50%) x 14 = 59.4% x 14 = 8.316, rounded to the nearest whole number = 8 ), less 6 non Majority Party districts (14 - 8 = 6). If the state plan had 7 Partisan District Majority Party districts, 6 Partisan District non Majority Party districts, and 1 highly competitive district, its SKEW would be 1 (2 – (7-6 – (0 x 1)) = 2 - 1 = 1).

I guestion treating non competitive and competitive CD's the same (they aren't, which is why we distinguish between the two). I would count a half point of something for competitive districts, rather than a whole point. Your formula gives no bonus at all for putting CD's in play. Not good in my view.

Interesting. The lawyers I work with shy away from examples entirely in writing, but not in discussion. They want text that is concise and unambiguous, even though that often makes for dense reading. Examples are for discussions to guide the writing of the legal text and for hearings to explain that text. Similarly, the rules are not the same as the textbook for the student, and I've done the textbook thing on all these measures multiple times on threads here. I'm not happy to do that every time I use the formula, I just don't have the time.

Note that since the erosity measure is relatively fresh with the advent of macrochops, I do think a longer exposition is in order. I doubt I'll feel that way a year from now if the metric hasn't changed. Even so, I will always be willing to justify my result and recognize an error in my calculation if present.

I've run many models for scoring political measures. If districts that are not toss ups are treated differently based on their competitiveness its very hard to get a meaningful SKEW. Competitive districts are rewarded in the POLARIZATION measure. I invite you to try rewarding competitive district in skew without favoring one party due to the geographic concentration (or lack) of partisans.

Edit: I don't think you followed my example in the link for the expected delegation, or the resulting difference in your example above. The rounding comes at the very end, not in the middle of the calculation. My linked example is for VA. For MI, 0.047*4*14=2.6 which rounds to 3 for the expected delegation difference, not 2.

[muon2]

Off topic here, but what does the dictum about minorities being able to elect candidates of their choice really mean? Suppose in a majority Asian CD, a majority of Asians vote for white candidates? If a CD has less than a majority minority VAP score, it's OK if a minority candidate is still elected. But suppose that enough vote for the other party, so that a minority candidate is not elected? It seems then you have to up to 50% minority VAP (or CVAP). Suppose a majority of Asians vote for white candidates? Do you focus on the color of the candidates, or partisan preferences? If most Asians are Democrats, but vote for white Democrats in large numbers, how can you tell what their preference is? It seems that the concept folks well, where you have minority block voting for their own race, but as you erode down from there, things tend to fall apart, and their is confusion/conflation between the two metrics of partisan preference and a candidate's race.

You are right and one can go into a lengthy thread on this subject alone. Suffice it to say there are a lot of experts who are paid well to tease out the answers to these questions. Google ecological inference to get an idea of some of the research and methods.

[Torie]

I realized the error, and I corrected the text to get the rounding done in the correct place. and revised the example, and actually did that prior to your posting your comment. You must have prepared your answer about an hour before you posted it.

I almost always put examples into contracts, and write them the way I did for the rule. I think it is good a good practice to follow, and if you want to communicate with others, in my view it is well worth the time (I often have great difficulty understanding what you and Jimtex are saying, and I suspect most do around here when it comes to very abstract or mathematical concepts). That way the reader can follow the logic easily rather than put stuff on a spreadsheet to see what is really going on, which in this case is to get the partisan ratio with a change rate that is twice that of the PVI change rate,  and then take the difference as the state partisan balance translated into CD shares, and then round.  That 4 times stuff just doesn't tie to anything readily recognizable.

I assume that the twice rate is tied to something empirically or mathematically. It does seem about right as an empirical matter, based on my anecdotal impressions.

I suppose if skew and polarization are added together, perhaps that is enough to reward competitive CD's. My Michigan map I think has a skew of 1 (it has two toss up CD's while the example had one, and otherwise the numbers match.

[muon2]

MI Torie 2015A

Political leaning by district (in order): r, r, r, e, D, e, D, d, d, r, r, d, D, D; 0R, 5r, 2e, 3d, 4D.
SKEW: 1 (R)
POLARIZATION: 16

Population range 4990, average deviation 1257
INEQUALITY: 10 (range), 9 (ave dev)

UCC scores
Detroit cover 6, pack 5; no penalties
Grand Rapids cover 2, pack 0; 1 for pack
Lansing cover 2, pack 0; 1 for cover
Saginaw, Jackson; 2 for single county
Total UCC chops 7

County chops
Kent 1; macrochop
Clinton 1; macrochop
Jackson 1
Saginaw 1
Lapeer 1
Macomb 1; macrochop
Oakland 2; macrochop
Wayne 2; macrochop
Total county chops 10

