Ohio Redistricting Contest

[jimrtex]

I've shared a couple of congressional plans to see what some possibilities might be. One thing I learned in the legislative phase was that fairness scores are very important. The electoral disproportionality has a weight of 4 per point of percentage difference. A two percent shift in electoral result between weak and strong in one district changes the score by about 4 or 5 scoring points and from even to weak by 9 points. An equivalent shift in the electoral result in a district would at most change the score by 1 point for competitiveness.

The geographic factors are also weaker than the fairness factor. An additional county split creates two fragments which is a 2 point penalty, but that same split could easily shift the fairness score by 4 or 9 points by shifting the category of a single district. Similarly, the compactness is averaged so it takes a net gain of 16% improvement in individual districts to gain 1% on the average which results in 1 point on the score.

With that in mind two shared plans represent two implementations of maximized fairness. Both plans score over 99 out of 100 points on that index. One plan minimizes county splits, and gets the number of splits down to 9. The other plan recognizes the need to have exact equality if no compelling state interest exists for the population deviation. Many more counties have to be split to get equality and this is used to improve the compactness quite a bit, but it still lands about 4 points lower overall than the plan that minimizes splits.

Minimum split plan

Exact equality plan

I was wondering how the weighting of the factors would play out.

So a 2 SR/6 LR/0/7 LD/1 SD plan

would give (3+6)/(3+6+7+1.5) = 51.4% partisan index.

If the 13 lean seats were all within 2.5%, that would be 39 competitiveness.  To balance the Cleveland seat, the two strong Republican seats would probably have to both be non-competitive.

Such a plan is probably feasible but would start straining the compactness and county split scores.   So you give up some competitiveness, while maintaining fairness, and reduce the splits and keep the compactness up?

BTW, there appears to be an error in the compactness scoring, which has a bias against more irregular districts.  I had a 19% district that appears to be a 29% district, while the Wayne County district is 63% rather than 62%.

[jimrtex]

BTW, there appears to be an error in the compactness scoring, which has a bias against more irregular districts.  I had a 19% district that appears to be a 29% district, while the Wayne County district is 63% rather than 62%.

Your comment about the compactness calculation is interesting, as I have had some suspicion, but no definite case to point at. If you haven't already, you should send your findings to the contest, and they'll forward them to the software developers.

I have done so, and they pointed me to the source code.  It appears that when they are calculating the diameter of the minimum spanning circle, they are assuming that the centroid of the convex hull around a district is the center of the minimum spanning circle.

I'm pretty sure that the minimum spanning circle for a district and the minimum spanning circle for a district's convex hull are the same.  And I conjecture that the point furthest from the centroid is on the circumference of the minimum spanning circle, but the center of the minimum spanning circle is not the centroid of the convex hull.

[jimrtex]

I have done so, and they pointed me to the source code.  It appears that when they are calculating the diameter of the minimum spanning circle, they are assuming that the centroid of the convex hull around a district is the center of the minimum spanning circle.

I'm pretty sure that the minimum spanning circle for a district and the minimum spanning circle for a district's convex hull are the same.  And I conjecture that the point furthest from the centroid is on the circumference of the minimum spanning circle, but the center of the minimum spanning circle is not the centroid of the convex hull.

That's an interesting shortcut if true. The center of the convex hull is not generally the same as center of the minimum bounding circle. As an extreme example, consider a half circle. Clearly the minimum bounding circle is the completed whole circle and the compactness is 50%. That bounding circle has a center in the middle of the straight edge of the half circle it bounds. The half circle is a convex shape and its centroid is 2/3pi (about 2/10) of the way in from the edge. That makes for a larger bounding circle.

There is no single solution to the problem, but there are many algorithms that iterate and converge to the solution. I'm surprised that they don't at least do some convergence to a proper minimum.

I think they had the convex hull for other reasons (it is a quick way to check visibility of a district as you pan, and it probably has utility as a first iteration of checking what district is being pointed at, or etc.   District polygons probably have 100s of vertices.

The code had the correct comments.  But they took the centroid, iterated through the points on the convex hull to find the largest distance from the centroid, and said that is the radius of the smallest spanning circle, squared it and multiplied by pi.

Does the Ohio Constitution require that larger cities be placed in as fewest districts as possible?

11.07(B) refers to "such district" in the singular, so each district that can not be formed from whole counties should preferentially be composed of whole townships and cities rather than city wards.   Which would mean that larger cities should be placed in as few districts as possible as long as it is not necessary to split wards.

[jimrtex]

I think they had the convex hull for other reasons (it is a quick way to check visibility of a district as you pan, and it probably has utility as a first iteration of checking what district is being pointed at, or etc.   District polygons probably have 100s of vertices.

