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51  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 28, 2014, 01:35:39 am
AZ (2)
   AZ-Gila and Rim 2575K
   AZ-Maricopa 3817K
I would consider letting Pinal County switch.

I would propose the following names:

Arizona
Grand Canyon
Grand Canyon State

Phoenix
Valley of the Sun

With so few counties, and their large area, there could be hearings in each county seat, as well as the Navajo, Hopi, Tohono O'odham, Fort Apache, and San Carlos Indian reservations.   Perhaps also, Mesa, Scottsdale, Sun City, Goodyear, and Colorado City.
52  General Politics / Political Geography & Demographics / Re: City of Hudson's weighed voting system under scrutiny on: June 26, 2014, 11:23:32 pm
It appears that Nassau County's weighted voting for the Board of Supervisors was introduced in 1936, much earlier than I had thought.  After a constitutional amendment was passed in 1935, county charters were granted to four large counties: Monroe, Westchester, Nassau, and Suffolk, one containing Rochester and the other three in the New York City suburbs.

Unlike modern county charters which are written and approved by the county citizens, these were written by the legislature.  Nassau County only had three towns and two cities, and it appears to have tried to compensate for this.

The largest town, Hempstead had 60% of the population and was given two supervisors on the board of supervisors.  The other two towns and two cities were given one supervisor each.  The voting weight of each entity was its census population divided by 10,000.  The charter specified the whole number of the quotient - it is unclear if that means truncation, by dropping the fractional remainder; or rounding to the nearest whole number.  Each entity was guaranteed one vote.  The votes for Hempstead were to be divided evenly between the two supervisors, which suggests that an even number total.  

And finally, no town could have a majority on the board.  In 1937, the county attorney interpreted this to mean that the Hempstead representation would be reduced so that it was less than a majority, without increasing the representation of the other units.  In addition a majority was considered to be a majority of the originally apportioned totals.  In effect, the votes were taken from Hempstead - and converted to permanent Noes.

As might be expected the result was not very good.  Hempstead, based on population would be entitled to 19 votes on a 31-vote council.  But the charter required its representation to be reduced to an even number less than a majority, or 14, which was divided between the two supervisors.  But the majority threshold was kept at 14.  This increased the power of North Hempstead and Oyster Bay since they became critical members of more coalitions.  Since the two Hempstead members could not form a majority, they needed another member to join them.  And since the majority threshold remained at 16, the four smaller entities could still not win.

Town           Vote   Swing  R.Pop.  R.Pow   Dev.  
Hempstead          7      13  61.62%  52.00% -15.61%
                   7      13
North Hempstead    6      11  20.53%  22.00%   7.19%
Oyster Bay         4      11  12.17%  22.00%  80.83%
Glen Cove          1       1   3.77%   2.00% -46.97%
Long Beach         1       1   1.92%   2.00%   4.20%

With only 6 members, there are only 64 voting combinations, with a total of 192 members voting No.  But since two members have the same vote, there are only 48 unique combinations of voting weights (for every combination where Hempstead 1 votes Aye, and Hempstead 2 votes Nay; there is an equivalent combination where the two votes are reversed).  And in this particular case, the number of votes for the two cities was also the same, reducing the combinations of voting weights to 36.  There is simply not enough material to work with, even when manipulating weights.

Historical tidbits: Queens County used to include the area that is now Nassau County.  First the western part of the county was made a borough of New York City, and then the eastern part of the county was detached to form Nassau County.  It was named after the Dutch name for Long Island, Isle of Nassau.

The original Queens County had 6 towns, Flushing, Jamaica, and Newtown were dissolved when Queens became part of New York City.  Flushing and Jamaica are still recognized areas of Queens.  Newtown was in the northern part of Queens, to the west of Flushing (opposite Manhattan).  Long Island City was an incorporated city in the western part of Newtown, where it also the name of a neighborhood.

The other three towns of Hempstead, North Hempstead, and Oyster Bay became Nassau County.  The Rockaway peninsula was detached from Hempstead and was also added to Queens Borough.   Glen Cove and Long Beach were created after the division.  In New York, cities can only be created by the state legislature, and the last, Rye, was chartered in 1942.  Villages may be created by the citizens, which is why the suburbs are covered with villages.

In New York, a village remains part of its town, while a city is independent.  In effect, it is similar to an independent city in Virginia, with the independence being from a different level of government.

Kings and Queens, Dukes, and Dutchess counties were created at the same time.  Dukes still exists, but as a Massachusetts county.  The original Dukes County included Martha's Vineyard, Nantucket, and the Elizabeth Islands.  The county was transferred to Massachusetts Bay Colony in 1691, where it is the only county with a royal name.

By 1940, Hempstead's share of the population continued to grow, and instead of 26 of 41 votes was restricted to 20 of 41, with 6 imputed Noes.  The restriction helps Hempstead's power match its population, and it also provides an opportunity for the two small cities to be the critical vote.  Since Hempstead is limited to just shy of a majority, either city can join with the two Hempstead supervisors to form a bare majority.  But Oyster Bay and North Hempstead are badly out of balance.

Majority = 21
Town           Vote   Swing  R.Pop.  R.Pow   Dev.  
Hempstead         10      15  63.75%  60.00%  -5.89%
                  10      15
North Hempstead    8       9  20.50%  18.00% -12.20%
Oyster Bay         4       9  10.47%  18.00%  71.89%
Glen Cove          1       1   3.05%   2.00% -34.47%
Long Beach         1       1   2.22%   2.00%  -9.97%

In 1950, Hempstead reached its peak share of population, but the weightings still badly mismatched.

Majority = 35
Town           Vote   Swing  R.Pop.  R.Pow   Dev.  
Hempstead         17      15  64.29%  55.56% -13.58%
                  17      15
North Hempstead   14      11  21.20%  20.37%  -3.90%
Oyster Bay         7       7   9.95%  12.96%  30.30%
Glen Cove          2       3   2.25%   5.56% 147.03%
Long Beach         2       3   2.32%   5.56% 139.80%

In 1960, Oyster Bay had passed North Hempstead as the second largest town.  While Oyster Bay proper is on Long Island Sound, the town spans the whole eastern edge of the county.  Its population quadrupled in the decade, as developed surged through Nassau County which nearly doubled to 1.3 million during the decade, and on into Suffolk County that increased 141%

Majority = 66
Town           Vote   Swing  R.Pop.  R.Pow   Dev.  
Hempstead         32      15  56.97%  55.56%  -2.49%
                  32      15
Oyster Bay        29      11  22.31%  20.37%  -8.69%
North Hempstead   22       7  16.85%  12.96% -23.07%
Glen Cove          2       3   1.83%   5.56% 203.28%
Long Beach         3       3   2.04%   5.56% 172.85%

The 1960 data was that which Banzhaf based his 'Weighted Voting Doesn't Work: A Mathematical Analysis' on.  His tables indicate that the apportionment was based on citizen population (excluding aliens), and that the weights were determine by dividing the (citizen) population by 10,000 then truncating the fraction.   It makes no difference in the result, and in terms of error is slightly worse.

Majority = 63
Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Hempstead         31      15  57.11%  55.56%  -2.72%
                  31      15
Oyster Bay        28      11  22.38%  20.37%  -8.99%
North Hempstead   21       7  16.71%  12.96% -22.44%
Glen Cove          2       3   1.78%   5.56% 211.52%
Long Beach         2       3   2.01%   5.56% 176.28%

Banzhaf had apparently assumed that a "majority" was a majority of the votes cast, and not a
majority of the votes initially apportioned and produced this table that showed that not only did the two small cities have no effect on the result, but that the supervisor from North Hempstead who represented 1/5 of the population.

Majority = 58
Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Hempstead         31      16  57.11%  66.67%  16.73%
                  31      16
Oyster Bay        28      16  22.38%  33.33%  48.93%
North Hempstead   21       0  16.71%   0.00%-100.00%
Glen Cove          2       0   1.78%   0.00%-100.00%
Long Beach         2       0   2.01%   0.00%-100.00%
53  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 26, 2014, 12:22:11 am
New York, New York.  The deviations get pretty high here, for obvious reasons.



District 1: LONG ISLAND.  Population 2,832,868 (deviation -1,042,747).  Obama 53.2%, Dem 55.2%.  Nassau and Suffolk.  A natural pair.  Way underpopulated, and there is absolutely nothing you want to, or even can do, about it- Queens needs to be in one of the two NYC districts, and adding it would overcorrect things even worse, and there's no compelling COI reason to go noncontiguous (or cross the Sound, which is functionally going noncontiguous).  Tilt D.
I'm going to use the following nomenclature: Long Island (NY)

Quote
District 2: BROOKLYN-QUEENS.  Population 4,735,422 (deviation +859,807).  Obama 77.4%, Dem 79.5%. Obviously very diverse, min-maj with no dominant group: 32W/25B/23H/16A (by VAP it's 33W/23B/21H/16A).

