Census population estimates 2011-2019

[jimrtex]

It's been an hour and Jim hasn't posted his updated spreadsheet yet.

State               2010    2020   10-20  20  Ch.   Need     Act    Rate    Need
Alabama            6.737   6.431  -0.307   6  -1      54     132   0.27%   0.67%
Alaska             1.117   1.101  -0.016   1   =     332      41   0.56%  14.89%
Arizona            8.999   9.502   0.503  10  +1     -60     877   1.29%   0.99%
Arkansas           4.129   3.998  -0.131   4   =    -406     123   0.41%  -4.69%
California        52.369  52.791   0.422  53   =    -547    3185   0.82%   0.33%
Colorado           7.087   7.644   0.557   8  +1    -157     814   1.51%   0.51%
Connecticut        5.049   4.718  -0.331   5   =    -195      19   0.05%  -1.96%
Delaware           1.358   1.383   0.025   1   =      96      89   0.95%   4.42%
Florida           26.435  28.562   2.127  29  +2    -223    3074   1.53%   1.15%
Georgia           13.627  14.010   0.383  14   =     378    1038   1.02%   2.30%
Hawaii             1.976   1.963  -0.014   2   =    -379      94   0.67%  -9.81%
Idaho              2.260   2.373   0.114   2   =     100     210   1.26%   3.29%
Illinois          18.043  16.705  -1.337  17  -1    -259     -39  -0.03%  -0.77%
Indiana            9.128   8.810  -0.318   9   =    -290     254   0.38%  -1.21%
Iowa               4.312   4.186  -0.126   4   =     242     137   0.44%   3.16%
Kansas             4.042   3.865  -0.176   4   =    -304      83   0.29%  -3.62%
Kentucky           6.120   5.894  -0.226   6   =    -336     159   0.36%  -2.44%
Louisiana          6.392   6.212  -0.180   6   =     223     210   0.45%   2.14%
Maine              1.933   1.818  -0.115   2   =    -264      10   0.08%  -7.61%
Maryland           8.131   8.059  -0.072   8   =     340     388   0.65%   2.64%
Massachusetts      9.217   9.128  -0.089   9   =     287     434   0.64%   2.13%
Michigan          13.902  13.054  -0.848  13  -1     344     109   0.11%   1.35%
Minnesota          7.472   7.436  -0.036   7  -1      50     380   0.69%   1.01%
Mississippi        4.201   3.936  -0.265   4   =    -358      23   0.08%  -4.46%
Missouri           8.433   8.059  -0.375   8   =     340     173   0.28%   2.26%
Montana            1.478   1.489   0.011   1   =       9      85   0.83%   1.13%
Nebraska           2.615   2.603  -0.012   3   =     -96     131   0.69%  -1.12%
Nevada             3.829   4.103   0.274   4   =     307     419   1.45%   4.98%
New Hampshire      1.917   1.836  -0.081   2   =    -278      36   0.27%  -7.78%
New Jersey        12.369  11.874  -0.494  12   =    -358     296   0.33%  -1.12%
New Mexico         2.937   2.785  -0.152   3   =    -238      40   0.19%  -4.09%
New York          27.244  26.154  -1.090  26  -1     269     653   0.33%   0.82%
North Carolina    13.413  13.805   0.392  14  +1    -317    1033   1.03%  -0.08%
North Dakota       1.070   1.145   0.076   1   =     294     117   1.61%  14.02%
Ohio              16.224  15.288  -0.936  15  -1     164     169   0.15%   0.65%
Oklahoma           5.297   5.247  -0.050   5   =     195     250   0.65%   2.41%
Oregon             5.408   5.593   0.185   6  +1    -105     436   1.08%   0.17%
Pennsylvania      17.862  16.775  -1.087  17  -1    -313     143   0.11%  -0.78%
Rhode Island       1.562   1.474  -0.088   1  -1      21      10   0.09%   0.81%
South Carolina     6.521   6.786   0.265   7   =    -260     559   1.15%  -0.73%
South Dakota       1.249   1.267   0.018   1   =     192      78   0.91%   8.32%
Tennessee          8.935   8.971   0.037   9   =    -414     516   0.78%  -1.47%
Texas             35.350  38.649   3.299  39  +3    -351    4459   1.65%   1.21%
Utah               3.917   4.260   0.343   4   =     186     477   1.60%   3.69%
Vermont            1.012   0.955  -0.057   1   =     461      -3  -0.05%  22.25%
Virginia          11.258  11.309   0.051  11   =     148     654   0.79%   1.41%
Washington         9.466  10.040   0.575  10   =     354     957   1.34%   3.01%
West Virginia      2.652   2.405  -0.247   2  -1      75     -51  -0.28%   1.21%
Wisconsin          8.010   7.636  -0.373   8   =    -151     150   0.26%  -0.69%
Wyoming            0.937   0.913  -0.024   1   =     498      22   0.38%  25.57%

Over this decade projections have changed very little.