The code had the correct comments.  But they took the centroid, iterated through the points on the convex hull to find the largest distance from the centroid, and said that is the radius of the smallest spanning circle, squared it and multiplied by pi.

If they wanted to do a quick approximation, a better technique would have been to take the three points on the convex hull furthest from the centroid, then circumscribe the circle around that triangle. That's a simple geometric construction.

The source code has been updated, but the plans still score the same way.

There are a couple of other compactness measures, so I'm guessing that the people in Ohio asked for Roeck's measure and that was what was entered.

I don't really see any value for a compactness measure for legislative districts.  The most countes possible in a House district is 6.  And use of whole townships and wards limit options within counties.  As a contest measure, it encourages increased population deviation, and splitting of cities.

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I don't think so, at least that's not the way I interpret it. In the current plan the contiguous part of Dayton is split between four HDs. Most of it is in HD 39 and 40, but small parts are in HD 37 and 39. I assume those small fragments are whole wards. Given the 5% tolerance, it shouldn't have been difficult to put Dayton in fewer districts, particularly since Kettering and Huber Heights are split as well.

I would interpret the current map to suggest the following: Once a city must be divided, then any need to keep to its boundaries disappears. Instead the city acts as a collection of wards that remain unbroken.

Using that interpretation I can see HD 39 and 40 splitting Dayton since it is too large for one HD. Then, HD 40 was too small it split Huber Heights with HD 36. HD 37 and 38 split Kettering, but are not counted as splitting Dayton between themselves since Dayton has been effectively reduced to a collection of wards by the original split between HD 39 and 40. That's an important sequence, because otherwise it would appear that HD 37 and 38 share two split units of city government - Kettering and Dayton.

Then again, it could be that the current plan is unconstitutional in Montgomery, and simply went unchallenged.
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You left out Riverside as well.  The wards in Dayton are pretty small (Dayton, Columbus, and Cincinnati all have at-large elections) so the wards have nothing to do with city elections.  Toledo has 24 wards and 7 city council districts.   Only Akron and Columbus use the wards as city council districts).

The townships in the western tier are small, so it would have been easy eliminate the split of Huber City and put all of Dayton into two districts.  I bet that you could get rid of the Kettering Split as well.  The only challenge in 2000 would have been that the average for 5 districts would have been 97.5%, so you could only have a variation of a little less than 3000 either side of the ideal.

I suppose I was reading "preference" as "feasible" to each level in the list of units.

It really isn't possible to create more than one house district in Cleveland without splitting wards, because of the size of the wards.  You can create the district in west Cleveland because the wards are a bit larger and five of them create a district.

In Franklin County, you can just barely create a contiguous district outside Columbus, stretching from the southeast corner to Hilliard City, for some reason Columbus has not annexed to the Pickaway County line.  But that would require splitting 4 townships in order to avoid a 10th "split" of Columbus.

It's quite feasible to place Cincinnati into 3 house districts.  With the enclaves (Norwood, St. Bernard, etc.) it is about 20,000 short of 116,530x3 which can easily be made up.  All of Springfield township fits in the NW Hamilton district.  The north central suburban district is displaced to the east, and then there is a district the full extent of the Clermont line.

[jimrtex]

I agree that the use of compactness is limited due to constitutional constraints, but I found that it did play more of a role for senate districts. In that case It could guide their grouping when not otherwise constrained.

Personally I don't think an average or median score is the best approach for applying compactness. I think a better technique is to count the number of districts that are less compact than some benchmark value. I would use the existing plan median value as that benchmark as it directly encourages improvement on the current plan.

Alternatively one can set two thresholds. One threshold would be like describe above for districts less compact than some median benchmark. A second threshold would define egregious districts that could have a larger penalty.

The problem is that the most "egregious" districts are often due to following political boundaries.  And by scoring them, it leads to a temptation to increase population variance or split city wards.  Once a city ward is divided, does the 5% safe harbor disappear at least for those districts that split the ward, and perhaps for all districts in the city?

These are the districts which are more than 1 SD below my mean of 41%.

Cuyahoga: 4 districts, two drawn in an attempt to use whole wards in Cleveland; one that includes Bratenahl to create better population balance; and one drawn with the objective of excluding Blacks.

Hamilton: 2 districts.  One includes the rat tail of Cincinnati.  If I exclude that ward, my compactness goes from 19% to 37%, but my district is split because that ward continues up into the middle of Cincinnati, and a district that is the full length of the Clermont border.  This is in my plan to place Cincinnati in 3 districts, which means the 4 suburban districts have to be drawn around the outside.

A Medina-Summit district using the northern tier of Cleveland suburbs, and which is placed in a senate district with two Cuyahoga districts.