NYC is obviously getting split into two districts here that average out to being slightly overpopulated; Queens + Bronx might actually have lower deviations (and would be contiguous), but in terms of COI the two LI boroughs belong together, I think.  Piece of evidence #1: the other three boroughs are part of the New York Public Library system, but Brooklyn and Queens are separate.  Piece of evidence #2: isn't it obvious that we should have one district for the Knicks and another for the Nets?  Anyway, Safe D.
An alternative would be Kings&Queens (NY) but Brooklyn-Queens (NY) is fine.

Quote
District 3: NEW YORK, NEW YORK. Population 3,439,726 (deviation -435,889).  Obama 81.4%, Dem 77.9%.  Again, min-maj, but more Hispanics and less blacks and Asians: 35W/19B/36H (39W/19B/33H by VAP).  The other three boroughs; perhaps it's not fair to Brooklyn that those people just get to be called New York, but "Manhattan-Bronx-Staten Island" is a mouthful.  It looks noncontiguous on the map, but I'm gonna say that the Staten Island Ferry counts as the requisite transportation link here.  Safe D.
At one time (IIRC, around the 1820s), Richmond, Kings, and Rockland counties comprised a congressional district.   At that time, Westchester County extended south to the Harlem River (Westchester town was in the southern part of what is now the Bronx), and Queens County included present day Nassau County, so matching the 3 water connected counties was not seen as that extreme.

If we were dividing up NYC, we'd recreate Brooklyn and reasonably include Queens.  Staten Island could be separate.  And if we are extending Brooklyn east, we could extend "the Bronx" north as far as White Plains and restore the Westchester name.  The remnant of Westchester would have to come up with its own name or be merged with Putnam.

Is the proposed name: New York, New York (NY) or New York, (NY)?  I'm fine with New York City (NY) or Manhattan-Bronx (NY) as well.

Quote
District 4: NEW YORK HUDSON VALLEY AND NORTH.  Population 3,941,721 (deviation +66,106).  Obama 56.2%, Dem 57.5%.  Kind of a mishmash, hence the uninspiring name: northern NYC suburbs, Hudson Valley, the Capitol Region, and the North Country.  I went by media markets and metro areas, as usual; the biggest judgment call was putting the North Country and Watertown in here rather than the Binghamton area, but this configuration had modestly lower deviations.  Eh, could go either way on that.  Lean D.
Hudson Valley and North Country (NY) ?

Quote
District 5: NEW YORK CENTRAL AND WESTERN.  Population 4,4428,337 (deviation +552,722).  Obama 53.5%, Dem 52.7%.  Utica, Syracuse, Ithaca, Rochester, Buffalo.  Western NY is more of an identity than whatever got thrown in District 4, at least.  Tossup.
Central and Western New York (NY)

How much would people in Syracuse object to a shorter Western New York (NY)?
54  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 25, 2014, 11:57:39 pm
This is a first cut based on equipopulous districts.  I think it may improve a bit as districts are split out.  With equal populations, you get a bit of problem with harmonics.  The weighting is based on population divided by 2,000, due to a limitation in the implementation of the algorithm that I am using.  I initially started with 10,000 as a divisor and worked my way downward.  I couldn't get it to work with 1,000.  Going from 10,000 to 2,000 the standard deviation declined from 1.90% to 1.53%, so some of the error is due the apportionment resolution.

With 100 districts, there are 2100 = 1.268x1030 voting combinations.  Since there are an average of 50 voters on the losing side, there are 6.338x1031 possible vote switches from No to Yes.  A total of 4.848x1030 of these are critical and will flip the outcome.  Overall, 7.6% of vote switches are critical.


District         Vote    Swing    R.Pop.   R.Pow    Dev. 
California 1     1867  5.86E+28   1.208%   1.209%   0.07%
California 2     1867  5.86E+28   1.208%   1.209%   0.07%
California 3     1867  5.86E+28   1.208%   1.209%   0.07%
California 4     1867  5.86E+28   1.208%   1.209%   0.07%
California 5     1867  5.86E+28   1.208%   1.209%   0.07%
California 6     1867  5.86E+28   1.208%   1.209%   0.07%
California 7     1867  5.86E+28   1.208%   1.209%   0.07%
California 8     1867  5.86E+28   1.208%   1.209%   0.07%
California 9     1867  5.86E+28   1.208%   1.209%   0.07%
California 10    1867  5.86E+28   1.208%   1.209%   0.07%
Texas 1          1805  5.66E+28   1.168%   1.168%   0.05%
Texas 2          1805  5.66E+28   1.168%   1.168%   0.05%
Texas 3          1805  5.66E+28   1.168%   1.168%   0.05%
Texas 4          1805  5.66E+28   1.168%   1.168%   0.05%
Texas 5          1805  5.66E+28   1.168%   1.168%   0.05%
Texas 6          1805  5.66E+28   1.168%   1.168%   0.05%
Texas 7          1805  5.66E+28   1.168%   1.168%   0.05%
New York 1       1942  6.10E+28   1.256%   1.258%   0.10%
New York 2       1942  6.10E+28   1.256%   1.258%   0.10%
New York 3       1942  6.10E+28   1.256%   1.258%   0.10%
New York 4       1942  6.10E+28   1.256%   1.258%   0.10%
New York 5       1942  6.10E+28   1.256%   1.258%   0.10%
Florida 1        1890  5.93E+28   1.223%   1.224%   0.08%
Florida 2        1890  5.93E+28   1.223%   1.224%   0.08%
Florida 3        1890  5.93E+28   1.223%   1.224%   0.08%
Florida 4        1890  5.93E+28   1.223%   1.224%   0.08%
Florida 5        1890  5.93E+28   1.223%   1.224%   0.08%
Illinois 1       1608  5.04E+28   1.040%   1.040%  -0.05%
Illinois 2       1608  5.04E+28   1.040%   1.040%  -0.05%
Illinois 3       1608  5.04E+28   1.040%   1.040%  -0.05%
Illinois 4       1608  5.04E+28   1.040%   1.040%  -0.05%
Pennsylvania 1   1592  4.99E+28   1.030%   1.029%  -0.04%
Pennsylvania 2   1592  4.99E+28   1.030%   1.029%  -0.04%
Pennsylvania 3   1592  4.99E+28   1.030%   1.029%  -0.04%
Pennsylvania 4   1592  4.99E+28   1.030%   1.029%  -0.04%
Ohio 1           1928  6.05E+28   1.247%   1.248%   0.10%
Ohio 2           1928  6.05E+28   1.247%   1.248%   0.10%
Ohio 3           1928  6.05E+28   1.247%   1.248%   0.10%
Michigan 1       1652  5.18E+28   1.069%   1.068%  -0.02%
Michigan 2       1652  5.18E+28   1.069%   1.068%  -0.02%
Michigan 3       1652  5.18E+28   1.069%   1.068%  -0.02%
Georgia 1        1621  5.08E+28   1.049%   1.048%  -0.06%
Georgia 2        1621  5.08E+28   1.049%   1.048%  -0.06%
Georgia 3        1621  5.08E+28   1.049%   1.048%  -0.06%
North Carolina 1 1594  5.00E+28   1.031%   1.031%  -0.07%
North Carolina 2 1594  5.00E+28   1.031%   1.031%  -0.07%
North Carolina 3 1594  5.00E+28   1.031%   1.031%  -0.07%
New Jersey 1     1468  4.60E+28   0.950%   0.949%  -0.09%
New Jersey 2     1468  4.60E+28   0.950%   0.949%  -0.09%
New Jersey 3     1468  4.60E+28   0.950%   0.949%  -0.09%
Virginia 1       2009  6.31E+28   1.300%   1.301%   0.12%
Virginia 2       2009  6.31E+28   1.300%   1.301%   0.12%
Washington 1     1688  5.29E+28   1.092%   1.092%  -0.03%
Washington 2     1688  5.29E+28   1.092%   1.092%  -0.03%
Massachusetts 1  1640  5.14E+28   1.061%   1.061%  -0.03%
Massachusetts 2  1640  5.14E+28   1.061%   1.061%  -0.03%
Indiana 1        1625  5.09E+28   1.051%   1.051%  -0.06%
Indiana 2        1625  5.09E+28   1.051%   1.051%  -0.06%
Arizona 1        1603  5.03E+28   1.037%   1.036%  -0.06%
Arizona 2        1603  5.03E+28   1.037%   1.036%  -0.06%
Tennessee 1      1594  5.00E+28   1.031%   1.031%  -0.04%
Tennessee 2      1594  5.00E+28   1.031%   1.031%  -0.04%
Missouri 1       1503  4.71E+28   0.972%   0.971%  -0.08%
Missouri 2       1503  4.71E+28   0.972%   0.971%  -0.08%
Maryland 1       1447  4.53E+28   0.936%   0.935%  -0.14%
Maryland 2       1447  4.53E+28   0.936%   0.935%  -0.14%
Wisconsin 1      1425  4.46E+28   0.921%   0.921%  -0.09%
Wisconsin 2      1425  4.46E+28   0.921%   0.921%  -0.09%
Minnesota 1      1329  4.16E+28   0.860%   0.858%  -0.13%
Minnesota 2      1329  4.16E+28   0.860%   0.858%  -0.13%
Colorado 1       1261  3.95E+28   0.816%   0.814%  -0.19%
Colorado 2       1261  3.95E+28   0.816%   0.814%  -0.19%
Alabama          2401  7.56E+28   1.553%   1.559%   0.35%
South Carolina   2323  7.31E+28   1.503%   1.508%   0.32%
Louisiana        2277  7.16E+28   1.473%   1.477%   0.30%
Kentucky         2175  6.84E+28   1.407%   1.410%   0.22%
Oregon           1924  6.04E+28   1.245%   1.246%   0.08%
Oklahoma         1882  5.91E+28   1.218%   1.218%   0.06%
Connecticut      1791  5.62E+28   1.158%   1.159%   0.05%
Iowa             1527  4.79E+28   0.988%   0.987%  -0.07%
Mississippi      1489  4.67E+28   0.963%   0.962%  -0.10%
Arkansas         1463  4.58E+28   0.946%   0.945%  -0.11%
Kansas           1432  4.49E+28   0.926%   0.925%  -0.11%
Utah             1385  4.34E+28   0.896%   0.895%  -0.16%
Nevada           1355  4.24E+28   0.876%   0.875%  -0.12%
New Mexico       1034  3.24E+28   0.669%   0.667%  -0.20%
West Virginia     930  2.91E+28   0.602%   0.600%  -0.26%
Nebraska          916  2.87E+28   0.592%   0.591%  -0.26%
Idaho             787  2.46E+28   0.509%   0.508%  -0.26%
Hawaii            683  2.14E+28   0.442%   0.440%  -0.38%
Maine             667  2.09E+28   0.431%   0.430%  -0.25%
New Hampshire     661  2.07E+28   0.427%   0.426%  -0.28%
Rhode Island      528  1.65E+28   0.341%   0.340%  -0.27%
Montana           497  1.55E+28   0.322%   0.320%  -0.39%
Delaware          450  1.41E+28   0.291%   0.290%  -0.45%
South Dakota      410  1.28E+28   0.265%   0.264%  -0.32%
Alaska            361  1.13E+28   0.233%   0.233%  -0.29%
North Dakota      338  1.06E+28   0.219%   0.218%  -0.35%
Vermont           315  9.84E+27   0.204%   0.203%  -0.42%
Wyoming           284  8.87E+27   0.184%   0.183%  -0.42%
55  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 25, 2014, 09:07:03 pm
One thing I noticed is the wide range in district sizes even if all were equal within the states. There are so many small states that the average district in CA is 20% larger than average.
California would be apportioned a 100st seat, which makes the normative population:

