opinion of using 'shortest splitline' algorithm for districting

[© tweed]

http://en.wikipedia.org/wiki/Gerrymandering#Shortest_splitline_algorithm
http://www.rangevoting.org/SplitLR.html

[muon2]

I don't like it for districts. Among my complaints:

It ignores any natural geographic features - it hops mountains and rivers in ways that ignore connectivity.

It splits existing political boundaries for counties and municipalities in ways that needlessly complicate elections and increase cost.

It tends to carve through major metro areas and if mapped at the level of whole census blocks it would appear just as ragged as some gerrymandered districts.

It surrenders compactness for minimum line length.

It fails in any state subject to the VRA.

[jimrtex]

It ignores any natural geographic features - it hops mountains and rivers in ways that ignore connectivity.

It splits existing political boundaries for counties and municipalities in ways that needlessly complicate elections and increase cost.

It tends to carve through major metro areas and if mapped at the level of whole census blocks it would appear just as ragged as some gerrymandered districts.

Unfortunately, the originator doesn't recognize these as weaknesses, but considers them features, since it avoids manipulation such as streets and mountains being moved.

It surrenders compactness for minimum line length.

This is more a matter of the particular algorithm that is used.  If stated as a goal of minimizing total bath length of internal boundaries, the districts would be compact.

It fails in any state subject to the VRA.

This proves the VRA is logically unsound.

[Vazdul (Formerly Chairman of the Communist Party of Ontario)]

I am opposed to the use of any algorithm for redistricting, simply because they have a terrible tendency to tear apart communities that, by any objective measure, should certainly be in the same district. Urban areas tend to get hit particularly hard. Just look at the top page on the RangeVoting link. That's three districts in Birmingham and whopping five in Indianapolis. Then dig a little deeper:

Arizona: Seven districts in Maricopa County, and Tucson is split right down the middle.

California: Sacramento split in four, Bakersfield in three, and Fresno in two, and that's just what's immediately noticable. I don't even want to know what's going on in LA.

Florida: Jacksonville and Orlando split right down the middle.

Georgia: Macon and Augusta split right down the middle, and Atlanta looks to carved four ways.

Iowa: Des Moines split in three and Cedar Rapids in two.

Illinois: Surprisingly not too bad outside of Chicago, but Moline-Rock Island and Decatur get screwed.

Kansas: Wichita, Lawrence, and the Kansas City suburbs each get split.

Louisiana: New Orleans and the northern (developed) part of Jefferson Parish get split.

Maryland: Is that a five-way split of Baltimore? And four districts bordering DC.

Michigan: Flint split in three and Grand Rapids in two.

Minnesota: Six districts in the metro, and it looks like the cities themselves are split between four districts.

Missouri: Kansas City (I mean the real, urban part of the city, not the suburbs within city limits) is split right down the middle. St. Louis is also split in two.

Mississippi: Jackson and Columbus split in two. Meridian split in three.

North Carolina: Four districts in Raleigh, Greensboro split right down the middle, and Fayetteville also split.

Nebraska: The Omaha area is split so that the district containing the majority of the area has to take in a bunch of rural territory.

New Hampshire: Manchester split right down the middle.

New Jersey: It's hard to tell because the picture is quite small, but it looks like Paterson is split in four. Newark is definitely split, and it looks like so is Atlantic City.

New Mexico: All three districts contain part of Albuquerque.

New York: What a mess! Three districts in Buffalo. Three districts in Syracuse. Rochester split down the middle. Albany split down the middle. Utica split right down the middle. The earmuffs look sane in comparison.

Ohio: Three districts in Columbus, and the Cincinnati-Dayton district is just horrible.

Oklahoma: Three districts in Oklahoma City, and Tulsa split right down the middle.

Oregon: Three districts in Portland, and Eugene split in two.

Pennsylvania: Ugh! I think that's a four-way split of Philadelphia and a three-way split of Pittsburgh. Lancaster is split right down the middle, as is Allentown. Really now, the lines may look prettier, but how does this make any more sense than the current gerrymander?

South Carolina: Three-way split of Columbia.

Tennessee: Nashville is split right down the middle.

Texas: Apart from doing god knows what to the metro areas, the map splits Austin three ways, as well as splitting Lubbock, Midland, Corpus Christi, McAllen, Laredo, Longview, and Tyler.

Virginia: A three-way split of the Richmond area, probably including Richmond proper. Charlottesville split right down the middle. And a district stretching from Newport News to Alexandria.

Washington: I believe that's a four-way split of Tacoma.

Wisconsin: Milwaukee split right down the middle.