A Montgomery-Greene district that is comprised of mainly Kettering and Beavercreek, but to which Moraine was added to get closer to the ideal population.  Moraine has annexed to the west, which increases the size of the smallest spanning circle, even though the bulk of its population is close to Kettering.  I can improve compactness by dropping Moraine, and being barely within 5%; or swapping West Carrollton for Oakwood (this boosts compactness because West Carrollton has greater area); or splitting Dayton.

A Lucas-Wood district that gets hit because it includes an unpopulated island in Lake Erie.

A Lorain district, because I drew the Lorain district along the shore line which includes Avon Lake.

A Mahoning district because I provide better population equality.

The two Lake districts because I switched a township to balance the population.

A Licking-Fairfield-Hocking district that is drawn in the way that it is because the constitution won't permit a logical split of Fairfield.

A Portage-Geauga-Stark district that includes Stark for better population balance.

A Mercer-Auglaize-Hardin district which is one of two whole county district that gets tagged, and that is largely because of the narrowness of Auglaize County.

A Preble-Darke-Shelby district (which is my county split in western Ohio) which is drawn in part to wrap around a Clark-Miami pairing.  The district on the other side of the Shelby split has 65% compactness, and I could get the district within 1 SD by switching townships or increasing population inequality.

The Erie-Ottawa district which gets dinged because the districts follow shoreline, and don't include Lake Erie in the calculation.  40% of the population of the district is in townships on the boundary which is Sandusky harbor.

An Ashtabula-Geauga district that includes the entire lakeshore of Ashtabula.

I think that all 17 districts represent reasonable and preferable policy choices (with the possible exception of the district in Cuyahoga which was drawn to exclude Blacks).

[jimrtex]

The contest site now has a corrected Roerk's measurement.  My mean score improved from 36% to 41%.

In comparing the individual districts on the contest map to those in the state map, there were 5 districts with significant differences.  The state software only shows two significant digits, vs. 4 for the contest.  Most districts either had the same value after rounding or were off by 1%.

Though they are the same plan, they were independently drawn.

The differences:

HD 16 in Franklin County.   Contest 51, State 48.  The state map appears to have messed up one of the wards (Ward 85), adding a 1/2 mile long strip of roadway, at least according to the Franklin County Board of Elections maps.  Because this happens to be at the extreme SE corner of a fairly compact district it extends the radius of the circle, while adding negligible district area.

HD 33 in Summit County.  Contest 38, State 41.  There is an industrial area of Akron on the eastern edge that includes a few enclaves of Springfield township (12 persons).  The area in Akron is uninhabited.  On the contest map I moved the enclaves into the Akron district to eliminate the discontinuity.  On the state map, I moved the industrial area into the suburban district because this would misclassify 12 fewer persons.  Because the industrial area sticks out to the east, and the Akron district has a slight east-west orientation it extended the circle while not adding that much area.

HD 40 in Montgomery County.  Contest 52, State 56.  This is a fairly compact district in the southern part of the county, south of Kettering.   Carlisle village is mostly in Warren County, but about 250 persons live in Montgomery County (maybe 5%).  These areas are part of Miami and German townships.  Only a tiny bit is in German Township, but it sticks out.

Under my understanding of the Ohio constitution, the district boundary should be between Miami and German townships, since the district is the composed of whole townships.  But the contest software treats Carlisle as if it were a township (many municipalities are legally townships).  And if you include all of the Montgomery part of Carlisle, the circle is extended.

HD 44 in Lucas County.  Contest 26, State 32.  The contest map includes an area of water with what appears to be two small islands.   These "islands" are actually dredging spoils and on Google maps, one is underwater, and the other looks to appear be covered with ice (as if the ice had lodged on the spoils and not yet melted.  The census shows these as water, so they are either shoals or intermittent dry land depending on lake levels, tides, and wave height.  The state does not include this area.

HD 98 in Erie and Ottawa counties.  Contest 23, State 18.  The difference here is that the contest geography includes water around the Lake Erie islands so that they are contiguous.

The state mapping software has a circular selection.  I selected census blocks centered on Ohio Stadium in Columbus.  To get enough population for a congressional district you need to get out to about the interstate loop (Jack Nicklaus Freeway).  At that point you pick up undeveloped areas with a few census blocks that are perhaps a 1/2 mile or mile across (ie a section).  The raw score for this circular district was around 80%.  By chopping off some of the more extreme areas, I can push it up to close to 90%.  If there were a circular selection that would only include areas wholly within a circle, I could probably get within a few percentage points of 100%.