After 2011, projected gainers were Colorado, Florida, North Carolina, Texas+3, and Virginia.
Projected losers were Alabama, Illinois, Michigan, Minnesota, Ohio, Pennsylvania, and Rhode Island.

In 2011, Arizona and Florida were still shaking off the effects of the housing bubble in 2008, which saw people without jobs upside down on their mortgages, and near-seniors not able to retire and move to Florida.  Oregon has been grasping a 6th seat for a long time, but not quite able to keep up with Washington, Nevada, Utah, Arizona, and Colorado. Mid-decade they had an uptick in population increase.

Meanwhile, New York has dropped from a rate that would have kept them losing a whole seat, to much slower growth. West Virginia went from anemic growth to an actual loss, and Virginia has slowed its growth, as the big government boom of the early Obama years has ended.

By 2011, North Carolina had gained a seat, and Minnesota had lost a seat, and if this were Australia, there would have been a redistribution.

By 2002, there were no changes.

By 2003, West Virginia was projected to lose its 3rd district, and Alabama keep its 7th. At the time West Virginia was at zero growth, and could have kept the district if it could only increase its rate of growth to 0.08%. It wasn't anything Alabama was doing, but simply that West Virginia had spun out.

By 2004, Texas would have gained a seat, and Pennsylvania lost a seat, triggering an Australian redistribution. There were no changes in the projections, but Alabama was getting narrowly close to losing a seat.

By 2005, Florida would have gained a seat, and Illinois lost a seat, triggering redistribution. The projections changed significantly. Arizona was projected to gain a seat, as was Oregon. Mid-decade growth in Oregon is roughly twice that of the early decade. California was also projected to gain a seat, but just barely. Virginia had fallen below (it had grown at a 0.86% rate, but if it increased to 0.89% it could keep the gain. Alabama was again projected to lose a seat, and New York to barely lose a seat.

By 2016, Oregon would have gained a seat, and Michigan lost a seat. Florida was now projected to gain a second seat, while California no longer was.

For 2017, Colorado would have gained a seat, and Texas a second seat. We would be busy speculating on the 8-district map in Colorado and 38-district map in Texas for the 2008 election. Meanwhile, New York and West Virginia would have lost a district.

In Australia, if it is too late to draw a full map, the most populous district is split in half, or the least two populous adjacent districts merged.

The projections for 2020 have not changed. There would be speculative maps for Arizona+1, Florida+2, and Texas+3, as well as Alabama-1, Ohio-1, and Rhode Island -1 (no speculation needed here, except who will win the Democratic primary between two incumbents).

[jimrtex]

Montana gaining a second seat really could be a good outcome for democrats,  western Montana has some pretty liberal areas and is actually trending Democratic is cases.   If the state is split in two that seat just might become competitive. 

Drawing a hook from Missoula along the Canadian border and connecting it with East Montana would result in 2 roughly R+11 districts. It'd be interesting to see what they would do

Montana has a redistricting commission. It drew two congressional districts in 1980. In the early 1990s when the loss of the 2nd seat was being litigated, the legislature ordered them to draw two districts. They apparently did so, but the final official report only had one district.

You could probably use the 1980 district boundaries, and then adjust them a bit each decade. Great Falls and Billings have probably had enough growth to keep the two districts pretty much in balance, and Silver Bow (Butte) has been in decline.

Maps of historical district boundaries

The numbers in the map names indicate the Congresses they were in effect. The First Congress began in 1789 (and under modern system would have been elected in 1788). The 51st Congress was elected in 1888, and the 101st in 1988.

Montana gained a second representative in 1912, but did not create two districts until 1918. Those districts were frozen until 'Reynolds v Sims' i.e. 66th (1918) through 89th (1964). It is quite possible that these districts were never equal population, since it appears that geography was more significant, following the Rockies.

90 through 92 (1966-1970) was the first equal-population map, and the boundary had to move eastward.

93 through 97 (1972-1980) and the line went further east, wrapping around Great Falls.

98 through 98 (1982) I'm not sure what changed or not changed. Perhaps there was litigation, and the districts had to made even more equal.

99 (1984) through 102 (1990) The boundary moved back west.

103 (1992) through 112 (2010) This is the single district map.

Perhaps there would have been a need for a larger change, and Gallatin (Bozeman) would put in the east, forcing the northern boundary back to the east around Great Falls.

