I'm not familiar with the constitution of Ohio. I only looked for general CoI and population equality. That said though there are some districts I hate and had no choice but to draw this way, there are worse ones in the actual map.

Minimum requirement is that for a county entitled to N+ representatives, N districts must be wholly contained within the county, with only one district crossing county boundaries.

Counties entitled to close to one representative (and the Ohio Constitution provides for a 10% leeway for these counties should be in one district).  For 2010 this applies to Wood, Richland, and Columbiana counties.

The other provisions say that to the extent feasible counties should not be divided.  The Ohio redistricting board has interpreted "not feasible" to mean "couldn't be bothered", when in fact it is demonstrably quite feasible to have very few extraneous county splits.

So I ended up redrawing all of Ohio's legislature for both houses. I started for basically two reasons, to get a feel for how the layout the state skews the partisan numbers, and to experiment with grouping three House seats into one Senate. The latter is actually a tad tricky, since you might have an area that's an obvious community of interest and has seven districts, but one has to be left out, and you end up with some awkward Senate districts. But those will come later. For now: House.

Just because Ohio doesn't follow their constitution is no reason for you to not do so.

The Ohio Constitution rules are terrible and internally inconsistent anyway. Not worth trying to follow.

Could you be more specific?

http://maps.google.com/maps?q=http:%2F%2Fwww.azredistricting.org%2Fmaps%2Fpubmaps%2F100911%2FLeg-Merge_as_of_100911.kmz&hl=en&sll=34.168218,-111.930907&sspn=12.693328,26.784668&vpsrc=0&t=h&z=7

They reworked some parts of that. http://www.azredistricting.org/Maps/Tentative-Final-Maps/Legislative/maps/Tentative%20Final%20Legislative%20Map%20-%20Statewide.jpg

(add " - poster size" at the end of the address for a 140 million pixel version that may crash your computer)

I count 13 utterly safe GOP, 3 usually safe GOP (at least for now - the one in NE Phoenix might get competitive towards the decade's end), 3 tossups two of which tilt R, one D (and the tilt R in Pinal might be safe by decade's end), 2 usually safe Dem, 9 utterly safe Dem seats. After looking at their demographic and competitiveness charts.

As it stands, the Democrats won all the 'competitive' districts (basically 8, 9, 10, 26)

A lawsuit is being filed alleging Georgia style malapportionment.



Here are the population totals.

7   203,026
4   204,143
27   204,195
3   204,613
2   204,615
24   206,659
19   207,088
30   207,763
8   208,422
29   211,067
10   211,073
13   211,701
9   213,224
11   213,377
23   213,451
26   213,659
6   214,244
15   214,941
22   215,912
21   216,242
1   216,451
14   217,693
20   218,167
18   218,677
28   218,713
5   219,040
16   220,157
25   220,795
17   221,174
12   221,735

That said, the top 14 (and 14 of the top 15) overpopulated districts are Republican held. The bottom 10 (and 11 of the bottom 12) districts are Democratic held. There is only 1 GOP district with negative deviation.

There is a 0.804 correlation between district population, and percentage of non-Hispanic whites.

So I ended up redrawing all of Ohio's legislature for both houses. I started for basically two reasons, to get a feel for how the layout the state skews the partisan numbers, and to experiment with grouping three House seats into one Senate. The latter is actually a tad tricky, since you might have an area that's an obvious community of interest and has seven districts, but one has to be left out, and you end up with some awkward Senate districts. But those will come later. For now: House.

Just because Ohio doesn't follow their constitution is no reason for you to not do so.

Revamping Baker v Carr to draw districts based on who is eligible to vote would be quite insane. That was never going to happen. Beyond the policy issues, administering such a metric would be a statistical, and subjective, nightmare.

This is a quite readable explanation of the issues involved, and explains why no revamping of Reynolds v Sims is necessary.

No More Weighting: One Person, One Vote Means One Person, One Vote

The 5th Circuit's opinion in Lepak is based on their early decision in Chen v City of Houston III.  See Part IV.   Their conclusion was that it was a political decision.  They ruled against the plaintiffs in Lepak on the basis that there were no intervening SCOTUS rulings that would cause them to revisit the earlier decision for the 5th Circuit.

The City of Irving "voluntarily" districted on the basis of population.  Once a city chooses to district on the basis of CVAP, the SCOTUS will have to take the case.

Incidentally, Chen also contains a finding that a 8.63% variation in city council districts is within safe harbor limits.

The poll question is poorly worded.  It is expecting a "yes" response for something that would be considered negative ("poor measure").   There is juxtaposition of "poor measure" and "affluence" when "poor" is the usual adjective used for someone who is lacking affluence, and the added word of "actual" in front of "affluence".

Don't you agree that it would be much better to reword the question in a way that would avoid confusing or leading respondents?

Any reasons why Franklin County, WA is growing so fast ?

Oil/Gas ?

Spillover.

Richland and Kennewick, two of the Tri-Cities are in Benton County on the south bank of the Columbia River.  Pasco is the third, and in Franklin County on the north bank.

The Hanford Site northwest of Richland was created to produce plutonium during WWII.  It was chosen in part because it was remote from population.  Richland was originally a company town for the workers (its population increased from 247 in 1940 to 21,809 in 1950).  Hanford no longer produces plutonium, but there are 9000 workers involved in environmental cleanup.

The area is also attractive to retirees, because it is drier than Seattle or Portland.