Under the existing plan, HD 13, which is Lakewood and three Cleveland wards to the immediate east has a lower score than HD 8, 11, and 17 which are arguably racial gerrymanders, and is one SD below the statewide average.  HD 11 connects two areas of Cleveland via Cuyahoga Heights and Brooklyn Heights.

If the original editorial cartoon had been about HD 13, we would be talking about gerrybricking.

Cartoon shows district that looks like brick, with perhaps some mortar dripping off.  Elbridge Gerry is depicted as a mason finishing a wall.  Caption reads, "That will do for a brick. Better make it a 'gerrybrick'"

The Roeck measure is hypersensitive to the wrong things, and perhaps not sensitive at all to others.  Districts such as 23, 50, and 91 score reasonably well.

[jimrtex]

My Congressional Plan

I was mainly drawing for compactness, though the final map really doesn't show that.

I started by drawing the Cleveland, Columbus, and Cincinnati districts.

In Cleveland and Cincinnati, I started with those cities and then added on cities incrementally that would produce the best Roerk score.  An interesting phenomena is that adding a larger city that increased the circle some would produce a better improvement than adding a smaller city that was already within the circle.  Basically it has a scale problem where it is oversensitive with smaller districts.

The Cleveland district ended up too far west to be a VRA district.  Cleveland itself has a Roerk score of 21.5% and so it was mainly trying to fatten up to the south.  It also split the remainder of Cuyahoga County between an area in the east and one to the south.

In Cincinnati the initial expansion was to the west because of the Cincinnati rat tail, and then to the north, as the circle extended into Butler County and Kentucky and became more like a pair of parentheses.  Since Hamilton County only has an excess of 80,000 over an ideal seat, the residual area were two areas on the east and west end of the county.

In Columbus, I started with the entire city, added in the enclaves of Whitehall, Bexley, Upper Arlington, Grandview Heights, and Marble Cliff, and the fractured townships (Miflin, Clinton, Franklin, and Norwich).  I then started lopping off the Columbus tentacles and cleaned up the boundary.   The area is fairly compact (56.2%) and uses whole wards, but prevents my plan from being competitive.  The remainder of Franklin County almost formed a doughnut, but I needed 8,000 more people and the ward that reaches Delaware County had the right number and didn't eviscerate any townships.

I then started with one district per county, with the remnants of Cuyahoga, Franklin, and Hamilton treated as a district.  I eliminated the districts one by one based on inverse population.  The eliminated district was joined to adjoining districts based on which union would produce the greatest mean compactness.  This tended somewhat to encourage growth of larger (more county districts) and non-compact districts.

When you join two counties together, the mean usually drops.  You might be eliminating two districts in the mid-50s and replace it with a single district of perhaps 45 (a unit square is 64%, a 2x1 rectangle 51%).   If a district has multiple counties, additions don't drop its score very much and may even improve it.  If a district has a low score because of some extensions, then it might be improved by almost any addition.  The original Hamilton remnant had a low score because it was comprised of two disjoint parts.  It also has a fairly small population (34th overall).  So it was joined to Clermont and then other districts added to it which didn't drop the score too much as the inclusion of the western part of Hamilton had less and less effect.

Whenever a district had 721,000 persons I stopped adding districts to it.  Eventually, I ended up with 13 not so equal districts, plus the original 3 city districts with a compactness of 52%.

There was the natural Canton-Youngstown district.  And the Cleveland area districts had a total population equal to almost exactly 5 districts.  I adjusted these a bit, and they now have a population equivalent to 5.0016 districts (0.16% excess).

The district to the east (Lake, Trumbull, Ashtabula, Geauga was quite a bit short so I started adding areas from eastern Cuyahoga County.  After this was done, I was able to slide the Cleveland district east, and it became 48.16% BVAP.  The Summit-Portage district needed just a bit, as did the the Lorain, etc. district.  I did end up having to split a sliver off of Westlake, but otherwise there are no city splits in this area.  Statewide, this split and the split of Columbus are the only city splits not associated with a county boundary.

I then did the Toledo district.  I think that was the only district I could create without splitting counties.  If a 1% deviation were allowed, I think a lot better plan could be drawn.  I had to add quite a bit to the south to get the northwestern rural district.  Using Roerk, a district with a 50-mile indentation is considered the 4th most compact.

The Dayton district is the only one that comes close to being created with whole counties, and fortunately includes Greene.  I had to shift a bit of Carlisle and Springboro to the south.  I was going to shift one of the western townships when I noticed those.  I really don't like the rule about cities crossing boundaries.  I think that it is too arbitrarily applied to merit raising the allowed deviation from +/- 1 to +/- 0.5%.   And once you get above exact equality you are going to be making N-1 splits.