Local chops
Detroit 1;
Detroit neighborhood; 1
Total local chops 2

CHOP: 12 raw (UC:13, UP:14, US:16)

Erosity by segment
seg 1/2: 3
seg 1/4: 7
seg 2/3: 9 (3 on county line, 6 internal Kent)
seg 2/4: 7 (2 on Kent county line)
seg 2/6: 1
seg 3/4: 2
seg 3/5: 1
seg 3/6: 3
seg 3/8: 8 (3 without the Clinton macrochop)
seg 4/5: 3
seg 5/8: 2 (1 without the Clinton macrochop)
seg 5/10: 3
seg 5/11: 3
seg 6/7: 1
seg 6/8: 1
seg 7/8: 3
seg 7/11: 1
seg 7/12: 6
seg 8/11: 1
seg 9/10: 6
seg 9/11: 10
seg 9/13: 6
seg 11/12: 1
seg 12/13: 13
seg 13/14: 9 (CD 13 in neighborhood 10 has two discontiguous pieces which adds one to erosity)

EROSITY: 108

This could drop to 102 if the Clinton macrochop became just a chop. The change of Saginaw from train's map, eliminating the macrochop, reduced that segment 4/5 from 12 to 3. The erosity within the Detroit UCC dropped from 50 to 43 compared to train's map. The chop went up, so both plans would survive a Pareto test.

[muon2]

I realized the error, and I corrected the text to get the rounding done in the correct place. and revised the example, and actually did that prior to your posting your comment. You must have prepared your answer about an hour before you posted it.

I almost always put examples into contracts, and write them the way I did for the rule. I think it is good a good practice to follow, and if you want to communicate with others, in my view it is well worth the time (I often have great difficulty understanding what you and Jimtex are saying, and I suspect most do around here when it comes to very abstract or mathematical concepts). That way the reader can follow the logic easily rather than put stuff on a spreadsheet to see what is really going on, which in this case is to get the partisan ratio with a change rate that is twice that of the PVI change rate,  and then take the difference as the state partisan balance translated into CD shares, and then round.  That 4 times stuff just doesn't tie to anything readily recognizable.

I assume that the twice rate is tied to something empirically or mathematically. It does seem about right as an empirical matter, based on my anecdotal impressions.

I suppose if skew and polarization are added together, perhaps that is enough to reward competitive CD's. My Michigan map I think has a skew of 1 (it has two toss up CD's while the example had one, and otherwise the numbers match.

It seems we are noting the distinction between contracts and statutes/ordinances. Statutes are generally devoid of examples.

The definition for the expected delegation in the link walks through the origin of the factor of 4 pretty carefully. The link has the citation to a study justifying the twice rate, and the definition even has examples. I've reread it, and I'm not sure why it was insufficient. I do provide links, I just don't like to repeat myself when a link will do. Such is the hypertexted world we live in.

[Torie]

How do I get 5 Detroit UCC chops, plus additional chops in individual counties again within the UCC? Is that due to somehow there being deemed a macro-chop into the UCC of MI-10, even though the only chop is an I-chop out into Lapeer? (Yes, that appears to be the case, alas.) In addition to that being problematic as a macrochop (perhaps a macrochop should be in should be when the chop is from a CD that wholly contains the adjacent county), that makes the penalty for a macrochop just massive, with respect to multi-county UCC's. I think I would relegate the macrochop concept to affecting just the erosity score, at least tentatively that is my view. So where we disagree, at least for the moment, is that I want some chop penalty for microchops, and less of a penalty for macrochops, and think I want a revision of the definition of a macrochop incorporating the concept of encroachments from adjacent counties wholly contained in another CD (with no traveling chops of course).

 The notion of jutting MI-08 out one more township making more ragged lines, and more population inequality, and getting rewarded for it, is well - troubling. The fix for this cliff mechanism would be to define macrochop as being the sum of 5% and whatever population play is available, so we don't have the incentive to "uglify" maps, and increase population inequality to boot potentially.



I assume if I knew the hood lines exactly, I could get rid of the discontiguous chop (did not know that was penalized, but it probably should be).

Regarding political balance, what are the odds of a r or d CD going for the party holding the edge? I ask, because if it is less than 80%, the odds are the Democrats would win more seats with my map than Train's map. And yet, my skew per Mike's system is one for the Pubs, and Train's is one for the Dems. That is troubling too. And what are the odds of the party holding the edge winning a 2 PVI CD as opposed to a 5 PVI CD? Surely the percentage odds vary considerably. I suspect we need more granularity here.