In 1980 the respective populations of Benton and Franklin were 112K and 37K; by 2000, 142K and 49K; in 2012, 182K and 85K.  So while they have had similar numeric growth (both 7K since 2010), the relative growth has been much greater in Franklin County.  There were two highway bridges, including one on I-82 that have facilitated growth of the north bank.

The Texas Constitution primarily deals with apportionment of representatives, rather than the actual creation of districts.  Based on the 2012 estimates, the ideal district population for the 150 house districts is 173,728, an increase of 3.6% from the 167,637 for the 2010 census.

The Texas Constitution provides for three types of districts:

(a) Multi-member districts for single counties, which are apportioned one representative for each multiple of 173,728.  Strictly speaking, the number of districts apportioned to a county is truncated: number_districts = floor(county_population /ideal_district_size), with the remainder treated as a surplus which may be included in the apportionment of a multi-county district.  In practice, if the average district size for the county is within 5% of the ideal, then the number is rounded: that is if,  number_districts = round(county_population/ideal_district_size), and

   0.95 < (county_population / number_districts) / ideal_district_size < 1.05

and it is treated as if there is no surplus.  In actuality, a total deviation of 10.0% is used.  In 'White v Regester', the SCOTUS approved a Texas house plan that had a deviation from 5.8% to -4.1%, overturning a district court decision that the deviation was too great ('White v Regester' also concerned use of multi-member districts, in which the SCOTUS upheld the lower court decision).

In its decision, the SCOTUS noted that the average absolute deviation was 1.82%, and only 23 districts, all single member, had absolute deviations greater than 3.0%.  The plan considered by the court was a hybrid plan, with 67 single member districts in smaller counties, 11 multi-member districts in larger counties, and 23 single-member districts in Harris County (Harris County was the only large county that was divided.

The map at issue in 'Smith v Regester' did not really conform to modern (post-1980) understanding of how to harmonize the Texas Constitution and equal protection under the 14th Amendment (post 'Reynolds v. Sims').  

After 'Reynolds v Sims', courts in Texas outlawed use of floterial districts, as well as a specific provision that discriminated against the largest counties.  In 'Kilgarlin v Hill', the SCOTUS determined that a Texas house plan that had deviation from +14.84% to 11.64% (26.48% total), and had 12 single member districts with a deviation greater than 10%, and 8 multimember districts that would elect 55 members would have a deviation greater than 6% violated equal protection.

Litigation elsewhere led to a conclusion that the Texas constitution should (or could) largely be ignored in drawing legislative district boundaries.  

FWIW, I suspect the reason 500 sq/mile is used as a cutoff is because you have lots of counties that have a small city that has borders that extend far beyond the actual populated area. Lots of places in Alaska like that for example. Similar to how the county I grew up in has a population density of only 35 people per square mile but the city is more urban than anywhere in many counties with 20 times the density, it's just the city and LOTS of empty space.

They went to a density-based measure in 2000 specifically because formal boundaries did not correspond to land use, either the boundaries extended beyond the developed area, or vice versa.

Reading the federal register it appears that the 500 ppsm was to permit automated delineation.

Before 1950, the Census Bureau simply defined places (towns and cities) with population above 2500 as urban, and everything else as rural.  Beginning in 1950, the census bureau began defining urbanized areas around cities of over 50,000 to recognize that there were often unincorporated suburban areas adjacent to large cities.  The delineation of urbanized areas was not automated.

The 1990 census was the first to completely cover the country in census blocks.  In defining urbanized areas, analysts were permitted to identify non-residential urban uses of census blocks, and calculate a density based on the residential area - using a threshold of 1000 ppsm.

In 2000, the process was automated, and urban areas were defined based entirely on density, with no regard to city or town boundaries.  Urban areas were also defined for much small populations - replacing the old definition based on city boundaries in small town America.

To permit the process to be automated, a density of 500 ppsm was adopted - which avoided a need to determine land use.   A typical census block in a suburban area might have a density of a few 1000 (5 acres X 16 houses x 2.5 persons/household = 5120 ppsm).  Even an area with acre lots would have 1600 ppsm.

In addition, the area of moderate density must be adjacent to an initial core of over 1000 ppsm, or reachable through jumps and hops, which will disqualify isolated small areas that might reach the 500 ppsm.

So I actually bothered to look it up with my own eyes, and while 500 people per square mile is emphatically the exurban fringe, the ratio of subdivisions to rural uses is higher than I had imagined.

Inside the dotted line is Buckingham Township, in Bucks County PA.  497 people per square mile.



And here's a view from the ground: new houses on one side of the road, corn on the other.



...

I think the lesson here is that 500 people per square mile is a very unnatural density- the largest-lot subdivisions will be higher, anything purely rural (even including hamlets, and in wet climates) will be lower.  You need a hodgepodge to hit that mark. 

If you get fine-grained enough, down to the block, 500 people per square mile is too low I think.  But at a township level it's more defensible.

The township doubled in population between 1970 and 1990 and again between 1990 and 2010.  I don't see how it could not be considered urban (don't be confused between the Census Bureau definition of urban - which is essentially non-rural; and terms like suburban.