In 1992, the Democratic and Republican representatives, and the Democrat (Pat Williams) won. Williams did not seek re-election in 1996, and the House seat has been Republican ever since.

With the two universities, the state capital, and Butte, the western district might be at least competitive for Democrats.

Historical Shapefiles

The animation on the first page is pretty cool.

[jimrtex]

Interesting that a Puerto Rican in-migration can't move the needle further in Florida, but a hurricane-driven bust in Texas *could* cost the third seat if sizable enough.

Florida's increase was only enough for a 2nd district, and that after recovery from the housing bubble took hold. Interstate migration has slowed down, and Florida must constantly be replenishing the retirees who move there in their 60s, and die within a few decades. There is more growth if you get younger migrants who are young enough to reproduce.

People who moved because their houses flooded, moved to Dallas and San Antonio and Austin, and did not leave the state. As long as oil holds at $60 there will be jobs in Houston. If you have a job and had flood insurance, you can live in an apartment or hotel, while your house is repaired or a new one is built. If you didn't have flood insurance, but have a job, you are still better off, than moving to where you don't have a job. And getting a job in San Francisco and renting a house in Stockton doesn't have a lot of appeal.

[jimrtex]

The most annoying thing about the estimates is that they change prior year(s) estimates (which i understand), but don't give you an easy way to see those changes.

On the estimates pages and also the American Fact Finder you can get previous vintages of estimates.

I think the changes are hard to visualize. If the 2016 and 2017 estimates  are the same, but the 2017 estimate is that there was an increase, then the 2016 estimate was revised downward. But that wouldn't be because they had missed a block of people dying or moving, but they overestimated some changes. So the growth curve did not change, but was modified. Perhaps an animation might work.

[jimrtex]

An alternate projection could use just the last two years of estimates to determine the rate of growth for the rest of the decade. That model gives an extra seat to MT at the expense of one from CA.

This would be interesting because it illustrates a paradox in the apportionment method. California would have gained in population share while losing in representation share.

The last two decades there has been an inordinate number of states with fractions under 0.5, that got rounded upward. This benefited larger states, because they can spread their deficit among a large number of districts. So even though California had a bit over 52/435 of the population, they got a 53rd seat. But now the anomaly of states with fractions under 0.5 is disappearing, and though California will be closer to 53/435 of the population they could lose a district.

[jimrtex]

I've been watching the census estimates throughout the decade and I've seen California move around a bit. To those that pay attention more closely, what are the odds or what will it take for the creation of CA-54?

In general terms, California would have to increase from 53/435 of the total population to 54/435 of the population. This means that California would have to increase at 54/53 - 1 or 1.89% faster than the country as a whole. But California is such a large share of the population (almost 1/8), that an 8% increase in California would produce a 1% increase in the total population, even if all the other states were static.

The USA as whole will increase about 7.7% over the decade, and based on projecting the first seven years estimates forward for 10 years, California will grow at 8.5%. But the growth rate in California has dropped the past two years.

In the first five years of the decade, California increased by 345K. 347K, 328K, 354K, and 331K; but in the last two years has only increased by 264K and 240K.

California needed 2.857M increase just to tread water. If the increase for the first five years had been sustained, California would have gained 3.410M, and the surplus of 553K would have gone a long way towards populating another congressional district.

But if we project the growth from the first seven years, then California would only grow 3.156M and the surplus would only be 299K. But if we project the last year's growth over the final three years, California would only have a 2.929M increase and California would just be treading water.

The Census Bureau also estimates the components of change, births, deaths, international migration, and domestic migration. Births and deaths are easy to estimate since most are officially recorded. This is not true for migration. You don't have to tell anyone you are moving, and you might not even know that you are changing residence. You might take a summer vacation, decide you like the location, and find a job.

Births have declined slightly (4%) over the seven years. This might represent a decline in the fertility rate (rate at which women in child-bearing ages have children), or a decline in the number of women of child-bearing ages, or both.

Deaths have increased by about 15% seven years. This is mostly due to aging baby boomers. The oldest baby boomers have aged from 65 to 72 during the first seven years. About 2% of 72-YO die, while only 1% of 65-YO will die.

The combination of the two has meant a decrease in the natural increase (births minus deaths) of about 21%, from 271K to 214K.

International migration has held steady, and actually increased the past three years.

Domestic net migration has increased sharply the last three years. Between 2010 and 2015, 3.2 million Californians left the state, and 2.9 million people moved to the state, for a net outflow of 300K. A lot of these are the same people. It may be exciting to live near the beach, but if the reality is that you have to commute from Barstow or Bakersfield to Los Angeles, you are too tired to go surfing on weekends. Or if you are divorced, you might move back home.