PCA / sqrt(NCA (NCA + 1) )

= 37.34M / sqrt(110) = 3.56M.

States down to 3.56 / sqrt(2) = 2.52 would be small, but not exceptionally so.

NV is OK, while NM, WV, NE, ID, HI, ME, NH, RI, MT, DE, SD, AK, ND, VT, and WY are exceptionally small.

The US Constitution requires at least one representative for each state.  And weighted voting ensures that the standard of Wesberry v Sanders that "as nearly as practicable one man's vote in a congressional election is to be worth as much as another's." is complied with.

So I'm treating these states as special cases, similar to what is done in Canada for the far north, or the UK for the smaller islands.

Overall the divided states should have districts in the 2.5M to 5.0M range.  Go ahead and propose the western Massachusetts district, and let's wait to see if there are other comparable situations.

Were we dealing with a state legislature, where the counties are artificial legal subdivisions, rather than sovereign constituents, I would observe that the 28 states apportioned one representative have a population equivalent to 18.14 representatives, and seek to eliminate 10 small states, and apportion 10 more to the larger states:

CA+ = 11, MT-WY merged.
NY+ = 6, VT-NH merged (19 shared among smaller states).
FL+ = 6, ND-SD merged.
AL+ = 2, AK-HI merged (18 shared among smallest states)
TX+ = 8, DE attached to MD, combined continues with 2 districts.
OH+ = 4, CT-RI merged.
SC+ = 2, ME-(NH-VT) merged (17 shared among smallest states)
VA+ = 3, NE-(ND-SD) merged.
CA+ = 12, ID-(MT-WY) merged.

The next addition would be a division of CT-RI, but the next merger would be KY-WV, and the latter has a larger combined population than the former.

Our final combined state districts would be:

Far West (HI-AK)
Northern Rockies (ID-MT-WY)
Northern Plains (NE-SD-ND)
MD-DE (2) (with Delaware added to Maryland Chesapeake leaving Maryland Potomac unchanged).
Southern New England (CT-RI)
Northern New England (ME-NH-VT)
56  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 25, 2014, 03:37:35 pm
I have a question related to population equality. For example, If the Boston metro is kept intact, and there is contiguity, then the only division is to separate Worcester and the counties to the west from the rest of the state. That creates MA-Bay with 1.5 times the state's quota and MA-Berkshires with 0.5 times the quota. Is that acceptable? Given the nature of the exercise in weighting, it seems to me that it should be.
I was thinking of Massachusetts as a state where strict contiguity might not be required, because of the extreme concavity caused by Rhode Island.  You have to choose between (1) population imbalance; (2) Using all of Norfolk, which would violate community of interest; (3) splitting Norfolk which violates the rule on splitting counties; or (4) Having a non-contiguity between Worcester and Bristol.
57  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 25, 2014, 12:31:57 pm
Minnesota is almost pathetically simple:

Minnesota Instate (Hennepin, Ramsey, Anoka, Washington, Dakota, Scott, Carver, and Wright Counties): Population 2,974,213 (deviation +322,251).  Obama 57.2%, DFL 56.0%.  Sherbourne might go here, but then you get bits of St. Cloud in the Instate region, which is wrong.  Otherwise, every county that borders Hennepin/Ramsey, and the counties themselves.  Usually quite D.

Minnesota Outstate (all other counties): Population 2,329,712 (deviation -322,251).  Obama 49.9%, DFL 51.5%.  Pretty swingy.
Would Minnesota Twin Cities or Twin Cities (MN) or Minneapolis-St.Paul (MN) be preferred names?

Is Minnesota Outstate pejorative?   Is Minnesota or Minnesota State acceptable even though they are overinclusive?  There will be 28 districts that will be named for the state.

What would the unwashed bumpkins from the hinterland prefer?


Minnesota—Twin Cities would be more inclusive, and, I think, would be a fine alternative to "Instate".  (Locally, the region is the "Twin Cities Metro".)  "Outstate" isn't pejorative, to my knowledge.  I don't think there's any other tidy way to refer to "everywhere that isn't near the Twin Cities".  Calling the rest of the state just "Minnesota" or "Minnesota State" would be very confusing and strange.  The Twin Cities doesn't particularly see itself as independent of the rest of the state... many locals have a cabin up north.
We'll see what the proposed names in Arizona, Colorado, and maybe Washington, Wisconsin, and Indiana are.
58  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 25, 2014, 12:18:44 pm
Georgia is, for all its zillions of counties, really easy to do.  And even with the mandate for coarse equality it all ends up being well within plus or minus 10 percent.



District 1: SOUTH GEORGIA.  Population 3,013,994 (deviation -215,224).  Obama 45.7%, Dem 48.0%.  36% Black (34% Black VAP).  I used the Atlanta media market as the dividing line here: everything south of it is in 1, everything within it (plus the few peripheral northern counties in other markets such as Rome) in 2 and 3.  Likely R, there's an opening for a Blue Dog in a good year here, but it's probably a narrow one.

District 2: ATLANTA.  Population 3,365,297 (deviation +136,079).  Obama 61.4%, Dem 58.2%.  40W/38B/13H (44W/37B/11H VAP), so min-maj.  These five counties were the original Atlanta metro area in 1950 and I imagine they're still considered to be the core of it today.  Obviously the exurbs spill far out into District 3 by now.  Safe D.

District 3: NORTH GEORGIA.  Population 3,308,362 (deviation +79,144).  Obama 36.6%, Dem 35.9%.  Pretty self-explanatory.  Safe R.
Good, I was concerned that there would have to be two Atlanta districts, which would force areas like Dalton to be placed with Savannah and Albany.   To avoid this, it makes sense to trim the suburbs fairly tight.