If I were going to create a whole county rule, I would permit multi-district areas that were within 1% deviation (ie, 4.99 to 5.01 rather than 4.95 to 5.05).  The only splits would be internal to these areas.  I would evaluate the splits on a relative basis.   A split where the smaller fragment is 3% of a county is better than one where the split is 40%.  This would encourage an attempt to follow county boundaries and splitting of larger rather than smaller counties.  If anything smaller than a township or city or city ward (large cities only) was split, the districts on either side of the split would have to have identical as possible populations.  In a state like Ohio, I could see letting cities choose to be considered in the county which they have the largest population, but that decision would be made prior to the census.

The Butler district was drawn around the Dayton district.  If you were creating logically compact metropolitan Cincinnati districts, the 4-county area has enough for 2.193 districts.  You could take the excess from Butler (including Hamilton city) and with Montgomery and Preble be right at 3 districts.  This would permit a more rural southern Ohio district, though there may not be enough people for that district and the eastern district.  You probably are going to be pushing into the Columbus suburbs.  You could also have a district that was based in Green-Clark-Miami which would give it more of a SW Ohio flavor.   Instead of 3 Columbus districts you end up with two more tightly drawn around Columbus.

I then adjusted the boundary for the southern district so that along with Hamilton it included exactly 2 districts.  The Cincinnati district was shifted to the west end of Hamilton, and the boundary in Hamilton is drawn to avoid splitting cities and townships.  At this point the eastern district was just a bit short, and there was no place to make an adjustment.  So Hocking got split.  I didn't really like splitting a small county, but I figured the people would prefer an eastern district over a Columbus district (which might not be the case if I trimmed some townships off eastern Fairfield or Licking counties).  The split in Hocking is 3 discontiguous townships - connected through other counties - and avoids the city of Logan.

This left the 2 Columbus suburban districts.  Originally, the doughnut was in the south/western district, and the north/western district was somewhat short.  I added the NE corner - Westerville to Reynoldsburg but it was still about 20,000 off.  I didn't feel like shifting the Columbus district, since I would have to do that on the SOS software (because it has wards and precincts).  So I moved Union to the other district and took in the NW corner of Franklin (Dublin and Worthington).   I was still just a few 1000 short, and I was at the Hilliard City limits, so would have had to go back to the SOS computer.

So I took the pieces of Dublin in Union County, and Reynoldsburg in Fairfield County.  Both cities are in 3 counties, and I already had the other two parts, so these don't bother me as much.  The Dublin city limits had an enclave, and I straightened out the boundary to follow roads, so technically I have split Union County under the rules.

By my count, I have 9 county fragments: Cuyahoga 4, Franklin 2, Hamilton 1, and Hocking 2, my compactness score is 44.6% (5 districts in the low 30s pulling this down).

Competitiveness is 21 (3 highly competitive, and 6 moderately competitive).

My partisan index is 59.0% (5 strong Republican, 2 strong Democrat, 4 lean Republican, and 5 lean Democrat and no even).  This gives me a fairness score pf 69.6 for an overall score of 176.2, which is pretty good for a plan with few county splits, pretty good community of interest, reasonably compact, and only two city splits (though Columbus is is triple split).

78.4% of Columbus is in the Columbus district.  If I wanted a better score, the clear solution is to split Columbus, which would give me 3 more competitive districts.   This wouldn't do much for the fairness score which would require pushing one or two of the leaning Republican districts to even.

[jimrtex]

I just got this congressional plan up.

It's designed to go for the points within the rules, and since there are already two earlier variations on this with strong adherence to county subdivisions, this plan often ignores municipal lines if it would help other aspects of the score.

This plan stuck with the 4 SR, 3 LR, 1 SD, 7 LD, 1 E plan. It has 0.1% electoral disproportionality. To get to 0 required a 3 SR, 5 LR, 2 SD, 6 LD, 0 E plan. CD 12 would have been the best to bring down by running it into Columbus, but the extra split didn't seem worth it for an additional 0.4 points.

All 11 lean districts became very competitive for 33 points in this plan and by carefully tracking the bounding circle limits on district involved in splits the compactness rounds to 49.0%.

It's possible to have fewer county splits than the 9 in a plan, but it reducing splits had a tendency to hurt compactness and prevent maximizing competitiveness.

Would a legislature or court sanction including Crestline as part of Richland County based on the 14 persons?  And is it really a good idea to include 30,000 people grabbed out Akron (74% Black and 90% D) to make a Medina district competitive?

Is it possible to get down to 3 Republican sinks or are there not enough Democrats in the right places to match up with them?  Or does the loss in fairness points not worth the extra competitiveness?

[jimrtex]

A scoring system for a contest must be carefully balanced to avoid unintended results.