To make a big change in the net, you only need small increases in the inflow and outflow. A 5% decrease in inflow, and 5% increase in outflow, doubles the net flow.

I really don't know the reasons for the change. It could be lower inflows from people who realize that a higher salary does not make California livable if you can't afford housing or face a supercommute. Or perhaps it is retirees, whose home equity has recovered enough since 2008 that they can sell and move to a location where their Social Security and pension will go further.

Western states of WA, OR, ID, NV, MT. UT, and AZ have had their highest domestic inflows in the past two years. It isn't quite true for Colorado, in part because Colorado has had robust inflow throughout the decade. There is also strong inflow along the South Atlantic coastal states from North Carolina to Florida. And there have been small upticks in places like MN, AR, TN, DE, NH, and ME. So there has been an increase in outflow to nearby states.

A more obscure effect is rounding. Imagine that you polled 1000 persons, and 434 said Good, 353 said Bad, and 213 said Otherwise.

So you write an article that says 43% Good, 35% Bad, 21% Otherwise (* percentages do not total 100 because of rounding)

Or perhaps the results were 436 Good, 357 Bad, and 207 Otherwise. This is reported as 44% Good, 36% Bad, and 21% Otherwise. In this case, the percentages add to 101.

It is not because the pollster in one case didn't interview enough people, and in the second case polled too many, it is the effect of rounding error. In other cases, the rounding errors cancel, and the percentages will add to 100 (434 Good, 358 Bad, 208 Otherwise, rounds to 43, 36, 21).

The same thing can happen with the apportionment of representatives, except there are 50 states and 435 representatives. It would be embarrassing for C-SPAN to have vote totals showing *Numbers do not total 435 due to rounding.

One might expect that if you represented each states representation as decimal fraction (e.g. 52.368) 25 of the fractions would be less than 0.500 and 25 would be greater than 0.500, While this is the statistical expectation*, it won't always be true. It is somewhat like flipping a coin 50 times. The most likely outcome is 25 heads and 25 tails, but it can be more or less. It is possible, though extremely improbable that all 50 fractions would be less than 0.5, or all 50 would be more than 0.5.

And even then the total of the fractions might not sum to 25. It is possible for example that the 25 fractions less than 0.5, average 0.4, and sum to 10, while the 25 fractions greater than 0.5 average 0.8 and sum to 20, giving a sum of fractions of 30. If the fractions sum to 30, we have to give an extra seat to 30 states, but only 25 would have fractions greater than 0.5 and "deserve" an extra seat. We would have to give the other five seats to the "least undeserving".

It happens that when "extra" seats are given out, that larger states like California are favored.

On the other hand, it is also possible that the total of the fractions is less than 25, even when there are 25 states with a fraction greater than 0.5. In that case, we don't have enough extra seats to hand out. When this occurs, larger states like California are disfavored.

As it turns out in 2000 and 2010, there were more extra seats to be handed out than there were states clearly deserving them. One of those was California, which received a 53rd seat when it was still closer to 52 than 53. In the earlier part of this decade, California was approaching actually having 53/435 of the population, but with the recent uptick in domestic outflow, could drop back closer to 52.5 or 52.6. And the distribution of fractions appears to be trending back towards the ordinary, and it might be that California could be apportioned 52 seats, even while its population share increased.

*Not exactly, but within a quibble.

[jimrtex]

This is a closer look at the states of interest.

State               2010    2020   10-20  20  Ch.   Need     Act    Rate    Need
Alabama            6.737   6.431  -0.307   6  -1      54     132   0.27%   0.67%
Arizona            8.999   9.502   0.503  10  +1     -60     877   1.29%   0.99%
California        52.369  52.791   0.422  53   =    -547    3185   0.82%   0.33%
Colorado           7.087   7.644   0.557   8  +1    -157     814   1.51%   0.51%
Florida           26.435  28.562   2.127  29  +2    -223    3074   1.53%   1.15%
Georgia           13.627  14.010   0.383  14   =     378    1038   1.02%   2.30%
Illinois          18.043  16.705  -1.337  17  -1    -259     -39  -0.03%  -0.77%
Michigan          13.902  13.054  -0.848  13  -1     344     109   0.11%   1.35%
Minnesota          7.472   7.436  -0.036   7  -1      50     380   0.69%   1.01%
Montana            1.478   1.489   0.011   1   =       9      85   0.83%   1.13%
New York          27.244  26.154  -1.090  26  -1     269     653   0.33%   0.82%
North Carolina    13.413  13.805   0.392  14  +1    -317    1033   1.03%  -0.08%
Ohio              16.224  15.288  -0.936  15  -1     164     169   0.15%   0.65%
Oregon             5.408   5.593   0.185   6  +1    -105     436   1.08%   0.17%
Pennsylvania      17.862  16.775  -1.087  17  -1    -313     143   0.11%  -0.78%
Rhode Island       1.562   1.474  -0.088   1  -1      21      10   0.09%   0.81%
Texas             35.350  38.649   3.299  39  +3    -351    4459   1.65%   1.21%
Virginia          11.258  11.309   0.051  11   =     148     654   0.79%   1.41%
West Virginia      2.652   2.405  -0.247   2  -1      75     -51  -0.28%   1.21%