I could see letting Forsyth, Douglas and Fayette, and perhaps others choosing to join Atlanta, but I bet that they would vote No.  We can also make an assumption that the districts are fairly stable, and these areas would not have been included with Atlanta if Georgia had received its 3rd district 30 years ago.  On the other hand, Forsyth had close to 200,000 4 years ago, after doubling within the previous decade.  That's not really exurban.

It appears you have done a good job delineating the counties that would identify with Columbus, Macon and Augusta.
59  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 25, 2014, 10:34:34 am
Minnesota is almost pathetically simple:

Minnesota Instate (Hennepin, Ramsey, Anoka, Washington, Dakota, Scott, Carver, and Wright Counties): Population 2,974,213 (deviation +322,251).  Obama 57.2%, DFL 56.0%.  Sherbourne might go here, but then you get bits of St. Cloud in the Instate region, which is wrong.  Otherwise, every county that borders Hennepin/Ramsey, and the counties themselves.  Usually quite D.

Minnesota Outstate (all other counties): Population 2,329,712 (deviation -322,251).  Obama 49.9%, DFL 51.5%.  Pretty swingy.
Would Minnesota Twin Cities or Twin Cities (MN) or Minneapolis-St.Paul (MN) be preferred names?

Is Minnesota Outstate pejorative?   Is Minnesota or Minnesota State acceptable even though they are overinclusive?  There will be 28 districts that will be named for the state.

What would the unwashed bumpkins from the hinterland prefer?

60  General Politics / Political Geography & Demographics / Re: City of Hudson's weighed voting system under scrutiny on: June 25, 2014, 08:55:00 am
Slater v. Cortland County Board of Supervisors 66 Misc.2d 108 (1971) found that Cortland County violated OMOV.  At the time, Cortland County continued to use the traditional form with one supervisor for each of the 15 towns and 6 wards of the city of Cortland.  The 11 smallest towns with about 1/5 of the total population could control a majority on the board.

It is interesting that the configuration had lasted until after the 1970 census.

The judge ordered that weighted voting go into effect immediately for the board of supervisors, with one vote per 100 persons, and ordered the county to implement a constitutional apportionment within 3 months.

Slater v. Cortland County Board of Supervisors 42 A.D.2d 795 (1973) was a follow-up where the judge approved a 19-district legislature with districts comprised of groups of smaller towns, or parts of larger towns and cities.  There was about a 25% difference between the largest and smallest districts, so that there was also weighting applied.

By 1990, Cortland County had 19 legislative districts with the voting weight of each identical to their population.  The city of Cortland had 8 districts, while the towns of Cortlandville and Homer had 3 each.  The other 13 towns were combined in 5 multi-town districts.  The division of the city of Cortland was quite balanced, with districts ranging in population from 2451 to 2496 (the largest only 1.8% larger than the smallest).  The results were quite interesting.

District        Vote   Swing  R.Pop.   R.Pow    Dev. 
17              3244   52076   6.63%   5.66% -14.59%
19              3058   51964   6.25%   5.65%  -9.60%
16              2922   51268   5.97%   5.57%  -6.65%
13              2853   50672   5.83%   5.51%  -5.51%
15              2744   49896   5.60%   5.42%  -3.26%
18              2632   48924   5.38%   5.32%  -1.11%
12              2614   48832   5.34%   5.31%  -0.61%
14              2587   48652   5.28%   5.29%   0.05%
2               2496   47728   5.10%   5.19%   1.73%
4               2491   47676   5.09%   5.18%   1.82%
7               2480   47636   5.07%   5.18%   2.19%
1               2479   47628   5.06%   5.18%   2.21%
6               2475   47596   5.05%   5.17%   2.31%
5               2474   47592   5.05%   5.17%   2.34%
8               2455   47484   5.01%   5.16%   2.90%
3               2451   47444   5.01%   5.16%   2.98%
9               2315   46344   4.73%   5.04%   6.50%
11              2172   45648   4.44%   4.96%  11.81%
10              2021   45264   4.13%   4.92%  19.16%

Unlike the other cases we've looked at, where the largest district was overpowered, it is the smallest districts that have the extra power.  I suspect what is happening is that the populations are similar enough that the distribution of the total vote for the various combinations is quite close to a normal distribution, with the effect that the combinations where the largest districts are critical are starting to become less probably.  In addition, a simple majority in a 19-member equal weight body is 10/19 (52.6%).  The extra 2.6% means that most 10-member combinations can still achieve a majority, give the relatively overall variation in Cortland.   For example, the combination of the 3rd through 12th smallest districts can produce a majority.

In 2010, the legislature was reduced to 17 members.  One district in the city of Cortland was eliminated; and Homer was combined with Preble and Scott, then divided into 3 districts.  Previously Homer had 3 districts of its own, and Preble and Scott had been its own district.  Population equality within divided towns was quite severe.  For example. the range for the 7 districts in the city of Cortland was from 2740 to 2747; for the three districts formed from parts of Homer, 2989 to 2995; and for the three districts in Cortlandville, 2819 to 2853.  The districts continued to be weighted by their population, but this has no effect.

District        Vote   Swing  R.Pop.   R.Pow    Dev. 
17              3379   12870   6.85%   5.88% -14.11%
14              3344   12870   6.78%   5.88% -13.21%
16              3192   12870   6.47%   5.88%  -9.08%
10              2995   12870   6.07%   5.88%  -3.10%
8               2990   12870   6.06%   5.88%  -2.94%
9               2989   12870   6.06%   5.88%  -2.91%
13              2853   12870   5.78%   5.88%   1.72%
11              2837   12870   5.75%   5.88%   2.30%
12              2819   12870   5.71%   5.88%   2.95%
2               2747   12870   5.57%   5.88%   5.65%
1               2744   12870   5.56%   5.88%   5.76%
5               2744   12870   5.56%   5.88%   5.76%
3               2743   12870   5.56%   5.88%   5.80%
4               2743   12870   5.56%   5.88%   5.80%
7               2743   12870   5.56%   5.88%   5.80%
6               2740   12870   5.55%   5.88%   5.92%
15              2734   12870   5.54%   5.88%   6.15%

Because of the high level of equality, and the reduced size of the legislature, there are no 8-member combinations that command a majority, with the largest falling short at 49.8%.  And as a corollary, all 9-member combinations form a majority.

So the result is the same as if the districts were treated as having equal population.  The range in population from 16% above to 6% below the ideal is pushing the OMOV limits, but may be acceptable given the emphasis in New York of recognizing the significance of towns within the overall government structure.
61  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 25, 2014, 02:13:30 am
So New Jersey is kind of a natural for three districts, given the whole North Jersey/Central Jersey/South Jersey division that people map onto the state.  Of course, not calling them exactly that feels really weird to type, and there are more judgment calls than one might think as to what, exactly, counts as Central Jersey.  Anyhoo:
I was thinking about East Texas and West Texas, and I think that North Jersey, Central Jersey, and South Jersey are better names.  New Jersey is probably the only state where part of the state name is commonly dropped.  York and Hampshire wouldn't know who you were talking about, and Mexico would feel insulted.  East Carolina and West Carolina might be OK.  I'd probably veto Nova.

Dropping the state name from districts that are named after cities would also work (eg Chicago, Philadelphia, or Detroit).
62  General Politics / Political Geography & Demographics / Re: Weighted Voting For Congress on: June 25, 2014, 01:46:22 am
So New Jersey is kind of a natural for three districts, given the whole North Jersey/Central Jersey/South Jersey division that people map onto the state.  Of course, not calling them exactly that feels really weird to type, and there are more judgment calls than one might think as to what, exactly, counts as Central Jersey.  Anyhoo:



District 1: NEW JERSEY SOUTH.  Population 2,211,987 (deviation -718,644).  Obama 60.7%, Dem 57.8%.  This district is pretty easy for me; it's basically all of the state that cares more about Philadelphia than New York.  Mercer is a bit of a borderline case: it often gets put in Central Jersey, and parts of it probably do identify more with NYC, but historically Trenton was either considered its own thing or closer to a satellite of Philadelphia, and this district is pretty darn underpopulated as it is.  Some folks want to put Ocean in the south as well, but they're just flat-out wrong.  Safe D.

District 2: NEW JERSEY CENTRAL.  Population 3,005,097 (deviation +74,466).  Obama 52.1%, Dem 50.3%.  Aside from putting Mercer in the South, this is just straightforwardly the most expansive definition of Central Jersey that's out there, which is appropriate for this exercise given the extent to which North Jersey really does have the lion's share of the population otherwise.  Of course one could argue that "Central Jersey" really is just the crappier parts of North Jersey. Tongue  Anyway, Hunterdon and Union could both plausibly go into the North, but that would stretch even the super-wide range proffered in the ground rules.  Tossup.