I was looking at some of the other entries and was checking whether the last entry really scored 204.4.  I don't think it does.  But I notice it had 9 Democratic districts and a partisan index of 50.0.

I then started wondering where the 51.4% came from, and found that it is based on the total votes cast for the Republican and Democratic candidates in the 4 races.  Since three races are from 2010 it is more heavily weighted toward 2010, when the Republicans won the three races (Auditor, Secretary of State, and Governor).  Because turnout was heavier in 2008 this effect is somewhat less.   34% of the votes used in the index were from 2008, and 66% from 2010, about a 2:1 ratio.

McCain had 47.7% of the two-party vote in 2008, while the 3 Republicans had 53.4% of the two-party vote in 2010.

2010 thus had a 2.0% R swing relative to the "typical election", while 2008 had a 3.7% D swing.

A district that had been ratcheted in to be a "highly competitive lean Democratic seat (52.4% D), would have been a generally non-competitive strong Democratic district in a presidential election year; and a "highly competitive toss-up, but still slightly Democrat" district in a gubernatorial election.  The complementary district that was a "highly competitive lean Republican seat (52.4% R) would be a "highly competitive lean Democratic district" in a presidential election, and a "generally competitive lean Republican' district during a gubernatorial election.   This assumes uniform swing, which may or may not exist.

[jimrtex]

2010 thus had a 2.0% R swing relative to the "typical election", while 2008 had a 3.7% D swing.

A district that had been ratcheted in to be a "highly competitive lean Democratic seat (52.4% D), would have been a generally non-competitive strong Democratic district in a presidential election year; and a "highly competitive toss-up, but still slightly Democrat" district in a gubernatorial election.  The complementary district that was a "highly competitive lean Republican seat (52.4% R) would be a "highly competitive lean Democratic district" in a presidential election, and a "generally competitive lean Republican' district during a gubernatorial election.   This assumes uniform swing, which may or may not exist.

I haven't seen a master scoresheet, is there one posted somewhere?

I also have wondered about the choice of elections. At one time there was a talk of using the three closest races. That would be AG, Gov, and Auditor from 2010. I'm not sure why they went with SoS instead of AG.

I have not seen one.  I don't think there ever was one posted after the legislative contest.  There was never a 3rd place winner announced.  So I don't know if they decided because I followed the Ohio Constitution that I couldn't be rewarded.

The AG race was much closer than the SOS race.  The rules say that the 3 offices are on the apportionment board.  But that is really pretty superficial reasoning.  I thought I saw a news article that said that a bill was going to be introduced, but I can't find that any more.  And I didn't see anything on the legislative web site.

I looked up the Democratic candidate in the SOS race, and the only thing that I came across was something about gun rights.  She had been a Columbus city council member and had been filmed in a debate about a law that would have made Ohio's gun carry laws uniform, and had apparently been particularly shrill, and this incident gets remembered a few years later.  So if the Democrats run a particularly inept candidate, and you include twice as many votes from 2010 as 2008, they should get more representatives in Congress?

I was looking through the winning entries, and was looking at the shared version of the 3rd place entry.  Take a look at Lorain County.  I tried to count the splits.  I zoomed in and zoomed in to finally figure out what had been done.

I looked at the two districts, 2 and 13, and thought it pretty weird, but figured maybe they wanted to only get charged 3 points for the triple split of Lorain, vs. the double split of two counties.  But that is really an egregious split, worse than your Akron right hook.

And it was dividing two Republican districts and District 2 included both Richland and Wayne, while District 13 was stretching from Columbus to Elyria.   So I gave all of Lorain to OH-2 and started chopping off bits of Richland, but that was getting into the city of Richland.  So I added some smaller counties to the west (Hancock&Wyandot) to OH-2 and then started taking a few townships at a time from Ashland.  But I couldn't get it right.  One was too high, and then the other.  They were about 5000 apart, and I found a township of about 2500 which would make them both about equal.  They were both too high!

I remembered that the colored map wasn't quite the same.  I thought that the map had been fudged to make the bizarre Lorain crossing less obvious.  But what happened the Toledo district had been underpopulated, and there was apparently a last minute change to get it into range, as well as getting the other two districts below the 0.5% threshold.  So I made the change to Hancock, and was easily able to get OH-2 and OH-13.   I split another county, but at least the districts weren't entangled.

And OH-13 went from 35.2% to 58.3% compactness with its appendages removed, enough to improve the average 1.6 points.  But alas, it had pushed OH-2 to above 57.5% R.  So I had gained 1.6 compactness points and lost 1 competitiveness and added a "split".