Alabama has only added 89K the first seven years, and is projected to add 43K more, but they would need another 54K beyond that to keep the seventh seat, which would require a better than doubling of the growth rate. It is not going to happen.

Arizona appears to be on the edge, but it really isn't. If an annual growth rate of 1.29% decreased to 0.99%, it could miss out. But the growth rate has been increasing, and was 1.56% last year.

Growth in California has dropped off significantly in the last few years. The projection is now whether California will keep its 53rd seat (it will), not whether it will gain a 54th.

Growth in Colorado has been steady to increasing a bit. To miss out on the 8th seat would mean a total collapse in the growth rate from 1.51 to 0.51%.

Florida has increased its growth rate so that is now pretty solid for a second seat. To miss out, it would have to drop down to 1.15% per year. Last year it was at 1.59%. But Florida is a long way from adding a 3rd seat.

Georgia is matching North Carolina, but it got its 14th seat in 2010 while North Carolina missed out.

Illinois is losing population, but only slightly. To lose a second seat would require a mass exodus. Since Illinois is losing at more than one district per decade (1.337) it would be a prime candidate to lose two districts next decade.

For Michigan to keep its 14th seat would require going from tepid growth to people pouring in.

Minnesota continues to drift away from keeping its 8th seat. Minnesota is projected to gain 7.2% this decade, but the country as a whole is gaining 7.7%. Minnesota has averages a gain of 0.69% this decade. Last year was a good year at 0.93%, but this is still short of the 1.01% it will need to catch up. The states that Minnesota is chasing are Arizona and Florida, and they are unlikely to make it easy.

Montana is expected to add 85K this decade, but need 9K extra. When you are a small as Montana, 9K represents an extra year's growth. Montana did gain 1.14% this year, which is a bit better than what is needed. For the decade, Montana is growing 0.9% faster than the country for the decade. At that rate it takes decades if not centuries to gain a seat. Montana may also suffer a bit from lowered activity in the Williston Basin.

The growth rate for New York has sharply dropped during this decade. While the compounded rate for the decade is calculated at 0.33%, the estimate for 2016 to 2017 was 0.07%. While some of this decline may be attributed to Puerto Ricans retiring to the island, there must be many other factors at work, including the decline of people moving into cities. Puerto Ricans returning to the mainland will want to live with relatives. Some who had moved back to Puerto Rico may have done so because their children had moved elsewhere.

North Carolina had barely missed out on its 14th seat and may have already had received it by the time of the July 2010 estimate base.

Ohio is only projected to grow at 1.5% for the decade, enough to cause it to lose a full seat.

Oregon was dawdling along just below the level needed for a sixth seat until 2013, when net domestic inflow increased dramatically to give it a boost. This must be tied to more people moving north from California, and the number moving south remaining steady or declining.

Pennsylvania will only gain 1.1% for the decade, and will lose a seat.

Rhode Island is only gaining 0.9% for the decade, and will be passed by Montana. Rhode Island is more certain of losing its seat, than Montana gaining one (at least one of these must happen).

Texas is on pace to gain three seats. A 17.7% over the decade, which is 10% faster than the national rate, results in a 10% increase in representation (10% of 36 is 3.6). The only reason that Texas is not gaining a fourth seat is that it got a favorable rounding in 2013. Unemployment is at 3.8%, job growth in percentage term was 2nd in the country, and oil prices are at the highest level since 2014.

Virginia was somewhat close to gaining a seat in the early part of the decade, but since then domestic migration has reversed to an outflow. An 8.2% increase is just slightly ahead of the US rate.

West Virginia is one of three states losing population (Illinois and Vermont are the others), and will lose 2.8% of its population. West Virginia is the only state with a natural population decrease (more deaths than births), a result of an aging population, and potential parents leaving the state, or holding off having babies in uncertain times.

[jimrtex]

So it's quite likely both MT and RI have just 1 CD?

RI will almost certainly lose a seat but MT will be right on the threshold of gaining a seat. Right now the projection using short term trends has them gaining a seat, the projection using long term trends has them staying at one seat (FWIW I prefer using short term trends).