Sorry Mike we disagree on so much, but that seems to be just the way it is - at least for the moment. I can't seem to get you to change your mind on much.

[Torie]

I realized the error, and I corrected the text to get the rounding done in the correct place. and revised the example, and actually did that prior to your posting your comment. You must have prepared your answer about an hour before you posted it.

I almost always put examples into contracts, and write them the way I did for the rule. I think it is good a good practice to follow, and if you want to communicate with others, in my view it is well worth the time (I often have great difficulty understanding what you and Jimtex are saying, and I suspect most do around here when it comes to very abstract or mathematical concepts). That way the reader can follow the logic easily rather than put stuff on a spreadsheet to see what is really going on, which in this case is to get the partisan ratio with a change rate that is twice that of the PVI change rate,  and then take the difference as the state partisan balance translated into CD shares, and then round.  That 4 times stuff just doesn't tie to anything readily recognizable.

I assume that the twice rate is tied to something empirically or mathematically. It does seem about right as an empirical matter, based on my anecdotal impressions.

I suppose if skew and polarization are added together, perhaps that is enough to reward competitive CD's. My Michigan map I think has a skew of 1 (it has two toss up CD's while the example had one, and otherwise the numbers match.

It seems we are noting the distinction between contracts and statutes/ordinances. Statutes are generally devoid of examples.

The definition for the expected delegation in the link walks through the origin of the factor of 4 pretty carefully. The link has the citation to a study justifying the twice rate, and the definition even has examples. I've reread it, and I'm not sure why it was insufficient. I do provide links, I just don't like to repeat myself when a link will do. Such is the hypertexted world we live in.

Oh, I don't mind using a link, but the link did not have an explanation of the 4 matter (at least not in the linked post), and I like the statute itself to be intuitive in any event as to what is actually going on. I said the twice rate seemed about right, but the link didn't get into that either. Whatever. The IRS regulations have tons of examples.  This stuff is even worse to wade through than the IRS code. Put the examples into something called "regulations" if that floats one's boat. Statutes do use lots of defined terms typically.

[muon2]

How do I get 5 Detroit UCC chops, plus additional chops in individual counties again within the UCC? Is that due to somehow there being deemed a macro-chop into the UCC of MI-10, even though the only chop is an I-chop out into Lapeer? (Yes, that appears to be the case, alas.) In addition to that being problematic as a macrochop, that makes the penalty for a macrochop just massive, particularly with multi-county UCC's. I think I would relegate the macrochop concept to affecting just the erosity score, at least tentatively that is my view. So where we disagree, at least for the moment, is that I want some chop penalty for microchops, and less of a penalty for macrochops.

There's no penalty for macrochops in the way you describe here. No map of MI can have less than 5 chops of the Detroit UCC, so if you have 5 you are doing as well as you can. Similarly all plans must have at least one chop of the GR UCC. I could subtract 6 from everyone's score and we wouldn't have learned anything about the respective plans.

Perhaps you were expecting that I would count just the excess above the minimum required, since that was how UCC penalties were first proposed in 2013. I want to have a consistent measure of chops at all levels - UCC, county, and muni. If I only count the excess chops then your Wayne and Macomb would be 0 chops and your Oakland would be 1 chop by the same logic. That is artificial and frankly hard to execute for the scorer, it's much easier just to look at any unit regardless of its classification and count the number of chops in a unit.

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You are never going to let up on me for the fact that Clinton happens to have a clean division that is just barely over 5% of the quota. All systems have edge effects when brackets are defined, and your fix sounds much more complicated than the problem. My threshold may be arbitrary, but brackets always are to some degree. What I don't want is something that I can't score - objectivity trumps the eyeball test for me on close calls like your plan.

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The map is towards the start of the thread. I just go off the precinct lines on that map.

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Multiplying by 0.8 (or 0.75 which is the value I gleaned from some 538 data a while ago) is not a statistically accurate way of judging the outcomes. You actually have to generate random distributions and accumulate trials, much like Silver does. What you are saying is that in a blowout wave election, you have a higher floor for the D's than train does. Statistically train's map will elect more Dems over time than yours will and that is what skew should reflect.

As to the granularity, it is my observation from looking that the actual data that we place too much granularity on much that is reported. Given the usual MOEs of polling, it's not very meaningful to talk about increments of 1% between candidates, but we do all the time. Similarly the statistics on the differences between PVI 2 through 5 in that data set weren't so compelling that I could justify them as different categories. I could report some fine granularity score, but it wouldn't be particularly meaningful as a matter of statistics.