District 3: NEW JERSEY NORTH.  Population 3,574,810 (deviation +644,179).  Obama 59.7%, Dem 57.4%.  This district is actually only 51.6% white (53.6% VAP), with Hispanics the largest minority in the low 20s.   Not much left to say about its boundaries.  Safe D.
Excellent!

That's exactly how I intended population limits to be used, only to be weighed in on judgement calls like Mercer.  Conceivably you could let counties vote to switch districts so long as the population stayed within limits.
63  General Politics / Political Geography & Demographics / Weighted Voting For Congress on: June 24, 2014, 07:43:52 pm


In the discussion about weighted voting for Hudson, NY we have come to the conclusion that weighted voting does not work particularly well for small bodies, or where the largest entities control a large bloc of votes.

I want to test on a body that has a size comparable to a legislature and which the districts are are of coarsely comparable sizes.  For my model, I have chosen a 100-member House of Representatives, the apportionment of which is shown in the map above.

What I need are districting plans for the 22 states that have more than one representative.

Guidelines:

(1) Don't split counties, with the possible exceptions of Los Angeles, CA and Cook, IL.  New York City may simply be treated as 5 counties, though of course they likely form communities of interest.

(2) Strong community of interest.

(2a) Each district should have a name, with the state name as part of the name.

(3) Coarse equality.  Precise equality is undesirable.  Even quality within 10% of the average for the state is not so good, unless it just happens to match a community of interest.  As a general guideline, try to keep districts in the range of 2/3 to 1-1/3 of the quota for the state.  You may go outside with justification.

(4) Connectivity is not a requirement, at this scale.  Contiguity might be waived in instances where there is a central district that spans across a state.

(5) Assume there is some mechanism in place to act as a check of excessively partisan plans.

(6) Plans may be subject to state plebiscites, so be prepared to advocate to the state voters that your plan should be adopted.

(7) Provide 2010 Census populations for the districts.  These will be adjusted based on the apportionment populations which include certain overseas Americans.
64  General Politics / Political Geography & Demographics / Re: City of Hudson's weighed voting system under scrutiny on: June 24, 2014, 06:24:35 pm
Dobish v State of New York 54 Misc.2d 367 (1967) was the follow on case to Dobish v. State of N. Y. 53 Misc.2d 732 (1967), which had been decided only a couple of months earlier.

In the prior case, the judge had declared the weighted-voting plan proposed for the Wayne County Board of Supervisors unconstitutional because if failed to produce voting power proportional to population, and had used computerize analysis to demonstrate this.

In this case, the judge relying on the expert testimony of Lee Papayanopoulos who had produced two alternatives, ordered Wayne County to adopt one of them.   Lee Papayanopoulos is the consultant who produced the the 1975, 2004, and 2013 plans for Hudson, and is currently a professor at Rutgers Business School.  In 1967 he was an IBM Systems Engineer and mathematics and special research specialist.  He is also author of 'Computerized weighted voting reapportionment; ACM AFIPS '81 Proceedings of the May 4-7, 1981, national computer conference.

I have not found a direct link between Papayanopoulos and Banzhaf, though Banzhaf has a BSEE from MIT.  At the time he wrote the article that weighted voting does not work, Banzhaf was editor of the Columbia Law Review.  Now he is more known for his anti-tobacco litigation.

I did come across this BBC broadcast that includes an interview with Banzhaf about 6 minutes in.
BBC broadcast on electoral methods
65  General Politics / Political Geography & Demographics / Re: City of Hudson's weighed voting system under scrutiny on: June 24, 2014, 02:33:49 am
Dobish v. State of N. Y. 53 Misc.2d 732 (1967) was decided by the Supreme Court of Wayne County.  Wayne County had proposed weighting the votes of the town supervisors, by weighing the vote to the nearest 1000.  The judge had a computer analysis done "by the New York Scientific Center, a division of International Business Machines Corporation, on an IBM 360 Computer, Model 40.".  50 years later, this is easily in range of a spreadsheet on a PC.

The analysis had found that for Wayne County, the voting power was not proportional to the population.  In a quite predictable by now result, the largest town of Arcadia had 11.9% additional power.  The tables in the opinion are remarkably similar to those that I have been producing, including using a fixed pitch typeface.  Because of the error, the judge ruled the plan unconstitutional.

But the judge had also gone further and had IBM adjust the weights for the largest towns downward, anticipating the adjusted voting weights now used in Hudson and Columbia County.  He did have a small error, in that he compared the voting power to the original weights rather than to the population.

The plan proposed by Wayne County, and ruled unconstitutional.

Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Arcadia          125    8454  17.61%  19.61%  11.36%
Sodus             79    4758  11.02%  11.04%   0.13%
Palmyra           69    4130   9.62%   9.58%  -0.41%
Williamson        61    3602   8.54%   8.36%  -2.14%
Lyons             59    3466   8.24%   8.04%  -2.41%
Ontario           54    3194   7.53%   7.41%  -1.65%
Macedon           48    2814   6.70%   6.53%  -2.53%
Galen             45    2626   6.32%   6.09%  -3.58%
Walworth          35    2046   4.96%   4.75%  -4.34%
Wolcott           35    2046   4.90%   4.75%  -3.14%
Marion            32    1858   4.53%   4.31%  -4.93%
Rose              22    1286   3.13%   2.98%  -4.72%
Savannah          17     970   2.45%   2.25%  -8.10%
Butler            16     926   2.23%   2.15%  -3.59%
Huron             16     926   2.20%   2.15%  -2.55%

By reducing the voting weight for the larger town - each iteration I reduced the weight of the town with the largest positive error by one - I was able to reduce the maximum error for the largest towns to less than 1%.  The errors for some smaller towns is due to lack of resolution in the original weights.   One could start with the population as the original weights, but then you end up with adjusted voting weights, that look like adjusted population.  The standard deviation for the error reduced from 4.09% (5.50% weighted), to 1.61% (1.29% weighted).

Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Arcadia          113    7820  17.61%  17.77%   0.86%
Sodus             77    4896  11.02%  11.12%   0.90%
Palmyra           68    4264   9.62%   9.69%   0.68%
Williamson        60    3768   8.54%   8.56%   0.23%
Lyons             58    3624   8.24%   8.23%  -0.08%
Ontario           54    3348   7.53%   7.61%   0.95%
Macedon           48    2960   6.70%   6.72%   0.40%
Galen             45    2798   6.32%   6.36%   0.60%
Walworth          35    2136   4.96%   4.85%  -2.21%
Wolcott           35    2136   4.90%   4.85%  -0.98%
Marion            32    1956   4.53%   4.44%  -1.99%
Rose              22    1334   3.13%   3.03%  -3.22%
Savannah          17    1030   2.45%   2.34%  -4.45%
Butler            16     974   2.23%   2.21%  -0.70%
Huron             16     974   2.20%   2.21%   0.37%
66  General Politics / Political Geography & Demographics / Re: City of Hudson's weighed voting system under scrutiny on: June 23, 2014, 08:58:03 pm
The plan in Saratoga County was similar.  One vote was apportioned for each 600 persons.  Towns with more than 20 votes were given an extra supervisor, with the vote for the town split between the two supervisors.  Using the population of each town as its voting weight, we repeat the pattern of the largest town having too much power.

Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Saratoga Spr.  16630  624945  18.67%  22.15%  18.68%
Moreau          8406  256993   9.43%   9.11%  -3.45%
Waterford       7231  220395   8.12%   7.81%  -3.74%
Milton          7114  216695   7.98%   7.68%  -3.80%
Mechanicsville  6831  207885   7.67%   7.37%  -3.89%
Ballston        5752  174445   6.46%   6.18%  -4.22%
Corinth         5167  156505   5.80%   5.55%  -4.34%
Clifton Park    4512  136317   5.06%   4.83%  -4.58%
Stillwater      4416  133433   4.96%   4.73%  -4.57%
Halfmoon        4120  124361   4.62%   4.41%  -4.67%
Saratoga        3515  105983   3.95%   3.76%  -4.77%
Charlton        3024   91069   3.39%   3.23%  -4.89%
Greenfield      2548   76669   2.86%   2.72%  -4.97%
Malta           2223   66831   2.50%   2.37%  -5.05%
Wilton          1902   57239   2.13%   2.03%  -4.96%
Galway          1746   52479   1.96%   1.86%  -5.07%
Northumberland  1353   40619   1.52%   1.44%  -5.19%
Hadley           982   29533   1.10%   1.05%  -5.02%
Edinburg         602   18057   0.68%   0.64%  -5.27%
Providence       556   16645   0.62%   0.59%  -5.45%
Day              466   13983   0.52%   0.50%  -5.23%

Splitting Saratoga Springs between two supervisors considerably improves the situation, but there is a problem with the coarseness of the apportionment.  Northumberland has 38% more population than Hadley, but each has 2 votes.

Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Saratoga Spr.     14  626781  18.67%  19.07%   2.17%
                  14  626781
Moreau            14  626781   9.43%   9.53%   1.06%
Waterford         12  529801   8.12%   8.06%  -0.70%
Milton            12  529801   7.98%   8.06%   0.94%
Mechanicsville    11  482867   7.67%   7.35%  -4.19%
Ballston          10  436753   6.46%   6.64%   2.91%
Corinth            9  391329   5.80%   5.95%   2.65%
Clifton Park       8  346515   5.06%   5.27%   4.09%
Stillwater         7  302187   4.96%   4.60%  -7.25%
Halfmoon           7  302187   4.62%   4.60%  -0.59%
Saratoga           6  258227   3.95%   3.93%  -0.43%
Charlton           5  214745   3.39%   3.27%  -3.75%
Greenfield         4  171459   2.86%   2.61%  -8.80%
Malta              4  171459   2.50%   2.61%   4.54%
Wilton             3  128403   2.13%   1.95%  -8.50%
Galway             3  128403   1.96%   1.95%  -0.33%
Northumberland     2   85513   1.52%   1.30% -14.34%
Hadley             2   85513   1.10%   1.30%  18.02%
Edinburg           1   42729   0.68%   0.65%  -3.80%
Providence         1   42729   0.62%   0.65%   4.16%
Day                1   42729   0.52%   0.65%  24.28%

Increasing the total voting weight to approximately 1000, so that each vote represents 0.1% of the county's population (89.096 persons) improves matters considerably.

Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Saratoga Spr.     94  629230  18.67%  19.08%   2.21%
                  93  621766
Moreau            94  629230   9.43%   9.60%   1.70%
Waterford         81  534826   8.12%   8.16%   0.49%
Milton            80  527746   7.98%   8.05%   0.79%
Mechanicsville    77  506706   7.67%   7.73%   0.78%
Ballston          65  423730   6.46%   6.46%   0.09%
Corinth           58  376442   5.80%   5.74%  -1.01%
Clifton Park      51  329706   5.06%   5.03%  -0.72%
Stillwater        50  323062   4.96%   4.93%  -0.60%
Halfmoon          46  296698   4.62%   4.52%  -2.16%
Saratoga          39  250762   3.95%   3.82%  -3.07%
Charlton          34  218310   3.39%   3.33%  -1.92%
Greenfield        29  185890   2.86%   2.83%  -0.88%
Malta             25  160058   2.50%   2.44%  -2.18%
Wilton            21  134394   2.13%   2.05%  -4.00%
Galway            20  127926   1.96%   1.95%  -0.45%
Northumberland    15   95946   1.52%   1.46%  -3.65%
Hadley            11   70290   1.10%   1.07%  -2.75%
Edinburg           7   44718   0.68%   0.68%   0.92%
Providence         6   38310   0.62%   0.58%  -6.38%
Day                5   31902   0.52%   0.49%  -6.99%

Even better is to simply give two supervisors to Saratoga Springs and make the voting weight the same as the population.  The standard deviation for the error is 1.49%, with a weighted value of 1.65%.

Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Saratoga Spr.   8315  624945  18.67%  19.06%   2.10%
                8315  624945
Moreau          8406  632555   9.43%   9.65%   2.24%
Waterford       7231  536669   8.12%   8.18%   0.84%
Milton          7114  527237   7.98%   8.04%   0.69%
Mechanicsville  6831  504975   7.67%   7.70%   0.44%
Ballston        5752  421231   6.46%   6.42%  -0.50%
Corinth         5167  376703   5.80%   5.74%  -0.95%
Clifton Park    4512  327739   5.06%   5.00%  -1.31%
Stillwater      4416  320623   4.96%   4.89%  -1.35%
Halfmoon        4120  298719   4.62%   4.56%  -1.49%
Saratoga        3515  254049   3.95%   3.87%  -1.80%
Charlton        3024  218155   3.39%   3.33%  -1.98%
Greenfield      2548  183523   2.86%   2.80%  -2.14%
Malta           2223  159929   2.50%   2.44%  -2.25%
Wilton          1902  137069   2.13%   2.09%  -2.09%
Galway          1746  125517   1.96%   1.91%  -2.33%
Northumberland  1353   97189   1.52%   1.48%  -2.40%
Hadley           982   70555   1.10%   1.08%  -2.38%
Edinburg         602   43255   0.68%   0.66%  -2.38%
Providence       556   39795   0.62%   0.61%  -2.76%
Day              466   33501   0.52%   0.51%  -2.33%
67  General Politics / Political Geography & Demographics / Re: City of Hudson's weighed voting system under scrutiny on: June 23, 2014, 07:33:26 pm
Iannucci vs. Board of Supervisors of Washington County and Saratogian, Inc. vs. Board of Supervisors of Saratoga County, 20 N.Y. 2d 244, 299 NE 2d 195, 282 NYS 2d 502, 1967 were a pair of cases decided in 1967 by the New York Court of Appeals, the state's highest court.

The court overturned lower court decisions that said weighted voting for county boards of supervisors was unconstitutional, but at the same time said that simple weighting based on population was not valid, and that instead that it was voting power that should be proportional to population.  It didn't really say that the counties schemes were invalid, but rather that the counties had not offered any evidence that their apportionment scheme would produce valid results, and that it would likely be expensive to prove it.

John Banzhaf III (re)creator of the Banzhaf Power Index was an amicus curiae and they cited his  law review article 'Weighted Voting Doesn't Work: A Mathematical Analysis'.  That article had included the example of the Nassau County Board of Supervisors, whose weighted voting scheme very badly did not work, since the votes of the supervisors from the two cities were totally irrelevant (Nassau County had (has) only three towns and two cities, and over half the population was in the Town of Hempstead.

It turns out that the counties schemes of simple weighting were valid, or were close to it.

In Washington County, one vote was apportioned for every 279 persons.  In addition, towns with more than 15 votes were given additional supervisors with the vote divided between them.  For example, Kingsbury, the largest town was apportioned 39 votes, and given 3 supervisors, each casting 13 votes.  The smallest towns had 2 votes.  The magnitude of votes was as if they were apportioning whole numbers of members to each town, and wanted to make sure every town had at least two.

If the populations of the towns had been used as the voting weights, we see the familiar pattern of the largest entity, in this case Kingsbury, being overpowering, while every other town is about equally underpowered.

Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Kingsbury      11012   41480  22.72%  27.27%  20.03%
Fort Edward     6523   19274  13.46%  12.67%  -5.85%
Granville       5015   14930  10.35%   9.81%  -5.14%
Whitehall       4757   14144   9.81%   9.30%  -5.26%
Greenwich       3969   11752   8.19%   7.72%  -5.65%
Fort Ann        3124    9266   6.44%   6.09%  -5.49%
White Creek     2365    6950   4.88%   4.57%  -6.36%
Salem           2258    6642   4.66%   4.37%  -6.27%
Argyle          1898    5564   3.92%   3.66%  -6.59%
Easton          1681    4918   3.47%   3.23%  -6.78%
Cambridge       1610    4712   3.32%   3.10%  -6.74%
Hartford        1058    3084   2.18%   2.03%  -7.12%
Hebron          1026    2984   2.12%   1.96%  -7.33%
Jackson          795    2342   1.64%   1.54%  -6.13%
Putnam           490    1460   1.01%   0.96%  -5.06%
Hampton          469    1378   0.97%   0.91%  -6.38%
Dresden          426    1254   0.88%   0.82%  -6.20%

But if we divide the votes for the largest towns among more than one supervisor, the results are much better.  The largest errors are for the smallest towns.  But that is not due to weighted voting, but rather apportionment error.  It appears that the quota of 279 was chosen so that Dresden would be entitled to slightly more than 1.5 votes, which would be rounded to 2.  White Creek does very poorly because its entitlement of 8.47 is rounded down to 8.

Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Kingsbury         13  536040  22.72%  22.71%  -0.03%
                  13  536040
                  13  536040
Fort Edward       12  492064  13.46%  13.29%  -1.25%
                  11  448836
Granville          9  364212  10.35%  10.29%  -0.56%
                   9  364212
Whitehall          9  364212   9.81%   9.70%  -1.15%
                   8  322640
Greenwich         14  580902   8.19%   8.20%   0.20%
Fort Ann          11  448836   6.44%   6.34%  -1.64%
White Creek        8  322640   4.88%   4.56%  -6.60%
Salem              8  322640   4.66%   4.56%  -2.18%
Argyle             7  281498   3.92%   3.98%   1.54%
Easton             6  240646   3.47%   3.40%  -1.99%
Cambridge          6  240646   3.32%   3.40%   2.33%
Hartford           4  159884   2.18%   2.26%   3.46%
Hebron             4  159884   2.12%   2.26%   6.68%
Jackson            3  119762   1.64%   1.69%   3.13%
Putnam             2   79758   1.01%   1.13%  11.43%
Hampton            2   79758   0.97%   1.13%  16.42%
Dresden            2   79758   0.88%   1.13%  28.17%

If we instead apportion 1000 votes, in effect giving each town one vote for each 0.1% of the population (48.476 persons) we get very good conformance.

Town           Vote    Swing  R.Pop.  R.Pow    Dev. 
Kingsbury         76  540471  22.72%  22.99%   1.22%
                  76  540471
                  75  532843
Fort Edward       68  479915  13.46%  13.57%   0.86%
                  67  472539
Granville         52  362635  10.35%  10.23%  -1.09%
                  51  355475
Whitehall         49  341167   9.81%   9.72%  -0.92%
                  49  341167
Greenwich         82  587125   8.19%   8.37%   2.18%
Fort Ann          64  450279   6.44%   6.42%  -0.44%
White Creek       49  341167   4.88%   4.86%  -0.36%
Salem             47  326897   4.66%   4.66%   0.00%
Argyle            39  270193   3.92%   3.85%  -1.67%
Easton            35  241983   3.47%   3.45%  -0.57%
Cambridge         33  227937   3.32%   3.25%  -2.21%
Hartford          22  151599   2.18%   2.16%  -1.03%
Hebron            21  144959   2.12%   2.07%  -2.41%
Jackson           16  110069   1.64%   1.57%  -4.37%
Putnam            10   68705   1.01%   0.98%  -3.15%
Hampton           10   68705   0.97%   0.98%   1.19%
Dresden            9   61825   0.88%   0.88%   0.24%

The standard deviation for the error is 1.63% (population weighted 1.38%).

So had Washington County used a finer apportionment, they likely could have used population-weighted voting for their board of supervisors.
68  General Politics / Political Geography & Demographics / Re: Is Missouri Southern or Midwestern? on: June 22, 2014, 08:11:30 am
As of July 1, 2012, Southern. Missouri made its choice.
Are New Jersey and Maryland midwestern?  Or Nebraska eastern?
69  General Politics / Political Geography & Demographics / Re: 1974 Michigan Proposal C on: June 20, 2014, 11:55:41 pm
Be careful about ascribing today's motives to issues that are decades old. The question should be about how the proposal was framed during the debate. Was it part of a swap to other taxes that would then rise? Was seen as a give away to Detroit? Would ag programs be impacted by the change?
INITIATIVES AND REFERENDUMS UNDER THE CONSTITUTION OF THE STATE OF MICHIGAN OF 1963 (pdf)

Citizens Research Council of Michigan - Publications

State Ballot Issues - 1974 (pdf)

It appears that most of the constitutional referendum from that era were related to taxation: limits on property taxes, impose a graduated income tax, etc.   I'd like to see the vote on November 1972 Proposition D, if the OP has a data source.

Under the Michigan Constitution at the time (and perhaps still), local governments were guaranteed a per capita share of sale tax revenues.  This may avoid the situation where cities compete for sources of sales tax revenue, either through annexation or recruiting retailers.

It might have also represented a transfer from Detroit to western Michigan.  People in that area would have access to apples and cherries, which they could can, and might also have home vegetable gardens, and have venison for meat.  People in Detroit would probably buy highly processed food, which has a high cost per food value.  The cost of potato chips is much more than an equivalent cost of potatoes.

The measure would have increased the percentage of sales tax revenues transferred to local governments to make up for the decreased the sales tax revenue.

It would have also cut out about 20% of sales tax revenues, leaving a big whole in the state general fund.

So the responsible burghers of western Michigan may have perceived the measure as (a) an ill-conceived populist measure that would require replacement by higher property or income taxes; and/or (b) a nefarious conspiracy by big-government liberals in Ann Arbor, Lansing, and Detroit to force imposition of a graduated income tax.

The Yes vote was especially high along the Wisconsin line of the Upper Peninsula.  I bet Wisconsin had lower sales taxes on food, and there was a perception or reality that this was costing merchants in Michigan business.  The same might be true for Cass County, where it would be an easy trip into South Bend for groceries, though this might also be due to food selection and prices.
70  General Politics / Political Geography & Demographics / Re: City of Hudson's weighed voting system under scrutiny on: June 20, 2014, 09:32:05 pm
Livingston County

Livingston County has a board of supervisors using weighted voting to balance voting power with population.   Livingston has no cities, and the largest town, Geneseo, only has 16.45% of the population.

Using voting weights proportional to population would give Geneseo 7.91% relative extra power, and every other town a negative error.  With adjusted weights, the match of power to population is quite good, with a standard deviation of 0.53%.  With 17 towns and no huge concentrations of population, this is about as good as weighted voting gets.

The town of Groveland apparently has a prison which contains over half of its population.

Wayne County

Wayne County adjusts voting weights so that voting power matches population.  The largest town, Arcadia has 52.4% of the population.  Splitting it in two would eliminate the need to use anything but simple weights.

Saint Lawrence

Saint Lawrence County has put its legislative history since the 1960s online.  It scanned its old typewritten minutes into PDFs, and created an index.  It is not at all clear which local laws went into effect, or were turned down in a referendum, or overturned by a court, because a decade later, the votes don't appear to be based on the law previously passed.

In 1966, weighted votes for the board of supervisors were established.  St.Lawrence has 32 towns and one city, Ogdenburg.  Ogdenburg had 4 wards, so under a traditional configuration had 36 supervisors.  The smallest town, Clare, has just over 100 persons, and the 5 largests towns (city), Potsdam, Massena, Canton, Ogdenburg city, and Gouverneur contain a majority of the population.  Clare had one vote and the larger towns dozens of votes.

By the 1980s, the laws provided for weighting of the votes of 22 legislators, so somewhere in between the board of supervisors was abandoned and replaced by a county legislature.  The weights were approximately equal, so it appears that perhaps equal-population districts had been created, but it was difficult to maintain equality, particularly when splitting was restricted to the largest towns.  In one proposal, the weights were mostly 10, with a few ranging to as much as 8 or 12, indicating that the weights were based on populations rounded to 10% of a quota.  In another proposal, the weights were numbers such as 4.7 and 5.1.   Since they added to 100.0, they must have been the share of the county population rounded to 0.1%.  It appears a goal was to provide smaller numbers that could be added up by hand.

In the 1990s, the debate was over switching to 11, 13, or 15 districts.   It must have been decided that a large board did not provide that much representation to the smaller towns, but rather multiple members to the largest towns, as well as added expense to pay that many legislators.  The votes on the various proposals did not appear to be weighted, so it appears that weighting never occurred.

The 2000s discussion included much more extensive minutes.  One member mentioned the one-year term, and limits set by a judge on the amount of permitted deviation, so the previous districts must have been overturned in court, and new elections ordered.

The current legislature has 15 members.
71  Other Elections - Analysis and Discussion / Gubernatorial/Statewide Elections / Re: 2014 California State Controller on: June 20, 2014, 12:53:37 am
Elections in California are routinely uncompetitive. Exactly two Republicans have won statewide elections in this century, and they both won as a result of the unusual circumstances of the 2003 recall. Perez and Yee are both more visible candidates from larger cities, but more importantly they're both Democrats. Nobody in this thread has given any reason that this race would be different from any of the other statewide races, all of which Democrats will win easily.
Steve Cooley was within 100,000 votes running for AG in 2010.

What was the relationship between Steve Poizner's election in 2006 to the Davis recall?
72  Other Elections - Analysis and Discussion / Gubernatorial/Statewide Elections / Re: Longest-serving State Attorneys General in the US on: June 20, 2014, 12:37:15 am
Here's a list of the longest-serving State Attorneys General in the United States in NO particular order:
1.) Greg Abbott (R):50th Texas State AG since December 2, 2002
Three of the last four AGs have been the longest serving.  Jim Mattox and Dan Morales both served 8 years.  Presumably the switch to 4-year terms led some to stay a little longer before running for governor or other office.

9 of the last eleven have run for governor or senator.  Crawford Martin died in office in 1972.  The last to simply to leave office was John Shepperd in 1957.

73  Other Elections - Analysis and Discussion / Gubernatorial/Statewide Elections / Re: 2014 California State Controller on: June 20, 2014, 12:13:51 am
Is Ashley Swearengin a good candidate? She is the mayor of Fresno, which is a pretty big city.
She is very photogenic.