BTW Congress uses a different method of apportioning seats ( the Huntington–Hill method) than jimrtex does (The Vinton or Hamilton method) that can produce slightly different results.

https://en.wikipedia.org/wiki/United_States_congressional_apportionment

I use Huntington-Hill. My use of "raw" may have misled you. I used a slightly cooked version.

The divisor methods don't nominally use a quota. We just divide state populations by the successive divisors and rank the quotients.

The divisors for Huntington-Hill are:

sqrt(n*(n+1) = 1.414, 2.449, 3.464, ... 52.498, ...

In 2010, California had a population 37,254,518 (disregarding the overseas population).

For California's 53 seat, we divide the state population by sqrt(52*53) = 52.498

37254518 / 52.498 = 709642.051

If 709642.051 is among the 435 largest quotients then California gets a 53rd seat which it did. But we notice that the quotients near the 435th seat are about equal to the quota for the USA population divided by 435 = 708,408. But for reasons, I'll explain later, I'll divide by 711,428 (Q' adjusted quota).

We divide every state's population by 711,428.

q' = P / Q'

P'(California) = 52.366

We can then divide by the divisors, so 52.366 / 52.498 = 0.997. Values close to one represent states just below or above the 435th seat. We still have to rank these values, to determine which are rounded up or not. If we were doing independent rounding, we could simply look at the value, and since it is less than 1, round down. But if we did independent rounding, we could not guarantee 435 representatives.

Dividing by a positive constant does not change the relationship for ranking purposes:

if a > b and c > 0 then a/c > b/c

For Webster's method, a state with population p is entitled to r representatives, where
Q = P_USA/N, where P_USA is the total population of the 50 states, and N is the number of representatives (435 in this case).

p/Q = r

We can look at the value of R, and say that a state should have r representatives, but that is only true if we are apportioning fractional representatives. But it nonetheless correct for the raw share of the population. If a state has 27.235 / 435 of the population, it should have 27.235 representatives, except for the silly notion that representatives must be whole persons.

For Huntington-Hill

p/Q = sqrt((r-1/2)*(r+1/2))

To simplify our expression, we will use q = p/Q where q is a quotient.

q = sqrt(r-1/2)*(r+1/2))

Squaring both sides and multiplying the two terms under the radical.

q² = r² - 1/4

Solving for r,

r = sqrt(q² +1/4)

This is the raw entitlement under Huntington-Hill. For example, a state with sqrt(2)/435 of the total population is entitled to 1.5 representatives.  1.5 = sqrt(2 + 1/4)

But if we do this for all states, and sum them up, we will end up with 436.841 representatives. But we can adjust our quota, so that it is Q' = P_USA/(435*(435/436.841). This will yield 435.015 representatives. Adjusting to 435/436.856 produces the expected 435 representatives.

So the "raw" numbers

r = sqrt(q'² +1/4)

Where q' = p/Q'

And Q' is the adjusted quota.

For 2010, it is 711,428. The adjusted quota is dependent on the overall distribution of populations, but it can be calculated easily and converges quite quickly. The adjustment is increasing slightly

436.856/435 for 2010
436.873/435 for 2017 estimate.
436.881/435 for 2020 projected.

This increase indicates a greater small state bias. Not unexpected considering that the 2nd and 3rd most populous states are fast gainers, and the most populous state is an average gainer.

Among states with 3 or fewer representatives:

AK, SD, WY, VT, HI, RI, NH, ME, NM, NE, and WV are losing population share.
MT is staying even
DE, ID, ND* are gaining population share, but ND is quite iffy, and DE is moderate.

While the difference is 0.43%, the cost to California is 0.43% * 52.5 = 0.23 representatives.

Anyhow, the raw numbers provide an estimate of how many representatives a state should have if independent rounding were done and the distribution is based on Huntington-Hill. It is particularly useful for seeing temporal trends (e.g New Jersey is losing about 1/2 a representative per decade).

I do use it as an estimate of the number of seats a state should have. If a state is entitled to n.xxx representatives (as represented by a mixed decimal fraction), then it should have either n or n+1 (with a minimum of one). Summing the values of n, I can calculate the number of guaranteed seats without rounding. For 2020 projections this is 412 seats, leaving 23 seats (435-412) to be apportioned by rounding. I then divide the projected population of each state by the divisor for the next seat; sqrt(n*(n+1)) and assign the 23 final seats based on the largest quotients. This does not determine the 413th-435th seats assigned, but rather that a state will be in the top 435.