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I've spent over two years working on spreadsheets to test models, and then bouncing the ideas off of threads here. In newer areas like erosity, I recognize some open questions that are worth discussion. However, for much of the scoring at this point I need some fairly concrete counterexamples, with a clearly spelled out fix that I can take back and test on the many maps for a dozen states that we have experimented on during these last two years.

[muon2]

I realized the error, and I corrected the text to get the rounding done in the correct place. and revised the example, and actually did that prior to your posting your comment. You must have prepared your answer about an hour before you posted it.

I almost always put examples into contracts, and write them the way I did for the rule. I think it is good a good practice to follow, and if you want to communicate with others, in my view it is well worth the time (I often have great difficulty understanding what you and Jimtex are saying, and I suspect most do around here when it comes to very abstract or mathematical concepts). That way the reader can follow the logic easily rather than put stuff on a spreadsheet to see what is really going on, which in this case is to get the partisan ratio with a change rate that is twice that of the PVI change rate,  and then take the difference as the state partisan balance translated into CD shares, and then round.  That 4 times stuff just doesn't tie to anything readily recognizable.

I assume that the twice rate is tied to something empirically or mathematically. It does seem about right as an empirical matter, based on my anecdotal impressions.

I suppose if skew and polarization are added together, perhaps that is enough to reward competitive CD's. My Michigan map I think has a skew of 1 (it has two toss up CD's while the example had one, and otherwise the numbers match.

It seems we are noting the distinction between contracts and statutes/ordinances. Statutes are generally devoid of examples.

The definition for the expected delegation in the link walks through the origin of the factor of 4 pretty carefully. The link has the citation to a study justifying the twice rate, and the definition even has examples. I've reread it, and I'm not sure why it was insufficient. I do provide links, I just don't like to repeat myself when a link will do. Such is the hypertexted world we live in.

Oh, I don't mind using a link, but the link did not have an explanation of the 4 matter (at least not in the linked post), and I like the statute itself to be intuitive in any event as to what is actually going on. I said the twice rate seemed about right, but the link didn't get into that either. Whatever. The IRS regulations have tons of examples.  This stuff is even worse to wade through than the IRS code. Put the examples into something called "regulations" if that floats one's boat. Statutes do use lots of defined terms typically.

I guess I'm still troubled at your reaction to this definition.

Definition: The expected delegation from a state with a known PVI is equal to 50%+2*PVI, so for example a D+5 state would be expected to have a delegation of 60% Democrats. Studies (e.g. Goeddert 2014) show that for every 1% shift in the national vote share there is an average shift by 2% in the number of congressional seats. Extending that to individual states, one can predict that in a 50-50 national election, a state delegation should have a Democratic fraction equal to 50% + 2*(state PVI). The percent difference between the Democratic and Republican fractions is then 4*(state PVI). The difference between the Democratic delegation size and the Republican delegation size should be 4*(state PVI/100)*(size of the delegation), where the division by 100 is to remove the percent. Using PVI-08, the expected VA congressional delegation would be 5.4 D to 5.6 R, and the expected delegation difference is -0.2 which rounds to 0.

It starts with an example of how a PVI would be reflected in a delegation.

It cites a source to justify the 2 for 1 increment in delegation to vote share.

It describes the Dem fraction (50%+2*PVI) and the Dem - Pub fractions mathematically. Did you want me to then explicitly say that the Pub fraction is 100%-Dem% and if I subtract Pubs from Dems it's equal to twice the difference from 50% (ie 4*PVI)? Egad, is numeracy that bad on this Forum? Technically that's considered a pre-algebra skill.

It ends with another example applying it to VA.

As a mathematical aside, this would be a typical middle school problem: There are 100 marbles in a bag. Train takes 6 more than half the marbles and leaves the rest for Torie. How many more marbles does train have than Torie?

[Torie]

The "definition" of "expected delegation" is not then used in the definition of skew, is part of the problem. I just read your definition of skew, and did not look further since there was no defined term in it. I appreciate it where 4 came from ultimately, but the idea of the double doubling takes some work. On the marble thing, I would divide 100 by 2, which equals  50, and then add 6 which equals 56, and then subtract 56 from 100, which equals 44. It's a step by step process.  I could even write the algebraic formula. x + y =100.  x = 100/2 + 6 = 56. 56 + y = 100. y = 100 - 56 = 44.  Would I want this junk in a statute? No!

The "definition" of "expected delegation" is not then used in the definition of skew, is part of the problem. I just read your definition of skew, and did not look further since there was no defined term in it. I appreciate it where 4 came from ultimately, but the idea of the double doubling takes some work.