[Vazdul (Formerly Chairman of the Communist Party of Ontario)]

This is more a matter of the particular algorithm that is used.  If stated as a goal of minimizing total bath length of internal boundaries, the districts would be compact.

The Shortest Splitline Algorithm is very precisely defined and can result in only one map.

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This proves the VRA is logically unsound.
[/quote]

No, what it proves is that using an algorithm to redistrict tears apart racial communities.

[Хahar 🤔]

It removes the only advantage that single-member districts have.

[minionofmidas]

There needs to be, in any sane redistricting (so not what America has got), a balancing test between reason and consistency. This doesn't have anything of the sort, and as a result is not something a sane person might propose.

[Antonio the Sixth]

Yeah, awful idea for all of the reasons already stated.

[Bacon King]

Haha, oh wow, this algorithm really does hate keeping cities intact.

[jimrtex]

This is more a matter of the particular algorithm that is used.  If stated as a goal of minimizing total bath length of internal boundaries, the districts would be compact.

The Shortest Splitline Algorithm is very precisely defined and can result in only one map.

It is one of a class of similar algorithms that have the objective of minimizing particular metrics.

[jimrtex]

Haha, oh wow, this algorithm really does hate keeping cities intact.

Medians are more probably to occur in areas of higher density.

The east-west median of population got stuck in the Detroit/Indianapolis area for 50 years or so, even as the mean continued moving westward.

[muon2]

Haha, oh wow, this algorithm really does hate keeping cities intact.

Medians are more probably to occur in areas of higher density.

The east-west median of population got stuck in the Detroit/Indianapolis area for 50 years or so, even as the mean continued moving westward.

True. The median is a point that only reflects how much of the data lies one either side of that point. The relative distance to that point does not matter, even though it would in the mean (or average). The median will either be at one of the data points or midway between two points if there are and even number of data points.

Since the median is located at a specific data point, the likelihood of it's occurrence is tied to the likelihood of finding any data point in general. That is the median is more likely to be at a part of the data set where data is more densely clustered. For the 2-D problem of the splitline algorithm, this means in areas of higher population density, ie cities.

[jimrtex]

Haha, oh wow, this algorithm really does hate keeping cities intact.

Medians are more probably to occur in areas of higher density.

The east-west median of population got stuck in the Detroit/Indianapolis area for 50 years or so, even as the mean continued moving westward.

True. The median is a point that only reflects how much of the data lies one either side of that point. The relative distance to that point does not matter, even though it would in the mean (or average). The median will either be at one of the data points or midway between two points if there are and even number of data points.

Since the median is located at a specific data point, the likelihood of it's occurrence is tied to the likelihood of finding any data point in general. That is the median is more likely to be at a part of the data set where data is more densely clustered. For the 2-D problem of the splitline algorithm, this means in areas of higher population density, ie cities.

In discussions about split line, one suggested alternative metric would be to consider density in the measure of the length of the cut line.  Lines that cut through less dense areas would be favored.

This is a pseudo-splitline.  I first sliced blocks into 11 equal-population slices based on longitude.  These were regrouped into a 3:4:4 pattern (based on less density to the west, and then resplit based on latitude.

http://www.redrawsf.org/

Click on View District Maps

Click on "Check 2010" map.

Be patient with the refreshes.  You can't interact while the map is repainting.  So when you zoom in, click on 3 or 4 steps up on the zoom bar, rather trying to drag the indicators.

[muon2]

In discussions about split line, one suggested alternative metric would be to consider density in the measure of the length of the cut line.  Lines that cut through less dense areas would be favored.

This is a pseudo-splitline.  I first sliced blocks into 11 equal-population slices based on longitude.  These were regrouped into a 3:4:4 pattern (based on less density to the west, and then resplit based on latitude.

http://www.redrawsf.org/

Click on View District Maps

Click on "Check 2010" map.

Be patient with the refreshes.  You can't interact while the map is repainting.  So when you zoom in, click on 3 or 4 steps up on the zoom bar, rather trying to drag the indicators.

The process makes more sense in an urban area where there is less variation in pop density. The uniformity in density shows up as districts that cover roughly the same amount of area. I'd still like to see this type of modified algorithm use the underlying street axes, so that the lines are less erose.

[jimrtex]

In discussions about split line, one suggested alternative metric would be to consider density in the measure of the length of the cut line.  Lines that cut through less dense areas would be favored.

This is a pseudo-splitline.  I first sliced blocks into 11 equal-population slices based on longitude.  These were regrouped into a 3:4:4 pattern (based on less density to the west, and then resplit based on latitude.

http://www.redrawsf.org/

Click on View District Maps

Click on "Check 2010" map.