Note that the divisor methods do not not guarantee an apportionment of between n and n+1 seats. It may be outside that range, for example n-1 or n+2. This is known as a quota violation, and is a known flaw of Huntington-Hill and other divisor methods. This requires an unusual (rare) distribution of fractions, and modeling for the US indicates that it will be quite rare for the USA, because of the large number (50) of entities getting seats.

It may be quite common when there are only a few entities, and one is relatively quite large. An example is the British House of Commons, where there are only four apportionment entities (England, Scotland, Wales, and Northern Ireland), and England has 80%+ of the population.

[jimrtex]

Interesting that a Puerto Rican in-migration can't move the needle further in Florida, but a hurricane-driven bust in Texas *could* cost the third seat if sizable enough.

I believe these estimates are supposed to be from July, 2017. So they would not take into account the Hurricanes. Like Muon said, it will be interesting if the Puerto Rican hurricane diaspora's impact also on New York, along with Florida.

Interstate migration estimates for 2016 show that a very large share of Puerto Rican migration flow is to Florida (40%). Texas was second, slightly ahead of New York and Pennsylvania.

Florida is solidly gaining its 2nd seat, up from early in the decade when it was projected to only gain one. But it is a long way off from a third seat.

[jimrtex]

In general terms, California would have to increase from 53/435 of the total population to 54/435 of the population. This means that California would have to increase at 54/53 - 1 or 1.89% faster than the country as a whole. But California is such a large share of the population (almost 1/8), that an 8% increase in California would produce a 1% increase in the total population, even if all the other states were static.

The USA as whole will increase about 7.7% over the decade, and based on projecting the first seven years estimates forward for 10 years, California will grow at 8.5%. But the growth rate in California has dropped the past two years.

In the first five years of the decade, California increased by 345K. 347K, 328K, 354K, and 331K; but in the last two years has only increased by 264K and 240K.

California needed 2.857M increase just to tread water. If the increase for the first five years had been sustained, California would have gained 3.410M, and the surplus of 553K would have gone a long way towards populating another congressional district.

I appreciate your answer. I did read it all. The reason I asked is because I recall looking at Census estimates maybe 2 years ago and it seemed like California was on track for a 54th seat and now suddenly it could actually lose a seat. I realize that bigger states are more prone to the potential of gaining or losing a certain number of seats (i.e. muon noting that CA-53 would be seat 433 and CA-54 would be seat 440).

Do you have or know of a spreadsheet where one could input population numbers to determine the overall seat apportionment?

One thing I do wonder about is if certain states might make their own efforts to ensure the accuracy of the overall count.

These are based on the actual estimates for each year (July) for 2010 through 2017, and projected forward to 2020.

Year   Estimate  Projection
2010   52.594   52.781
2011   52.689   53.389
2012   52.778   53.426
2013   52.858   53.416
2014   52.947   53.431
2015   52.999   53.370
2016   52.968   53.195
2017   52.914   53.037
2018   52.860   52.918
2019   52.752   52.766
2020   52.590   52.590

In July 2010, California was estimated to have 52.594/435 of the US population. This was up from the 52.589 from the Census. Projected forward for the remainder of the decade this would be projected to reach 52.781 in 2020 (the first estimate was only for one quarter). Through about 2014, the increase in share was about 0.090/435 per year, or about 0.900/435 per decade, enough to likely gain the 54th seat, or put it in the realm of possibility.

The population share increase in 2015 declined to 0.052 in 2016, and the projected 2020 population declined. In 2016 and 2017, California's population share declined. It was growing slightly slower than the country as whole (0.1%). But the projected share for 2020 was greater than the estimate for 2017 which could only happen if the short term trend reversed itself.

Imagine you are on a roller coaster. You are going up the first rise, and have risen 400 feet in four seconds. You project that after 10 seconds you will rise 1000 feet.

You are entering the crest of the rise, and are at 450 feet after five seconds. You quickly calculate 450/5 * 10 = 900 feet after 10 seconds (you can't reach your smartphone and people are screaming, so you don't realize your assumption that the increase is constant and not slowing is wrong).

After you have begun to drop you are at 350 feet after seven seconds, and calculate 350/7 * 10 equals 500 feet after 10 seconds. You don't realize that you are projecting an increase because the projection is decreasing.

That is what is happening in California.

The projected estimates for 2018, 2019, and 2020 assume that the 2016-2017 decline will be repeated, which would get you back to the share in 2010 (i.e. California grew slightly faster than the USA in the first half of the decade, and slightly slower in the second half).

This might not be accurate. The growth rate began to decline in 2015, turned negative in 2016, and became even stronger in 2017. The net domestic outflow which is triggering the decline in share appears to be accelerating.