[muon2]

The "definition" of "expected delegation" is not then used in the definition of skew, is part of the problem. I just read your definition of skew, and did not look further since there was no defined term in it. I appreciate it where 4 came from ultimately, but the idea of the double doubling takes some work. On the marble thing, I would divide 100 by 2, which equals  50, and then add 6 which equals 56, and then subtract 56 from 100, which equals 44. It's a step by step process.  I could even write the algebraic formula. x + y =100.  x = 100/2 + 6 = 56. 56 + y = 100. y = 100 - 56 = 44.  Would I find this junk in a statute? No!

The "definition" of "expected delegation" is not then used in the definition of skew, is part of the problem. I just read your definition of skew, and did not look further since there was no defined term in it. I appreciate it where 4 came from ultimately, but the idea of the double doubling takes some work.

Ah I see my shortcoming. I started with the definition of expected delegation, and only at the end did I get to the term expected delegation difference. It's in there, but not bolded at the front as it should be to be used in skew.

For good or ill I can show you many statutes that just give the numeric formula to be used, and even though it might derived from a prior formula in the same section, the statute gives no clue as to their relationship. I've even suggested that such a relationship be made clearer, but the prevailing view is to treat statute like a black box and just do what is there without asking why.

[Torie]

Multiplying by 0.8 (or 0.75 which is the value I gleaned from some 538 data a while ago) is not a statistically accurate way of judging the outcomes. You actually have to generate random distributions and accumulate trials, much like Silver does. What you are saying is that in a blowout wave election, you have a higher floor for the D's than train does. Statistically train's map will elect more Dems over time than yours will and that is what skew should reflect.

Interesting. What would be the expected take of the minority party of competitive seats using "random trials?"

The fix for Clinton is to allow for population play, and not have to use it to get under the threshold. It seems like a good fix to me. Would you address that precise issue for me?

I understand in the case of the MI map, there is no escape from the Detroit UCC penalty, so the issue at least for Train's map and mine is irrelevant. But my concern is more what triggers the macrochop since in other states that might matter, and I certainly would want to penalize an unnecessary macrochop into a multi county UCC, if someone chose to go there in a MI map. Thus I suggested the whole county fix, which perhaps you might wish to address.

Per your research, how much using "random distributions," do the odds vary between a PVI of 2 and 5? Could you be more precise than just saying it's not statistically meaningful?

[muon2]

The fix for Clinton is to allow for population play, and not have to use it to get under the threshold. It seems like a good fix to me. Would you address that precise issue for me?

I don't know what the phrase means, so I can't do anything to systematize it.

[Torie]

The fix for Clinton is to allow for population play, and not have to use it to get under the threshold. It seems like a good fix to me. Would you address that precise issue for me?

I don't know what the phrase means, so I can't do anything to systematize it.

It means the difference between the population of a CD and the population of that CD if it were 0.5% off from its "perfect" allocable share of the population. Where that difference is enough to jiggle the lines in a county to get rid of the macro-chop, then it's not a macro-chop, and you need not jiggle the lines, as we did in Clinton above. That leaves out the issue of generating microchops elsewhere to get even more "play," which is one reason why micro-chops need to be penalized out of the box, to shut down that game (which game might well still be worth playing even with some penalty if the macrochop of a multi-county UCC, or even a single county UCC, is right on the cusp (of however one defines a macro-chop, which definitional issue is another issue that I raised above)).

I might add that nobody in their right mind would ever consider the line in Clinton to get rid of the macro-chop to be superior to the clean, less erose looking, line that I drew, with better population equality to boot. Sometimes, such a sad outcome in order to have applicable metrics, might be unavoidable, but at least one can try to mitigate that syndrome.

In my view, your system really incentives game playing when matters are on the cusp, which I consider a major problem. In drawing maps per your system, I have to spend a lot of time game playing. The sad thing is that I will never be as good at is as you are, no matter how hard I try. You have a gift there, you master gamesman you.

[muon2]

I understand in the case of the MI map, there is no escape from the Detroit UCC penalty, so the issue at least for Train's map and mine is irrelevant. But my concern is more what triggers the macrochop since in other states that might matter, and I certainly would want to penalize an unnecessary macrochop into a multi county UCC, if someone chose to go there in a MI map. Thus I suggested the whole county fix, which perhaps you might wish to address.  

The trigger for a macrochop can either be due to a chop into a selected list of counties (like the ones in UCCs) or it can be due to a population trigger and applied to any county. I'm wary of the first method because I think that will lead to pressure to place chops in counties not on the list. I think we agree that is not a desirable feature.

I didn't follow that there was a specific fix proposed. If it is something that can be made systematic it can be investigated. I still haven't quite seen the problem that would be fixed either.