I remembered that the colored map had a slightly different Lorain crossing.  So I implemented that,  But it was kind of ugly, so I played around and here is what I came up with.

https://districtbuilder.drawthelineohio.org/districtmapping/plan/1481/view/

This bit of tweaking got OH-2 back below 57.5% R, which gave me a competitiveness point.

But it also pushed OH-11 to a tossup, which changed the partisan index to 52.5% (from 51.2%), which cost 3.6 fairness points.

Since the partisan index is supposed to represent the number of seats one, a 0.3% change means a prediction of 1.3% more Republican seats.  But that 1.3% of 16 seats has to come in OH-11.  Making it 0.3% more Republican is not going to help out in Cincinnati.  1.3% of 16 seats is equivalent to 20.8% of OH-11.  But if 0.3% provides a 20% better chance of getting rid of Dennis Kucinich, would 1.5% make it a certainty?  Clearly not.

So we have a non-representative set of elections, that nonetheless produce a continuous variable.  We convert that into an a pair of arbitrary discrete scores (numerator and denominator) calculate a partisan index which kind of looks like a continuous variable, but you really have to play around with the combinations.

It also turns out that turning the Columbus district into a Strong Democratic seat helps out adding 0.5 to the denominator, is a lot more valuable in terms of "fairness" than the loss of a competitiveness point (it is still under 57.%).

We've created redistricting Yahtzee.

If we wanted to calculate a probable seat yield, wouldn't we just model swing as a normal probability distribution?   In close races, swing may be somewhat uniform - though we do have the local results for the individual races to test that.

BTW, I was playing around with the current map.  I started out merging OH-10 and OH-11 which are the Cleveland seats and the least populous.  This gave an excess for combined district which can be distributed to neighboring districts.  It turns out that the 6 northeastern districts along with the Toledo district have enough population to create 6 districts (7 into 6), which means the other 11 have to be reduced to 10.  The smallest adjacent districts are OH-4 and OH-5.

I was speculating about an incumbent protection procedure where each representative in turn could add to his district.  A district that had 600,000 (121,000) short would add 10% of 12,100 persons.  They would have to take that from one neighboring district with a larger population.  If there was a split county between the districts, then the adjustment would have to attempt to eliminate the split, with similar rules for townships.  A representative who chose later in the same round could not take back the same territory that had just been taken from him.   After all the representatives from districts with less than the ideal population had gone, the representatives from districts with excess population would have to discard some population.  In the case of the two merged districts, each of the two representatives would have to give up some of their former district.

So you would have alternating Push and Pull, or Give and Take rounds.  The percentage could gradually increase as the districts become closer in population.

I couldn't get the representatives to play.  So instead, I assigned each split county to the district which had the largest share,  When there were more than two districts in the 3 largest counties, I assigned the remainder of the county to the district with the 2nd largest share,

I then adjusted the districts based on which county shifts would improve compactness the most (eg it was as if the representatives would always pick a county based on compactness considerations).  The unexpected result was that OH-6 (the Ohio River district didn't have its ends lopped off.  It's compactness is in the low teens.  But it is so long that reducing the  length by one county didn't improve the compactness by that much.  It might be that for that purpose, it would be better to use the reciprocal of the Roeck measurement, or equivalently use the harmonic mean.

ps is Charles related?

[jimrtex]

This is my revision of the official plan.

https://districtbuilder.drawthelineohio.org/districtmapping/plan/1493/view/

I went through the split counties and assigned them to the district with the largest share of the population.  I kept Lucas, Lorain, Medina, Summit, and Montgomery split between two districts.  I made a few adjustments to avoid split districts.

I eliminated the splits of Toledo, Akron, Dayton, and Cincinnati.

I used my version of the Columbus district (OH-3), because it was a bit cleaner.  It might have been modified to keep Upper Arlington out, but that doesn't work very well with a Columbus and south district.  I also used my version of the Cleveland district (OH-11) since it included all of Cleveland and is reasonably VRA compliant.

Because they lost all of Toledo, OH-4 and OH-5 were pushed south but became more visually compact because of it and were able to return Clark to the SE districts.  I rearranged OH-7 and OH-16.  It doesn't make sense to have a district include Lorain and Stark and wrapping around south of Wayne.  The Youngstown-Canton-Akron-Cleveland-Lorain-Toledo area has the population for 6 districts, and one of those should be in the Canton-Youngstown area.  There is room for 5 districts in the more immediate Cleveland area, and we used up our stretch to create the shoreline district.

I also realigned OH-10 and OH-15, so that OH-15 didn't loop around Pickaway and southern Fairfield, through southern Franklin and up through Madison and Union, while OH-15 came across from Dayton to Fairfield.

