Census Estimates for 2007 -> 2010 Apportionment

[jimrtex]

Could you tell me the formulas you enter into your Spreadsheet? I am trying to make one for myself.

A brute force method:

In Column A: State Name.
In Column B: Estimated Population.
In Column C: Priority value for 2nd seat (C.row = B.row/sqrt(2*1))
In Column D: Priority value for 3rd seat (D.row = B.row/sqrt(3*2))
repeatr for at least 54 columns (or however many seats you think California will have).

So you will have a 54 by 50 array of priority values.   Find the 385th largest value (each of the 50 states is guaranteed one seat, and 435-50 is 385).  Determine the number of priority values for each state that is greater than or equal to the threshold value.

Short Cut (simplest calculation but may have an error in extreme cases):

1) Determine average per CD for country (AVE = total_estimated_population /435)
2) Estimate number of CDs for each state (XCD = state_population/AVE )
    eg a State with 7.85/435 of the total population would have a XCD value of 7.85
3) Determine whole number of CDs for each state (NCD = max(int(XCD),1) )
    The state with a XCD value of 7.85 would have an NCD value of 7.
4) Determine total number of whole CDs for US.  This should be around 435 - 50/2 = or 410,
    since the average truncated fraction will be around 1/2.
5) Determine priority value for next CD for each state:
    PV = state_pop/SQRT(NCD*(NCD+1))
6) Determine states with N highest priority values for next CD (where N is 435 minus
    the value from step 4).

This does not produce a complete set of priority rankings, but rather the relative ranking for the next CD among the 50 states (eg Wyoming would be somewhere around 800 for a 2nd CD, but at worst would be 50th in this ranking).

[jimrtex]

I noticed that the Census Bureau adjusts its previous estimates for all previous years in the decade.  That is, the latest estimate gives a different estimate for July 2006, July 2005, etc. than was given in the report made in December 2006.   This is not a new phenomena, it has happened every year.   For example, these are the estimates for Alabama.

Each row represents the estimates made in December of that year.  Each column represents the estimated July 1st population.   So for example, the December 2004 estimate for the July 1, 2004 population was 4,530,182; while the December 2007 estimate for the July 1, 2007 population was 4,508,540.

	2007	2006	2005	2004	2003	2002	2001	2000
2007	4,627,851	4,590,240	4,539,611	4,508,540	4,488,071	4,471,006	4,463,224	4,451,887
2006		4,599,030	4,548,327	4,517,442	4,495,089	4,477,571	4,466,618	4,452,375
2005			4,557,808	4,525,375	4,501,862	4,480,139	4,467,461	4,452,339
2004				4,530,182	4,503,726	4,481,078	4,468,031	4,452,307
2003					4,500,752	4,478,896	4,466,440	4,451,601
2002						4,486,508	4,468,912	4,451,975
2001							4,464,356	4,451,493

There are interstate variations.   For example, the revision in July 1, 2006 population estimate (estimate issued in December 2007 vs. estimate issued in December 2006) ranged from +1.2% for Utah to -1.0% for Louisiana.   For Louisiana, the 2007 estimates show a slightly smaller (-8K) population in 2005; a larger drop for 2006 (252K vs. 220K in the previous estimate); and a recovery of 50K for 2007.

So the changes in projected population for 2010 (and consequent apportionment changes) reflect not only varying rates of growth throughout the decade, but also revisions of earlier estimates.  In general, Muon's method of annualizing the 2000-2007 change and projecting it forward to 2010 should still be valid - though as time passes it will be less sensitive to changes in growth rates.  For example, the estimated rate of change from 2004-2007 might be better for projecting the rate of change for 2007-2010 than the estimated rate of change from 2000-2007 while still benefitting from the use of a multi-year average.

[jimrtex]

How long has it been since a census didn't give California any Congress seats?

1920 was the last.  California had 11 House seats before and after the census.

That was because Congress did not reapportion after the 1920 census.  California should have had 14 representatives (it went from 11 to 20 from 1910 to 1930).

California did not gain a seat after the 1850 census (staying at 2), but it did not enter the Union until September 9, 1850, which was probably after the census.

[jimrtex]

The first column is the apportionment based on projected 2010 population, if fractional representatives could be apportioned using the following formula:

   sqrt ((population/average)^2 + 0.25)

where population is the state population, and average is the approximately the US population/435.  The average is adjusted slightly upward so that the sum of state's apportionment is 435.   Using this formula, a state with a population of
sqrt (n*(n+1))*average will have an apportionment of n + 0.5 representatives.

The second column is the change in apportionment from 2000 to 2010.  For example, based on its relative share of the population, Texas should gain slightly more than 3 seats.