Be patient with the refreshes.  You can't interact while the map is repainting.  So when you zoom in, click on 3 or 4 steps up on the zoom bar, rather trying to drag the indicators.

The process makes more sense in an urban area where there is less variation in pop density. The uniformity in density shows up as districts that cover roughly the same amount of area. I'd still like to see this type of modified algorithm use the underlying street axes, so that the lines are less erose.

Think about if you sliced Illinois along a north-south axis into equal population slices.  In the north you would get extremely narrow slices running from Lake Michigan to the Mississippi.  You could then calculate a proportionality measure for each slice E-W length (average) / N-S width.

Find the narrowest slice and combine it with its narrowest neighbor, and calculate its proportionality measurement  ((E-W)/(N-S)) / magnitude.  Quit once the proportionality values are below some level (1.5?. 1.62?).

Repeat the process slicing east to west in the merged slices.  It might take another iteration in the Chicago area.

There was also a splitline done of San Francisco using election precincts, but it never made it out to the block level - 2010 block numbers are not the same as 2000 block numbers, and the precinct definitions didn't include all the zero-population blocks, and some precincts split blocks.

The boundaries still ended up being jagged.  California has some tight population limits for precincts, and there are requirements for polling places being within precincts. In high density areas, there might be precincts with 5 or 7 city blocks, so even when the street grid is regular, the precincts don't match the grid.

If I were implementing a splitting algorithm, I would try to partition near the center of area.  For example, for a given angle, find the cutline that would split the area into two equal areas, round to the nearest integer number of districts based on population, and find two cutlines parallel to the first.

If you try to split to equalize population, there can be corner cutting (see the first split in Illinois, which cuts across the outer fringes of the Chicago area.  Triangular area are less compact (total interior angle = 180 degrees, with smallest interior angle <= 60 degrees) and you can get some extreme needle-like districts.

If your cut line is more near the center, you will be more likely to not cut adjacent sides, and will introduce 4 new vertices with around 90 degree interior angles.

Perhaps even better is to do a 3-way partition using a modified 120-degree wye.  This would introduce 9 vertices with a total of 900 degrees, so could help keep the number of sides of some districts above 4.

[muon2]

IIRC you had a version some time ago where you took a splitline but then adjusted it to conform to the nearest county (or municipal) lines. This seemed to me like a preferable implementation of the concept since it corrects for political subdivisions while maintaining the core idea of splitline.

[jimrtex]

IIRC you had a version some time ago where you took a splitline but then adjusted it to conform to the nearest county (or municipal) lines. This seemed to me like a preferable implementation of the concept since it corrects for political subdivisions while maintaining the core idea of splitline.

I'd forgotten that, but that was what had sparked my interest in splitline in the first place.

The way I oriented the cutline was to determine the minimum-area bounding rectangle around the area being divided, and then set the direction of the cutline perpendicular to the long axis of the rectangle.

I then divided the area (not the bounding rectangle) into two parts of equal area.  If the population of the two areas was X and Y; I found the two cut lines parallel to the first cutline that would divide the population into floor(X):ceil(Y) and ceil(X):floor(Y) and chose the one that produced the more equal division of area.

I then would adjust that cutline back and forth to get to a single split county.

But maybe the thing to do would be rather than finding the orientation of the cutline first, would be to choose the cutline orientation based on which angle left the fewest (net?) persons stranded on the wrong side of the county line:

For each trial angle (0 to 180- degrees)

   Find cutline that divides into equal areas.

   Adjust cutline so areas have population equivalent to integer number of districts, and
   and choose the one that creates the more equal area.

   Determine the population on each side of the cut line in counties that are split (modulo the
   district magnitude; since we can always create whole districts within that portion of the
   county*).

   For each subset of split counties, calculate the total population to the left of the cut line,
  and for the complementary subset, the total population to the right of the cut line.  In both
  cases modulo the district magnitude.  Take the absolute value of the difference.  This is the
  minimum number of persons that need to be split out of a single county.

  The quality of the cutline is the length of the original cut line times this stranded population.

end for each angle

For winning cut line, place all but one county one either side of the adjusted cut line, and split that county along a line parallel to the original cut line.

* An alternative method might be to apportion whole districts to larger counties (eg in Texas, apportion Harris 5, Dallas 3, Tarrant 2, Bexar 2, Travis 1, El Paso 1, Collin 1, Hidalgo 1), and in each of the counties distribute the residual population proportionately.   Then do a split line for the remaining 20 districts, and then refine the results.