The 2010 density is 606 ppsm.  The Philadelphia Urbanized Area includes most of the western part of the township (west of York Road) expanding northward from (Doylestown).   I'll refer to northwest as "west", away from Philadelphia.   About 2/3 of the population in the eastern half is in the Philadelphia UA, but very little of the land.   The subdivisions are thicker to the west, so I suspect that enclaves are being closed up and added to the UA, while to the east you have exclaves.   There is also a strong of hops so that the UA just reaches across the Delaware into New Jersey at New Hope/Lambertville along US 202.   Note about 1/4 of the employees in some of the census tracts work out of state.   It is about an 1-1/2 into NYC via either I-78 or I-278 (which would be the quicker route into Brooklyn or Staten Island), so I'm guessing it would be more NJ than NY.

The numbering of the census tracts shows the development of the area.   When census tracts are modified, they are renumbered, so as to avoid comparing different areas between censuses.

The tracts are 1045.02, 1045.03, 1045.05, 1045.06 (with .01 and .04 missing).

So originally it was all tract 1045 (census tracts have a target population of around 5000).  The first split would have been between 1045.01 to the west, and 1045.02 to the east, which still exists.  Then it is likely that 1045.01 would have been divided between 1045.03 to the south, adjacent to Doylestown and 1045.04.   And then 1045.04 would have been split between 1045.05 and 1045.06.

1045.05 is the middle part of the western half somewhat pie-shaped.  The subdivision on the western edge is prominent in the satellite view because the trees haven't grown up around the houses yet, so probably 10 years or less.  This area has an average family size of 3.6, which means most families have children.  Since few families have 4 or 5 children any more, you have to have 2 in most families to get that close to 4.  Compared to 1045.02 to the east, this area is better educated, less German, and less likely to have been born in Pennsylvania.  So the area to the east which is less developed must have a residual population that is native to the area (at least Bucks County.

As an aside, it blows my mind that 500 people per square mile is considered "urban".  I have a hard time applying that adjective to areas ten times as dense sometimes.  (This is what happens when you grow up in a suburb whose density is roughly 9000 persons per square mile.)

Historically, any town with a population above 2500 was classified as "urban", while anything else was considered rural.   Around 1950, the Census Bureau started defining urbanized areas to reflect that the fringe around larger cities wasn't necessarily being formed into incorporated cities.

In 2000, the delineation of urban areas was switched to be entirely based on density, to recognize that city limits quite often do not reflect land use - often including large swaths of undeveloped land, and other areas that are not legally defined as cities or town.  An area must have 2500 persons to be classified as an "Urban Area".  Urban Areas with population above 50,000 are "Urbanized Areas" while those between 2500 and 50,000 are "Urban Clusters".

9000 per square/mile is pretty dense.   An area with single family houses might have half that, without any land being used for parks, schools, or commercial areas.

The 500/square mile is not the average for the entire area, but rather for each area that is added.  Agricultural land won't come close to qualifying, even if it is on the edge of a town and some lots have been carved off and a few houses built.   And any formally subdivided land will easily surpass ir - though it might not reach the 2500 total population limit.

An area with 3 and 4 acres lots would be near the threshold, but it would difficult to sustain over large areas.

Great map, Sheliak.

And thanks for that explanation of metro areas, jimrtex. I'd wondered before why the census's metro areas often seem to include a layer of rural counties that wouldn't be counted by the everyday understanding of the metro area.

It is somewhat schizophrenic.   An extreme example is Armstrong County which is part of the Amarillo metropolitan area and has a population just under 2000.  It also has an interstate highway, so it is an easy commute into Amarillo.

Wayne county Michigan still losing people but only down to 1,792,000 from 1,820,000 in 2010. So Wayne county is on pace to lose 140K by 2020. Also on the bright side Michigan only lost 275 people in the last 2 years compared with 55k between 2000 and 2010. So Michigan will still lose a congress seat in 2020 unless we have some huge growth in the next 8 years but are we at risk to lose 2 seats. Does anyone know, would negative growth cause it.

To lose an N^th seat, a state has to have a growth rate about 1/N slower than the country.   So to lose a 14th seat, would mean that Michigan would have to grow about 7.1% slower than the country as a whole.  Between 2000-2010, the country grew about 10%, but will probably grow around 8% between 2010-2020.  So if Michigan had no change for the decade it would be just a bit less than 7.1% slower.   So if Michigan has zero change the rest of the decade, it will be at a rate to lose 1 seat and no more.

But there is a complication of rounding.  In 2010, Michigan was entitled to 13.9 representatives.  Projecting the changes forward to 2020, would result in 12.9 representatives, which would round to 13.   If Michigan were to lose population, it would edge toward the 12.5 mark and be subject to loss of an additional representative.   This would require a loss of 3.8% or around 338,000.   Because rounding is not done independently, there is a fuzzy zone, perhaps from a loss of 2.5% to a loss of 5.0%.  At 2.5% Michigan would have to be lucky to lose the extra seat, at 5.0% it would be lucky keep the seat.

I'd heard the Governor here mention Oregon being #1 in manufacturing as a share of the state's gross product (something I found surprising) and yesterday his office posted a link to the source article of that stat which has info on all the states:

http://www.areadevelopment.com/RegionalReports/Q1-2013/states-leading-US-manufacturing-resurgence-2665542.shtml





Thoughts?

Refining must count as manufacturing.

So the governor of Oregon was proclaiming that Oregon was a lot like Louisiana and Indiana?

They added Benton County MS to the Memphis metro. That decision belongs in the deluge. It's an hour outside of town and at least a half hour beyond any signs of civilization. We're not Atlanta. People don't commute across three counties here.

The procedure for defining core-based statistical areas is automated.