The third column apportions whole representatives so that there are 435 representatives, using the priority ranking.

The fourth column is the projected percentage increase in population from 2000 to 2010.  The US rate of growth is 10.1%.

The fifth column is the additional percentage increase needed to gain one more representative (that is, to catch Oregon #435) or to lose one more representative (that is, to catch New York #436).

California           52.692    0.450  53   11.1%  -1.4%
Texas                35.259    3.096  36   20.7%  -0.4%
New York             27.201   -2.071  27    2.3%   0.3%
Florida              26.883    2.228  27   20.1%  -2.5%
Illinois             18.241   -0.920  18    4.8%   0.6%
Pennsylvania         17.499   -1.448  18    1.7%  -1.1%
Ohio                 16.127   -1.390  16    1.4%   1.5%
Michigan             14.185   -1.151  14    1.9%   1.4%
Georgia              14.176    1.540  14   23.6%   1.4%
North Carolina       13.283    0.863  13   17.8%   0.8%
New Jersey           12.321   -0.666  12    4.5%   0.6%
Virginia             11.168    0.238  11   12.5%   2.1%
Arizona               9.631    1.702  10   33.9%  -2.4%
Washington            9.397    0.293   9   13.7%   0.3%
Massachusetts         9.100   -0.705   9    2.2%   3.6%
Indiana               9.044   -0.347   9    6.1%   4.2%
Tennessee             8.898    0.109   9   11.5%  -5.5%
Missouri              8.402   -0.244   8    7.0%   0.3%
Maryland              8.061   -0.123   8    8.5%   4.6%
Wisconsin             7.990   -0.297   8    6.2%  -7.2%
Minnesota             7.449   -0.155   8    7.9%  -0.4%
Colorado              7.149    0.495   7   18.4%   4.1%
Alabama               6.598   -0.279   7    5.6%  -2.6%
South Carolina        6.416    0.209   6   13.9%   0.5%
Kentucky              6.070   -0.185   6    6.9%   6.3%
Louisiana             5.942   -0.968   6   -5.4%  -8.5%
Oregon                5.455    0.155   6   13.4%  -0.3%
Oklahoma              5.181   -0.164   5    6.7%   5.3%
Connecticut           4.982   -0.294   5    3.9% -10.8%
Iowa                  4.247   -0.294   4    2.9%   5.2%
Mississippi           4.158   -0.258   4    3.6%   7.5%
Arkansas              4.090   -0.064   4    8.4%   9.3%
Utah                  3.982    0.501   4   26.3% -13.3%
Nevada                3.981    0.859   4   41.1% -13.2%
Kansas                3.966   -0.211   4    4.5% -12.9%
New Mexico            2.887    0.037   3   11.6% -14.8%
West Virginia         2.588   -0.245   3    0.3%  -4.6%
Nebraska              2.569   -0.118   3    5.1%  -3.8%
Idaho                 2.276    0.219   2   22.5%   9.4%
New Hampshire         1.952   -0.018   2    9.0% -25.9%
Maine                 1.933   -0.096   2    4.6% -25.1%
Hawaii                1.904   -0.031   2    8.3% -23.8%
Rhode Island          1.568   -0.124   2    1.3%  -5.9%
Montana               1.460   -0.018   1    8.6%   2.2%
Delaware              1.353    0.045   1   14.6%  11.6%
South Dakota          1.243   -0.024   1    7.6%  23.3%
Alaska                1.108    0.020   1   12.6%  41.8%
North Dakota          1.025   -0.085   1   -0.5%  56.8%
Vermont               1.009   -0.055   1    2.8%  60.0%
Wyoming               0.900   -0.011   1    8.2%  87.5%

California is increasing slightly faster than the US population.  With its large population, a relative increase of about 1.9% will add one representative.  In 2000, it got a favorable rounding for its 53rd representative.  During this decade it has solidified its hold on the seat.  The change from last year (when a 54th seat was projected) is due to a slowing down in growth plus revisions from previous years.  Despite a raw entitlement less than 53, California is closer to gaining a seat (+0.7%) than losing one (-1.1%).

Texas had a raw increase of just over 3 seats, but may gain a 4th seat based on a favorable rounding.  There are an unusual number of states with a fractional apportionment below 0.5 (32 vs 18 above).  This results in 4 states with such a fraction getting an extra seat (OR, TX, MN, and PA).  In general, this is favorable to larger states since they can distribute their shortfall among more representatives (in 2000, California gained its 53rd seat that way).  Texas could lose the 36th seat with a very small decrease in the projected increase.

New York could hold on to a seat (losing 1 rather than 2) with a slight uptick in population, or downtick by Texas, Minnesota, or Oregon.