After putting all of Cincinnati in OH-1 it became very ugly.  It was just barely possible to get up to Butler County when the rest of Hamilton County had to connect with Clermont.  And that still required a split of Butler to make up for the added people from SE Cincinnati.

So I switched to my version of the Cincinnati district which is wholly in Hamilton County.

Because OH-13 was the largest district in Summit, Portage, Trumbull, and Mahoning counties it became very large.  The excess was a consequence of putting all of Toledo in OH-9.  This required shifting Mahoning to OH-6, which in turn moved the southern tip into OH-15 (the Toledo change had pushed OH-4 and OH-5 south through the Columbus area.

I was able to get small count balance through the center of the state, and have 13 split counties.  8 are substantive splits, including the 6 largest counties, Cuyahoga, Franklin, Hamilton, Summit, Montgomery, and Lucas, plus Lorain and Trumbull.  There are population balancing splits in Darke, Hardin. Wayne, Muskingum, and Ross.

I haven't fully balanced OH-3, OH-12, and OH-15, but collectively they are within 476 of the ideal.  The rest can be fully equalized by small adjustments within already split counties:

1 -> 2     913 Hamilton
2 -> 15   372 Ross
12 -> 6  (-103) Muskingum
6 -> 13 (-2045) Trumbull
13 -> 14 1238 Summit
14 -> 11/16 795 Cuyahoga
7 -> 16  (-366) Wayne
11/16 -> 9  327 Cuyahoga
9 -> 5  240 Lucas
4 -> 5 (-177) Hardin
5 -> 8  60 Darke
8 -> 10 (-2534) Montgomery

If you wanted a more favorable Republican plan,

Move Clark to OH-8, and parts of SW Montgomery and N Warren to OH-8, OH-2 takes in more of Hamilton, and OH-1 moves north into Butler County.

You could swap Muskingum for Athens and Morgan, but the structural solution is to put Stark and Mahoning together, which gives you more of a tossup.  The remainder of the OH-6 and OH-7 can be shifted west into Licking, while OH-15 shifts a bit further north along the river.

[jimrtex]

http://drawthelinemidwest.org/ohio/congressionalwinners/

Under "Scoring", "Plan Scores" is a link to an Excel spread sheet with all the scores.

[jimrtex]

This has some links to the congressional and legislative maps from past decades.

http://www.sos.state.oh.us/SOS/ReshapeOhio/Links.aspx

It appears that the constitution has only been loosely followed as to creating legislative districts from whole counties.  I thought we were simply following the constitution, and not trying to eliminate county cuts.

Only in 1980 does it look like there was any effort to combine whole counties.

They have followed the constitution with regard to creating as many districts within the county as possible, for the most part.

It appears that maybe they got into problems in NE Ohio with the house districts though.  Lake County was split into 1 whole district and two parts, and this was also used for the senate districts.

[jimrtex]

This has some links to the congressional and legislative maps from past decades.

http://www.sos.state.oh.us/SOS/ReshapeOhio/Links.aspx

It appears that the constitution has only been loosely followed as to creating legislative districts from whole counties.  I thought we were simply following the constitution, and not trying to eliminate county cuts.

Only in 1980 does it look like there was any effort to combine whole counties.

They have followed the constitution with regard to creating as many districts within the county as possible, for the most part.

It appears that maybe they got into problems in NE Ohio with the house districts though.  Lake County was split into 1 whole district and two parts, and this was also used for the senate districts.

On your last comment, I assume you are referring to the 1970s map. Indeed Lake did not have enough for two full house districts and the population in NE OH also seems to force at least one unconstitutional construction. The treatment of Lake seems like my split of Cuyahoga, though I see that Mahoning also does not get a constitutional senate district in the 1970s plan.

Yes.  I was referring to the 1970s map.

The constitution was changed in 1967, so I think that the the 1972 plan was the first to use the new system.  I find it interesting that there was no real attempt to form districts from whole counties, but then in 1982 there was.

[jimrtex]

Democrats have filed a lawsuit against the Ohio legislative districts claiming that it violated the Constitution, and asking that new districts be put in place before the March primary.

Ohio Supreme Court]Ohio Supreme Court Case Search, search for 2012-0019

The complaint muddles up the legislative and congressional redistricting which were done by two different bodies.

It also misinterprets 11.07(c) which says that only one geographical unit (township, city, ward, etc.) may be split between two districts.  The erroneous interpretation is that a single district can only contain parts of one geographical unit.  But a district does not divide a geographical unit; but rather a geographical unit is divided between two districts (or among 3 or more districts).

They might have a better case based on 11.07(a) and 11.07(b), which require a district to be comprised of whole counties or whole geographical units.  But this has not been rigorously enforced in the past, and it is unclear how to apply this to single districts, rather than the totality of the map.