The Census Bureau starts by defining Urban Areas which are densely populated areas (500+ per square mile).  If 50% of a county population is in urban areas of at least 10,000 population; or the county has 5,000 persons in single urban area with more than 10,000 persons it is a "Central County".

Shelby, TN: 97% of population is in Memphis UA or Arlington UC.
Tipton, TN: 19,000 population in Atoka UC
Fayette, TN: Not a central county, 7K in Oakland UC, tiny bits in Memphis UA and Arlington UC

DeSoto, MS: 80% of population is in Memphis UA
Tunica, MS: Not a central county, 4K in Tunica UC
Tate, MS: Not a central county, 7K in Senatobia, UC
Marshall, MS: Not a central county, 6K in Holly Springs, UC
Benton, MS; not a central county, no Urban Areas

Crittenden, AR; 79% of population in Memphis UA

The definition of an Urban Area includes hops and skips which permit an UA to extend along highways, and in this case across the Mississippi to West Memphis.  The definition of central counties is done for the entire country.  I just showed the counties that ended up in the Memphis MSA.

So you have the following Central Counties:

Shelby TN, DeSoto MS, Crittenden AR for Memphis Metropolitan Statistical Area
Tipton TN for a hypothetical Atoka Micropolitan Area

Then it is determined whether Outlying Counties should be added to the CBSA.  This is based entirely on commuting patterns:

If 25% of the employees resident in the county work in a central county, the county is an outlying county; or if 25% of those employed in a county come from a central county, the county is an outlying county.

Tipton TN: 60% of employed residents work in other Tennessee counties, and probably most of these in Shelby.

Fayette, TN: 64% in other Tennessee counties.

Tate, MS: 32% in other Mississippi counties, and 19% in other states.   Since most of those working in other states probably work in Shelby County, only about 1/5 of the Mississippi intercounty workers have to be to DeSoto County.

Marshall, MS: 44% in other states, 22% in other Mississippi counties.

Benton, MS: (3153 employed workers): 22% in Benton County; 49% in other Mississippi counties, 29% in other states.  Basically gets included because there are very few jobs in the county, and the population is not high enough to support much of a commercial or service sector.  Likely no Walmart, few doctors, etc.   So you have school district employees and farmers.

50% of Benton employees worked in a M/MSA (this would include both outlying and central counties, but most of the jobs are going to be in Shelby and DeSoto counties, and places like Jackson, TN and Tupelo, MS are a long haul).

It wouldn't surprise me if there were a lot of people who worked for FedEx or other jobs at the airport.  Many of these would not be 9-5/M-F jobs, so the commute would be at off hours (it is right at 60 minutes).  If you wanted to own 40 acres in the country, it could be affordable, and if you were working 4 nights a week, have daylight to keep up on it.

Tunica, MS.  8% of workers in other Mississippi counties, 8% of workers in other states.  So Tunica is included based on the reverse flow of employees in the casino and related businesses (restaurants, hotels, bars) driving in. Tunica itself only has 3800 locally-employed employees.

There is also a contiguity requirement, but both Fayette, TN and Marshall, MS supply this to Benton, MS.

There is also the Combined Statistical Area, the lovely-named Memphis-Forrest City CSA.  Forrest City Micropolitan Statistical Area is sort of a satellite of Memphis Metropolitan Statistical Area with 15% employment interchange.

Texas Counties that have grown more than 5% between the 2010 Census and July 1, 2012

Andrews      16  9.0%   Permian Basin
Williamson  456  7.9%   Austin Suburbs
Kendall      35  7.6%   San Antonio Suburbs
Hays        168  7.6%   Austin Suburbs
Hemphill      4  7.2%   Panhandle
Fort Bend   627  7.2%   Houston Suburbs
Midland     146  7.1%   Permian Basin
Travis     1095  7.0%   Austin
Denton      707  6.7%   Fort Worth, Dallas Suburbs
Collin      834  6.7%   Dallas Suburbs
Montgomery  485  6.4%   Houston Suburbs
Guadalupe   139  6.3%   San Antonio Suburbs
Rockwall     83  6.0%   Dallas Suburbs
Comal       114  5.5%   San Antonio Suburbs
Lipscomb      3  5.4%   Panhandle
Ector       144  5.2%   Permian Basin
Gaines       18  5.1%   Permian Basin

The ten fastest-growing counties with a population over 10,000 and the likely reason for their growth were:
10) Franklin County, WA (Pasco)  - Tri-Cities area has been growing

All but Franklin County experienced double-digit growth.  Williams County, ND grew by almost 20%.

The growth in the Tri-Cities has been decidedly eastward (away from Hanford), and part of the Urbanized Area extends into Walla Walla County.    In 1980 the Tri-Cities were Richland 34K, Kennewick 34K, and Pasco 17K.  Pasco wasn't really a city, and it was a stretch to call it "Tri-"

In 2010, it was Kennewick 73K, Pasco 59K, and Richland 48K.

BTW, why are links preferred over perimeter?

There are three reasons to consider links.

1) Perimeter-based compactness measures have a well-known bias against subdivisions based on irregular natural features such as rivers and mountains. County-based division runs into this problem when counties use those same natural divisions. The other large class of compactness measures are based on bounding shapes like circles or polygons, which are weak at penalizing peninsulas jutting into a larger district. Links don't penalize natural irregular boundaries, but do weigh against jutting peninsulas.