Pennsylvania is losing population share faster than Ohio, but Ohio will lose 2 seats because it was so near to losing its 18th seat in 2000.

New Jersey will likely lose a seat (compared to last year's projection) due to a slowing in its population increase from the early part of the decade.

Arizona could be limited to one new seat if the projected increase is slightly high.

Washington as noted elsewhere could gain a 10th seat.

If Missouri doesn't lose a seat in 2010, it will in 2020.

If Minnesota doesn't lose a seat in 2010, it probably will in 2020.

Colorado will likely gain a seat in 2020, while Alabama will probably lose 1.

South Carolina could gain a seat in 2020.  It has had 6 representatives since 1930.  I suspect some of the recent gain is an overflow from Charlotte, NC across the border.

I did not make an adjustment for Louisiana, but it would have lost its 7th seat even without Katrina.

If Oregon doesn't get a 6th representative in 2010, it will in 2020.

Utah could gain a representative in 2020 as well if they get lucky.

West Virginia and Nebraska will be very suceptible to the loss of a representative in 2020, while Idaho could gain one.

Rhode Island could be vulnerable to loss of a representative in 2020.  It was estimated to have lost population from 2006 to 2007.

Montana appears to be stuck just short of regaining its 2nd representative.

From 2000 to 2010, all western states except HI, MT, and WY are estimated to be growing faster than the country as a whole.  This is also true of the South Atlantic states from DE to FL, with the exception of MD.  The other two fast growing states are TX and TN.

[jimrtex]

Thanks for making maps. I'm a visual person.

I see a few problems:
First Map (9 districts)
-The yellow district isn't really connected. The biggest issue is Clallam and Kitsap. This also makes the dark green district disconnected as well because SW King County and Jefferson County do not go together (culturally).
-Other than that there are only a few minor changes you could make, but it looks like you tried really hard. The biggest problem is that some counties just have to be split up, and placed with similar counties otherwise there are geographical dissimilarities.

The yellow (Bellingham) district really is connected according to sources like Mapquest or Rand McNally. San Juan county borders Clallam and Island county borders Kitsap. The dark green (Olympia) district is physically connected through the part of Pierce on the Peninsula and Vashon Island. Cultural connection was not a factor for me, except that I disallowed maps that spanned the Cascades except along the Columbia River. Placing Jefferson with either Bellingham or Vancouver would require an additional county to be split.

I would side with Ottermax on this.  Across a body of water, I would require either a bridge or ferry link to establish contiguity.  If there were no such links, I would permit nearest point contiguity if necessary to establish contiguity (eg to connect all parts of county, or to connect counties that would otherwise be disconnected.

So, I would reject the Clallam-San Juan and Island-Kitsap links, since the two island counties have connections to the east.  I would also require you to change the Vashon Island link using the ferry from the south end of the island into Tacoma and then across the Narrows Bridge.

If someone were to produce a map with districts crossing the northern Cascades that split fewer counties, I might be inclined to accept that.

[jimrtex]

I'm not convinced that ferries and bridges are the only cross-water connections to allow. Distance should be given some consideration, as the ferry connection from Edmonds/Snohomish to Kingston/Kitsap is greater than the distance from Kitsap to Island at Hansville. Also I would think that an arbitrary cross-water connection where the counties officially connect is no worse than a cross-mountain connection with no pass or adjacent counties in the plains that share a short but finite border with no road.

The Edmonds-Kingston connection is longer only because Kingston has a harbor indentation and Edmonds is slightly to the north of the headland.  There is no connection at Hansville which is completely off the highway system.  The San Juan-Clallam boundary might only exist because of Canada, which makes the Straits of Juan de Fuca an inland waterway.  If Vancouver Island did not exist, the Clallam border would at most only extend 3 miles north, and there wouldn't be the SW corner of San Juan County.

To take another example, I would permit a Richmond-New York link in New York State based on the Staten Island Ferry, while disallowing a Bronx-Nassau link based on the marine boundary.

I would also apply a rule regarding corner connections or near-corner connections: something like the boundary must be 5% of the total boundary of one of the counties, where the boundaries might be idealized:

For the total boundary, use the circumference of a circle with area equal to area of the county, (ie C = 2 sqrt (pi * area) ).  This avoids a penalty for irregularly shaped counties.  And for the shared-boundary, I would apply some sort of algorithm that would reduce kinky borders such as one that follows a meandering stream.

Requiring a highway link might be difficult to apply.  Should Washington 20 be disqualified as link between Whatcom or Skagit and Okanogan counties, but allowed as a link between the two together and Okanagan? 