It could help that it is a snoozer of an election, with no senatorial race, and the gubernatorial race non-competitive.  Republicans are more likely to VBM, and more likely to vote.  City elections are non-partisan in California, so there is the potential for city council members and other mayors saying nice things about her. Her emphasis has been on economic development, which could help with independent voters.
74  General Politics / Political Geography & Demographics / Re: City of Hudson's weighed voting system under scrutiny on: June 19, 2014, 10:28:57 pm
Searching for: "local law" "weighted voting" "New York" "county" I came across some other counties:

Madison County

Its local law specifies the procedure for deriving the voting weights.  There is one supervisor for each town; and the City of Oneida elects 2 supervisors from at large from each of 2 supervisor districts.  The supervisor districts in Oneida are each comprised of three wards.  So there is certainly precedent for changing how Hudson is represented on the Columbia board.

In Madison, an initial simple apportionment is done based on one vote for every 49 persons or fraction thereof.  Since the total is exactly 1500, I suspect that the quota was derived from a preferred total.

The initial voting weights were then adjusted such that the effective voting power was proportional to the population share within 5%.  Separate calculations were done for 1/2, 3/5, 2/3, and 3/4 majority.  In all cases, the total is 1500.  In Columbia and Hudson, the total varies.
The Oneida supervisors from each district cast equal votes, so I suspect that their vote being even was another constraint.

The Town of Sullivan has about 20.9% of the population.  Its population-based share of the vote is 313/1500.  Its weight for the various majorities varies dramatically:

1/2: 280
3/5: 291
2/3: 347
3/4: 615! (astonishment, not factorial).

Ontario County

It simply provides the weights for 1/2 and 2/3 majority with no explanation.   The cities of Geneva and Canandaigua elect 3 and 2 supervisors, respectively, with each elected from a pair of wards.

Schenectady County

Schenectady County has a county legislature.  When the legislature was created in 1965, the county was divided into 4 districts, 2 in the city of Schenectady, and 2 comprised of towns outside the city.   The legislators are apportioned among the districts on the basis of population.  The nominal size of the legislature is 15, but is adjusted when the apportionment error for any district is greater than 7.5%.  In one decade, the council was reduced to 13 members (4, 3, 3, 3).

In the 2010 census, it was discovered that no size less than 24 would be sufficient to produce an error less than 7.5%.  Faced with a dilemma of greatly enlarging the legislature, or changing the districts, both of which would cause problems since the legislature is elected by halves every two years, the charter was changed to simply apportion 15 members and weight the votes.

District 1 (3) Weight 1.0572
District 2 (3) Weight 1.0799
District 3 (5) Weight 0.9939
District 4 (4) Weight 0.9048

As one would expect, with such a small number of members, and relatively little difference in the weights it did not matter.  It still takes 8 members to pass a motion.  The 7 weightiest members only have 49.6% of the vote, and the 8 lightest 50.4%.

I suspect that there would be a pretty good OMOV case, since the county itself asserted that a deviation of greater than 7.5% was too much, but essentially gives one vote to districts that are almost 10% under.

Cattaraugus County

Cattaraugus County has a county legislature with 21 members elected from 10 multi-member districts (3 x 1, 5 x 2, 1 x 3, 1 x 5).   The largest includes the city of Olean, and its surrounding town of Olean, plus a portion of a neighboring town.   The other districts were comprised of one or more towns and cities.   Several of the two-member districts are made up of a half dozen or so towns, and could easily be split into single-member districts if you weren't super fussy about the population.

At some time (2000?), weights were imposed on top of this, but they range from 87% to 1.13%.  I suspect that the larger two-member districts were because they couldn't get a perfect split.  But with weighting, that would not be a problem.

The population represented ranges from 4.13% to 5.37%, while the voting power ranges from 4.54% to 4.98%, with the smallest districts favored the most.

If there were no weighting, all members would have 1/21 of the total power of 4.76%.  Arguably this is a OMOV violation, as a 30% variation in population is recognized with a 9.6% variation in power.
75  General Politics / Political Geography & Demographics / Re: City of Hudson's weighed voting system under scrutiny on: June 19, 2014, 01:57:51 am
My conjecture about the source of power appears to be correct.  The following is based on Monte Carlo methods (100,000 samples) and the 1960s proposed weighting for the New Jersey senate.

Pop.: Share of the state's population.

Range: Share of losing voting combinations within range of majority, based on the county population share.   For example, for Essex County, there are 35,007 losing combinations within 15.22% of 50% (34.78% to 50%).   For Cape May County, there are 2129 combinations within the range (49.20% to 50.0%).  For the state, there are 252,420 such losing combinations that are in range of a county (a losing combination with a total vote of 49.5% is in range for all 21 counties, would be counted 21 times in the 252,420 total.  The Range share is the county number of combinations to the state total.

If a losing vote result were displayed on a vote board, one could quickly determine which senators might be able to reverse the vote.  50% of combinations are losing, yet Essex County might be able to reverse 70% of the losing votes.   Nonetheless its range share is less than its population share, because there are fewer combinations around 35% total vote than 50%.

For the smaller and midsize counties, the range share and population share are quite comparable.  At first glance, it would appear that the larger counties have less opportunity to be swing voters.

Loser: For a senator to be a swing voter, the motion had to lose, it has to be in range of him being able to change the outcome unilaterally, and the senator had to have voted against the motion.   Since the random model assumes the senator will vote No on 1/2 the votes, it would be expected that 1/2 the time he voted No on a losing motion that he could flip.  But this is not true for heavyweights.  In effect, much of the time they caused the motion to fail.   If a motion receives as 40% Yes vote, it can be due to two reasons: (1) Essex voted Yes with its 15%, and the other counties voted 25%:60% against, which is quite unlikely; or Essex voted No with its 15%, and the other counties voted 40%:45% which is quite possible.

Of the 35,007 voting combinations that Essex County was in range to be able to flip, they voted No on 22,870, or 65.3% of them.   For smaller counties, the share was quite close to 50%.  Interestingly, Warren was a bit higher.  This is likely related to the discontinuity in the population distribution, with the five smallest counties, including Warren, having similar populations, and Ocean having considerably more.  There is a similar, though smaller gap between Atlantic and Burlington.

Power: The Banzhaf Power Index is the share of combinations for which a senator is a swing voter, relative to the total number of such voters, for the state.  While Essex was in range to be able to flip only 13.87% of such combinations, because it was on the losing side in 65.37% of them, it ended up being a swing voter in 16.49% of such combinations, vs its 15.22% population share.

Theor.: Power was calculated using Monte Carlo methods.  The theoretical value using all combinations was generated by the program lpgenf


County         Pop.  Range    Loser   Power   Theor.
Essex         15.22% 13.87%   65.33%  16.49%  16.39%
Bergen        12.86% 12.21%   59.44%  13.21%  13.26%
Hudson        10.07%  9.95%   55.76%  10.10%  10.10%
Union          8.31%  8.38%   53.98%   8.23%   8.22%
Middlesex      7.15%  7.29%   52.89%   7.02%   6.99%
Passaic        6.70%  6.88%   52.22%   6.54%   6.58%
Camden         6.46%  6.64%   52.02%   6.29%   6.34%
Monmouth       5.51%  5.71%   51.88%   5.39%   5.37%
Mercer         4.39%  4.61%   51.43%   4.31%   4.27%
Morris         4.31%  4.53%   50.61%   4.17%   4.19%
Burlington     3.70%  3.89%   50.43%   3.57%   3.56%
Atlantic       2.65%  2.78%   51.40%   2.60%   2.55%
Somerset       2.37%  2.47%   50.83%   2.29%   2.32%
Gloucester     2.22%  2.32%   50.62%   2.14%   2.17%
Cumberland     1.76%  1.86%   49.76%   1.68%   1.70%
Ocean          1.78%  1.88%   49.36%   1.69%   1.70%
Warren         1.04%  1.09%   52.22%   1.03%   1.00%
Salem          0.97%  1.01%   49.88%   0.92%   0.92%
Hunterdon      0.89%  0.93%   48.77%   0.83%   0.85%
Sussex         0.81%  0.85%   48.79%   0.76%   0.77%
Cape May       0.80%  0.84%   49.37%   0.76%   0.77%


This shows the distribution of the total votes cast for the various combinations.  The bin sizes is 2%, with the centra bin 49% to 51% of the maximum vote.  The vertical lines correspond to the center of the bin.  The dimple at the top is likely real, rather than random luck.  Votes from the largest counties will tend to push the distribution away from an expectation of an balanced vote.

The ripples on the side slopes might also be real.  The three largest counties have 38% of the total vote, and would be expected to vote together 1/4 of the time.  That makes for a very large thumb on the legislative scales.

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