2) County or municipal integrity are proxies for communities of interest. Links also are proxies for communities of interest with respect to associations between counties. Perimeter and area measures don't add anything to identify potential communities of interest. Links can add more than just a compactness measure.
 
3) Perimeter calculations or bounding methods require GIS software with enough sophistication to calculate lengths and areas. That's fine for those who are experts in the field, but I'm looking to make redistricting more accessible to the public. I'd like users to be able to proceed with a spreadsheet and standard mapping software like Mapquest or Google Maps. Links can be simply counted by the mapper using nothing more sophisticated than a highway map.

Any redistricting process that allows meaningful citizen input will have to provide the GIS and demographic data, and likely at least simple software.  The Census Bureau has road and street layers, and it image data can be meshed in as well.  The software used in the Ohio redistricting commission supported image data, but the Ohio sponsors did not wish to pay the licensing fees to Google/Bing.

It's not only the cost and availability, but also the level of sophistication needed by the user. Most perimeter calculations are not simple to understand without a reasonable background in geometry. Counting links is not hard, just like counting county splits is an easy thing fr a user to see and understand. The math of counting links gets only a little more complicated when comparing plans with different region counts, and is still less complicated than understanding a purely geometrical concept.

Eve if the math for perimeters were easy to understand, it leaves the problems associated with perimeter-based formulas as I noted in point 1.

Relative compactness measures are used in an attempt to restrict abuse by gerrymanders that use block assignment.  But the true abuse is block assignment.  Total perimeter length is just as effective (more effective in actuality) as county links in measuring compactness of county-based plans.

Perimeter is a grade-school math concept.   Given a simplified outline anyone could measure it on a map.  Not they wouldn't have to, since any reasonable software would be calculating it as they clicked, particularly it it were a contest criteria.

The map of Washington was not necessarily what a contest entrant would see.  It was a presentation of the data that was being used for the contest.  Both the actual borders, and the simplified borders would be available, as well as information about whether the border was passable or not.

It is certainly easier to measure the length of the Okanogan-Lincoln border or the Columbia-Franklin border than to try to figure out why I think one is "1" and the other is "0", and you think the opposite.

BTW, why are links preferred over perimeter?

There are three reasons to consider links.

1) Perimeter-based compactness measures have a well-known bias against subdivisions based on irregular natural features such as rivers and mountains. County-based division runs into this problem when counties use those same natural divisions. The other large class of compactness measures are based on bounding shapes like circles or polygons, which are weak at penalizing peninsulas jutting into a larger district. Links don't penalize natural irregular boundaries, but do weigh against jutting peninsulas.

2) County or municipal integrity are proxies for communities of interest. Links also are proxies for communities of interest with respect to associations between counties. Perimeter and area measures don't add anything to identify potential communities of interest. Links can add more than just a compactness measure.
 
3) Perimeter calculations or bounding methods require GIS software with enough sophistication to calculate lengths and areas. That's fine for those who are experts in the field, but I'm looking to make redistricting more accessible to the public. I'd like users to be able to proceed with a spreadsheet and standard mapping software like Mapquest or Google Maps. Links can be simply counted by the mapper using nothing more sophisticated than a highway map.

Any redistricting process that allows meaningful citizen input will have to provide the GIS and demographic data, and likely at least simple software.  The Census Bureau has road and street layers, and it image data can be meshed in as well.  The software used in the Ohio redistricting commission supported image data, but the Ohio sponsors did not wish to pay the licensing fees to Google/Bing.

There are ways to simplify borders for calculating perimeter.  This has the additional advantage of resolving whether one can directly link Lincoln and Okanagan counties, since there is an extreme penalty for doing so.

Is that the actual test required by Section 4? I haven't really dug through the oral arguments, but I do recall it being mentioned that almost any standard would capture Alabama (and thus, force any possible constitutional issue to be settled on preclearance itself).

The "standard" would be, "we know those Alabamians are a devilish lot, and we need to keep an eye on them."

If black Alabamians are just as likely white Alabamians, how can it be said that their right to vote is being denied or abridged.   If black Massachusetts citizens are 15% less likely to vote than white Massachusetts citizens, how can it be said that Massachusetts is not discriminating against blacks?  What other explanation is there?

I don't believe your erosity estimate is robust enough or accurate enough to be used as a metric.

First, Tennessee is not shaped like a circle, and 10 is not a large number.

And while the total perimeter of a large number of circles does approach a limit of sqrt(N) * 2*pi*R, where R is the radius of the containing circle, it might not do so monotonically.   7 small circles can be placed in a hexagon shape, with rounded vertices that would have a relatively small outer bounding circle.  Add in an 8th and the bounding circle will expand quite a bit, remove a 7th, and the shrinkage will be small.  Going from 6 to 7 had little cost, going from 7 to 8 a large amount.

This can be illustrated with an idealized-Iowa-like state which has infinite granularity but where boundaries are restricted to North-South and East-West lines.   We draw equal sized districts (the population density is non-varying).



P is the total perimeter of the districts, so the shared (green) perimeters are counted twice, and the outer black perimeter is counted one.  This allows us to use sqrt(N) for our estimate, rather than sqrt(N)-1.   This has the advantage that sqrt(1) is non-zero, while sqrt(1)-1 is zero.

So the perimeter of our single district state is 4.00, while for a 2-district state it is 6.00.  But E, the estimate of the 2-district perimeter, is sqrt(2/1)*4.00 or 5.66.  We grossly underestimated our total perimeter.   This is not that surprising.   Our districts are non-compact by Iowa standards, with a length twice their width.