In other cases, a highway might clip the corner of a 3rd county, but people would be travelling between the two counties.  For example, Colorado 82 NW from Aspen clips the corner of SW Eagle County, but it is a long ways from the Eagle and Vail areas, which would be reached by first going to Glenwood Springs in Garfield County.  The other roads out of Pitkin County are closed in winter.

The county commissioner in southern Hinsdale County, Colorado must travel through 6 other counties (5 county seats) during winter to get to the county seat of Lake City (around 250 miles).  In summer, the trip is reduced to 3 other counties.

I like the idea of requiring a highway link, but I don't know how to practically state a rule.

[jimrtex]

I understand what you are saying, but I see no political difference between boundaries drawn on water and those drawn on land. If there is no practical highway rule, why should there be a ferry rule?

Also, if there is a ferry rule, one has consider at what width does the rule apply. There are any number of lakes rivers and streams that divide counties. Would the rule prohibit a cross-river link if there is no bridge along that stretch? I think that it becomes very hard to define a clear test that isn't arbitrary.

Maritime boundaries are sometimes fairly arbitrary, and provide no economic, transportation, or other demographic linkage.  For example, Queens and Richmond counties in New York share a border, as do Bronx and Nassau counties.  Even given the bizarre shape of some New York City CDs, no one* has considered linking these areas.  But it is quite possible that an automated process might connect those counties if it might reduce the number of cross-border districts, especially given the otherwise low connectivity of those counties.

*Though New York once had a CD that combined Rockland and Richmond counties.

Use of sea areas also increases the possibility of mischievous districts that link to land areas by a shared (unpopulated) water area.  This is already done in New York City.  In 2002, the Democrats in Texas proposed linking a part of eastern Nueces County via Corpus Christi Bay with a rural strip in western Nueces County and several smaller counties in South Texas.  Nueces County has a population equivalent to about 2.2 House seats, and under the Texas and US Constitutions must have 2 whole districts within the county, with the remnant shared with adjoining counties.  So two districts were drawn in Corpus Christi and some smaller towns in the southern and western parts of the county, and the eastern part of the city, where the incumbent lived was linked around the north side of the city via water.   During the floor debate the Representative for the area ended his speech by inflating a rubber raft.

A county must be self-contiguous, by land, if possible.  If that is not possible, the link may be bridge or ferry.  Only if that fails is a third test used, which is nearest crossing.  In the Seattle area, it is reasonable to draw district boundaries across Lake Washington using the 2 bridges.  It would be wrong, IMO, to connect Kenmore and Renton via the lake.  It would also be wrong to connect areas in south and north Seattle via the lake or via Puget Sound, even if those waters within the city limits.

If you wanted a less arbitrary rule, you could consider local opinion, perhaps as expressed by local governing bodies.  Such expression should be made before the redistricting commences.  For example, if the Clallam and San Juan county commissioners agree that the two counties are neighbors for districting purposes, they are neighbors.  If the Whatcom and Okanogan commissioners say that they are not neighbors, they are not.  There would have to be a reasonableness test applied, so that even if King and Pierce counties said they weren't neighbors it would be rejected.

[jimrtex]

I like your idea for a means for a redistricting commission to accept agreement for non-adjacency. I also would suggest that the default starting point is to use adjacency as set by the map, be it land or water. However, in my interpretation, I wouldn't arbitrarily link Richland and Rockland counties, since it would technically pass through Kings, New York, Bronx, and Westchester counties in the Hudson. That's a lot of split counties!

I could see an initial object application of a rule, with the commission then making a subjective determination.

I wasn't suggesting that Rockland and Richmond be linked, but noting that it had been.  In the 1820s' 1824, the CD's in the downstate area were:

CD 1: Queens and Suffolk).  Nassau wasn't split off from Queens until around 1900 when the remainder of Queens was annexed to NYC.

CD2: Kings, Richmond, and Rockland.  I had forgotten that Brooklyn was also included in the district.

CD3: New York (3 representatives elected AL)

CD4: Putnam and Westchester (the Bronx was split off from Westchester around 1900) at the time the modern 5-borough NYC was established.

CD6: Orange

At the time, Orange had more than Kings and Richmond combined, so it appears that Rockland was added to the southern counties to make up the numbers.

[jimrtex]

How long has it been since a census didn't give California any Congress seats?

1920 was the last.  California had 11 House seats before and after the census.

Ah, thanks. It has been a long while. My how tiny Cali's population was back then.

But that was because Congress didn't reapportion after the 1920 Census.  They should have had 14 representatives.  Because of the skip, they went from 11 to 20 after 1930 (Virginia currently has 11, and Illinois has 19).