We continue to 3 district, where P is 7.33.  Our estimate is based on the 2-district case.  That is E(N+1) = P(N)*sqrt((N+1)/N).   E(3) = 6.00 * sqrt(3/2) = 7.35.  In this case our estimate is good.   We have the very-elongated district L:W = 3:1, and two somewhat compact districts L:W = 4:3.  This really says that 3 districts are about as good or about as bad as 2 districts.  If we based our estimate for 3 districts on the 1 district case, our estimate would be 4.00*sqrt(3/1) or 6.93, which would have been too optimistic.

But for a 4-district case P is 8.00, but our estimate of P(3)*sqrt(4/3) = 8.47 is much higher.  Our districts are all maximally compact.

As we continue on, the estimate for 5 districts is quite low, followed by slightly high, slightly low, slightly high, and then quite high when we once again reach a compact symmetric case for 9 districts.

The first example really wasn't how we were subdividing regions.  In this 2nd example, we nibble off smaller regions one at a time.



Somewhat surprising is the two-district case, where we do better than estimated, and much better than where we split into two equal areas.  But it less surprising when we recognize that both regions are fairly compact, with only a corner missing from an almost square larger district.  And of course smaller areas have smaller perimeters (P1/P2 = sqrt(A1/A2) for two similar polygons.  The perimeter of the small region with 1/9 the of the total area, has a perimeter of 1/sqrt(9) or 1/3 of that of the total area.

Adding a 3rd district is not quite as compact as expected base on the two-district case.  But our larger regions is beginning to become less compact.  Our estimate based on two-districts was 6.53.  We only did 6.67.   But an estimate based on 1-district is 6.93, and when we create 3 equal area districts the perimeter is 7.33.

Adding a 4th district is quite efficient as we only have to chop off the panhandle of our large region.   Our 4 districts are are as compact as 3 equal area districts can be, and better than the 4-district symmetric equal-area case of our first set of examples.  That is, we can get a smaller perimeter by having greater variation in region size.

As we continue on, we are worse or better than the estimate based on the previous case E(N+1) = P(N)*sqrt((N+1)/N), depending on if we are able to cut off a panhandle of larger district, or the new district is cut off from the body. In all cases, other than for N=8, we are better than the equivalent equal-area version for the same number of districts.

It is instructive to look at the 4-district case in more detail.  An estimate based on 1 district would be that we would have a perimeter of 8.00.  We managed to do better, with a 7.33.  And based on the 4-district case, we should be able to do 9-districts in 7.33*sqrt(9/4) with a perimeter of 11.00.   We managed to do only 12.00 even with maximally compact districts.

What went wrong?  We essentially gamed the system by creating districts for grossly different size, and then were unable to maintain that when subdividing the larger region.  

If we use your proposed estimate method, which only measures interior perimeters, our estimate is even worse.  The interior perimeter of the 4-district case is 1.67.  The estimate for the 9 district case would be 1.67 * (sqrt(9) - 1)/(sqrt(4) - 1) = 3.33.  But in reality it is 4.00.

If we adjust these numbers so they are equivalent to my values for total perimeter, the estimate for the  9-district case would be 10.67, which is even further from my estimate of 11.00, and the actual value of 12.00.  Your estimate is based on how well you did in creating the first three small districts, with no knowledge of the area in the larger district beyond other than one side and an idea of its area (because we knew that it could be divided into 6 more areas).

We could do better, by making an estimate for dividing the larger area into 6 districts.  The total perimeter for the 4-district case is 7.33, 4.00 of which is the total perimeter of the 3 small districts, and 3.33 for the 4th district.  The estimate for the total perimeter after dividing the larger area into 6 districts is 3.33 * sqrt(6/1) = 8.16.  Add in the 4.00 for the original 3 districts, and the estimate is 12.16, which is just above the actual 12.00.   We went from a slightly non-compact area (length:width of 3:2) to 6 maximally compact districts.

In your Tennessee example, a better estimate of dividing the eastern edge of the state into 3 districts could be obtained from using that area alone, and not basing it in part on the rest of the state which had a mix of district sizes between smaller ones in the Memphis and Nashville areas, and the more rural areas between the mountains and the Mississippi.

If we use county-county links to measure erosity, this is problematic, since it would require determining links between counties in Virginia, North Carolina, and Georgia, and those in Eastern Tennessee.  There may be scaling problems because of county size styles.   And how well we divide eastern Tennessee is probably only marginally related to how easy it is to travel across the mountains between Tennessee and North Carolina.   A better approach would be to calculate the internal erosity among all counties in the area being divided, and estimate downward.

There are 25 counties in your 3-district Eastern region, 6 counties in your greater Nashville region 2-district region, and 14 counties in your Western-Memphis region.   The inter-county link counts for these 3 regions is 50, 9, and 26 respectively.

We can estimate the erosity if each of these county areas were consolidated into N regions:

Erosity(N)/County_Links =  (sqrt(N) - 1) / (sqrt(ncounties) - 1)

For the eastern region:

Erosity(3) = 50 * (sqrt(3) - 1) / (sqrt(25) - 1) = 9.15

For the greater Nashville region:

Erosity(2) = 9 * (sqrt(2) - 1) / (sqrt(6) - 1) = 2.57

For the western-Memphis region:

Erosity(2) = 26 * (sqrt(2)-1) / (sqrt(14) - 1) = 3.93

These are reasonably close for the first two, if we ignore your proposed county splits (10 and 3).  As to be expected, we missed badly in the 3rd, because there we simply chopped part of Shelby County from the region.

Add these to the 5-region erosity for a final estimate:

42 + 9.15 + 2.57 +3.93 = 57.65

BTW, why are links preferred over perimeter?

The southern border of Colorado should be straightened out.

Which professor was "clubbed"? I don't recall that.

Which population measure is used for the differential? Is it CVAP?

Henry Louis Gates

CVAP - it's from the Current Population Survey - which includes voting questions following each even-year November election.

Voting and Registration in the Election of November 2010 - Detailed Tables

Here is an update coverage formula:

If a racial or ethnic minority that constituted 3% or more of the population, had registration or voting in the 2010 election that was 5% or more below that for non-Hispanic whites, it is covered.

States that are not covered:

Southern states where black participation is comparable to white participation.
AL, LA, MS, SC, TN

Midwestern states where black participation is comparable to white participation
IN, MO, OH

State where AIAN participation is comparable to white participation
ND

States with no significant non-white population.
IA, ME, NH, VT

Covered:
AK: B(lack), H(ispanic), AIAN
AZ: B H
AR: B
CA: B H A(sian)
CO: B H
CT: B H
DE: B H
DC: B H
FL: H
GA: H
HI: B H NHAOPI
ID: H AIAN
IL: A H
KS: B H AIAN
KY: B
MD: A H
MA: B A H
MI: B
MN: B
MT: AIAN
NE: H
NV: B A H
NJ: A H
NM: H AIAN
NY: B A H
NC: B H
OK: B H AIAN
OR: H
PA: H
RI: B H
SD: AIAN
TX: B A H
UT: H O(ther)
VA: B A H
WA: B A H O
WV: B
WI: B
WY: H AIAN

Formula used White non-Hispanic alone; Black alone; Asian alone; Hispanic (of any race), so Black Hispanic, and Asian Hispanic are counted in two groups.

The Census Bureau does not break out AIAN, NHAOPI, and Other racial categories.   I subtracted from Total, the White non-Hispanic alone, Black alone, Asian alone, and Hispanic (of any race) to get an "Other" population.  This resulted in a double exclusion of non-White Hispanics (New York ended up with a negative value because of the relatively large number of Puerto Ricans and naturalized Dominicans who also identify as Black.  I generally characterized this population as AIAN: AK AZ ID KS MT NM ND OK SD WY.  HI was classified as NHAOPI, NC as a mixture of AIAN and multi-racial; and NV, UT, and WA as a combination of AIAN and NHAOPI.   Because of the methodology these numbers are statistically unreliable.

So is one outcome that SCOTUS throw out Sect V unless an up-to-date Sect IV is created? If so, Congress could use the table above, but it would seem unlikely with the current divisions.

The questioning in oral arguments certainly suggested that an up-to-date formula


The current test is based on a combination of certain state actions in conjunction with low overall participation.  The actions included use of literacy tests or failure to provide election materials in Spanish for the 1972 election.   But it has been decades since literacy tests have been used.  And any failure to provide Spanish language materials has been largely incidental and not systemic.

The low overall voter participation is not necessarily an indication of state discrimination, and even it was it is quite rare for turnout to below 50% of CVAP (only Hawaii in 1996 and 2000 failed).  Only about a half dozen states would fail a 60% test (some of this is due an aging of the population - 1972, baby boomers were 8 to 27, with the older ones in their prime non-voting years).  In 2008, there was a 24% differential in those not voting between 18-24 51.5% not voting, and 65-74 27.6%.

About all you have to go on is disparate effect.  What is Massachusetts doing that causes Blacks to not participate in elections?  If nothing, then it will be easy to preclear any changes.  It's probably not a good idea to be changing polling places 60 days before an election, except in extreme circumstances, such as a polling place being severely damaged by flood or fire.  At worst it will cause Massachusetts to evaluate what they are doing - sort of like the good kind of affirmative action.

If the 2008 election were used, KY and MI would be off the covered list, and IN, IA, LA would be

In 2008, many states were being caught on a 5% differential in White-Black registration, which was not being matched in voting.  Blacks who reported being registered to vote were turning out at higher rates than whites who reported being registered to vote,

The CPS doesn't have a large enough sample size to be reliably used for racial groups in individual states.   The base estimates of persons who were over 18 of a particular race were bouncing all over the place between 2008 and 2012, without even adding complications about citizenship and voting behavior, which are a couple of questions that might be misreported (income is also probably misreported).

It might be able to use the ACS, without any questions about voting behavior.  This permits a larger sample over a longer period of time.   The November CPS has the voting question because it is believed respondents will have a better memory of whether they had voted a few weeks earlier.   The ACS could be matched with statewide voter registries, assuming they also included whether a voter had voted or not.

I can't speak to Shelby County in particular, but if one were to apply the standards in the VRA, but replace 1964, 1968, and 1972 with 2000, 2004, and 2008, Alabama would not be subject to statewide preclearance.  They had over 50% of the voting age population vote in all three of those elections.  [The atlas does not yet have the 2012 numbers.]

2000 had by far the lowest turnout of those three elections.  Here's a map with the states in green having below 50% of the VAP voting in 2000, but over 50% in both 2004 and 2008 while the states in yellow were below 50% in 2000 and at least one of 2004 or 2008.

You would have to use CVAP.    The 15th Amendment is explicitly limited to citizens.

Since 1992, Hawaii was the only state to fall below 50% voting in a presidential election, in 1996 and 2000.

Even 60% would not be a difficult test to meet.

There's been a robust debate about erosity ad connectivity on another thread, but it brings up an issue to consider here. If we assume some sort of connection map, whether by the definitions above or on the referenced thread, there is the question about counting the severed connection (erosity) or the maintained connection (connectivity). I think there are two strong reasons to support erosity as the better measure.

First, if there are no split counties or a plan makes a split into a number of apportionment regions of a whole number of districts then there is no relevant difference. For example if there is no weighting then a plan that has L total links and the regions cut x links, then the erosity is X and the connectivity is L-x. Comparing two different plans with the same number of regions is just a matter of preferring a lower number for erosity or a higher number for connectivity, but the ranking is the same. Adding weights to the links doesn't change this math. One suggestion was to modify weights based on the need to split certain counties, which could change the math by changing L for the plans. I think this creates an unneeded distortion and the ranking on that thread did not change based on the weighting method.

Plan 1: 45 enclosed links, 137 weight. (115 original measure)
Plan 2: 46 enclosed links, 144 weight. (122)
Plan 3: 40 enclosed links, 121 weight. (99)
Muon: 44 enclosed links, 130 weight. (105)

However there are reasons why measuring the cut links could have an advantage over the measuring the remaining enclosed links. Part of this starts with some geometrical theory. The links in the map are associated with boundary pieces between counties. As such they correspond to line segments on a map rather than areas. Suppose one has a nearly circular area to divide into a number of nearly circular pieces (I'm using nearly circular as approximate language for compact and when the number of divisions is large it's a very good approximation.) The total area enclosed does not change with the number of pieces but the total length of the boundaries do. In fact in the limit of a large number of circular pieces N the area is fixed but the boundary increases by a factor equal to sqrt(N) - 1. Since the erosity is tracking the boundary one would expect it to follow that relation based on the number of regions. Connectivity has no analogous formula related to the number of regions since it requires knowledge of the total link count L as well as the number of regions.

Of course in the case of equal region counts I've already claimed it doesn't matter, but if one wants to compare plans with different region counts it does. Here the recent discussion about TN is a good illustration. And for simplifying the discussion I'll use an unweighted set of connections as I did in that thread.



There were two plans of seven regions with erosities of 63 and 60 respectively.



However, Torie made a case for an eastern region that was based on the natural geography. My result was a plan that only has five regions but an erosity of 42.


Forcing a choice based on a higher number of regions excludes a potentially reasonable 5-region plan. Connectivity offers no direct way to compare a five-region plan to a plan with seven regions, but erosity does. Since the erosity should scale by sqrt(N) - 1, all the plans can be projected to the equivalent 9-district erosity by using that scale factor. The 7-region plan with erosity of 60 scales to an equivalent 9-district erosity of 72.9 (60 * 2 / 1.646). The 5-region plan with an erosity of 42 scales to an equivalent 9-district erosity of 68.0 (42 * 2 / 1.236). The scaling shows that though two additional county splits would be needed in a 5-region plan, the natural division of the east does provide a reduced erosity when scaled appropriately.

I don't believe your erosity estimate is robust enough or accurate enough to be used as a metric.

First, Tennessee is not shaped like a circle, and 10 is not a large number.

And while the total perimeter of a large number of circles does approach a limit of sqrt(N) * 2*pi*R, where R is the radius of the containing circle, it might not do so monotonically.   7 small circles can be placed in a hexagon shape, with rounded vertices that would have a relatively small outer bounding circle.  Add in an 8th and the bounding circle will expand quite a bit, remove a 7th, and the shrinkage will be small.  Going from 6 to 7 had little cost, going from 7 to 8 a large amount.

This can be illustrated with an idealized-Iowa-like state which has infinite granularity but where boundaries are restricted to North-South and East-West lines.   We draw equal sized districts (the population density is non-varying).



P is the total perimeter of the districts, so the shared (green) perimeters are counted twice, and the outer black perimeter is counted one.  This allows us to use sqrt(N) for our estimate, rather than sqrt(N)-1.   This has the advantage that sqrt(1) is non-zero, while sqrt(1)-1 is zero.

So the perimeter of our single district state is 4.00, while for a 2-district state it is 6.00.  But E, the estimate of the 2-district perimeter, is sqrt(2/1)*4.00 or 5.66.  We grossly underestimated our total perimeter.   This is not that surprising.   Our districts are non-compact by Iowa standards, with a length twice their width.

We continue to 3 district, where P is 7.33.  Our estimate is based on the 2-district case.  That is E(N+1) = P(N)*sqrt((N+1)/N).   E(3) = 6.00 * sqrt(3/2) = 7.35.  In this case our estimate is good.   We have the very-elongated district L:W = 3:1, and two somewhat compact districts L:W = 4:3.  This really says that 3 districts are about as good or about as bad as 2 districts.  If we based our estimate for 3 districts on the 1 district case, our estimate would be 4.00*sqrt(3/1) or 6.93, which would have been too optimistic.

But for a 4-district case P is 8.00, but our estimate of P(3)*sqrt(4/3) = 8.47 is much higher.  Our districts are all maximally compact.

As we continue on, the estimate for 5 districts is quite low, followed by slightly high, slightly low, slightly high, and then quite high when we once again reach a compact symmetric case for 9 districts.