California had a massive influx of population after WWII, caused by people moving west (and exposure to more of the country during the war). Good economic times, and pent-up demand caused the baby boom. The boomers are now reaching retirement age. Social security is portable, and California has extreme housing costs. If you own a home, now is a good time to cash out (tax free) and move to Arizona/Nevada/Utah/Idaho.

It may also be too expensive for middle or low income persons to live in California. If you live in Kansas and are making $10/hour at Walmart, moving to California and making $15/hour is not an upgrade.

It is also possible that there is chain migration of aliens from California to other states. Many immigrants first move to live with relatives, even if they are somewhat distant. If you don't speak English, living with a second cousin-once removed-in-law, will provide support. If all your relatives live in California, you will locate in California. But over time, people may find jobs elsewhere, and with a bit of English, you might be able to find work in Phoenix or Las Vegas or Salt Lake, and recognize a small community that speaks your native language.

Also, the question that the Census Bureau asks is whether a person had a different residence one year ago. This is not the same as a citizenship question. Someone stationed in Germany with their family who is transferred to the United States, will be living in a new residence, and show up as an international transfer.

In 2016 top domestic interstate inflows were:

Florida 605K
Texas 532K
California 515K
North Carolina 331K
Georgia 305K
Arizona 273K
Virginia 264K
New York 261K
Washington 257K
Pennsylvania 252K
Colorado 223K
Illinois 204K

In 2016 domestic interstate outflows were:

California 658K
New York 450K
Texas 444K
Florida 433K
Illinois 346K
Virginia 275K
Georgia 258K
Pennsylvania 257K
North Carolina 256K
New Jersey 227K
Ohio 212K

Once migration is established it may become two-way. People move to a different state, get homesick, divorced, lose a job, and move home. A couple retires to Florida, after the husband dies, and the widow breaks her hip, she moves back to New York to live with her daughter (23 years later).

In 2016, California had 1173K domestic migrants (in and out), but only 143K net outflow. Small changes in inflow or outflow can have big changes in the net.

If we look at the ratio of inflow to outflow in 2016:

Arizona 1.42
Florida 1.40
Washington 1.34
Nevada 1.33
Oregon 1.30
North Carolina 1.29
South Carolina 1.29
Idaho 1.28
Utah 1.25
Alabama 1.22
Texas 1.20
Montana 1.20

New York 0.58
Illinois 0.59
New Jersey 0.64
Connecticut 0.67
Alaska 0.74
California 0.78
North Dakota 0.79

So California had 4 persons moving in, for every 5 moving out.

[jimrtex]

Do you have or know of a spreadsheet where one could input population numbers to determine the overall seat apportionment?

Column A(2:51): State Names
Column B(2:51): Populations (leave out DC and PR, unless you want to experiment)
A52: Cell with number of representatives, set to 435, but you can vary.
B52: Quota =SUM(B2:B51)/A52
Column C(2:51): Estimate. =B2/$B$52, etc.
Column D(2:51): Minimum number of seats. =MAX(INT(C2),1), etc, ensures all states get one representative, and avoids division by zero.
D52: Minimum seats = SUM(D2:D51)
Column E(2:51): Divisor for next seat:

Huntington-Hill: =SQRT(D2*(D2+1)), etc. (Geometric mean of n and n+1)
Webster's = D2 + 0.5 (Arithmetic mean of n and n+1)
Dean's = D2*(D2+1)*2/(D2+D2+1)  (Harmonic mean)
Jefferson's = D2+1
Adams's = D2

Webster's is same as St.Lague, Jefferson's the same ad D'Hondt

Column F(2:F51): Quotient = B2/E2, etc. May also use C2/E2, etc.
Column G(2:G51): Quotient Rank = RANK(F2,F$2:F$51), etc.
G52 extra seats to apportion A52-D52

Column H(2:H51):= D2 + IF(G2 <= $G$52, 1, 0), etc. add one for largest quotients.
H52 total apportionment = SUM(H2:H51), should match A52

[jimrtex]

Alabama has inflow?!

I don't know.

The population estimates include estimates of components of change (births, deaths, domestic net migration, international net migration).

Some years this was positive, others negative. Over 7 years, the net was 1153 persons. 2017 had the biggest inflow, but only 3K.

The other number is from the 2016 ACS, and estimates the state-to--state flows. The margin-of-error is quite large 122,220 +/- 9,811 into Alabama, 99,892 +/- 7,271 out of Alabama (90% confidence levels). If you take the smallest differentials 112,409 to 107,163 is a ratio of 105%.

For previous years the ratio would have been 1.13, 0.96, 1.07, 0.96, 1.09. 1.10, which are pretty consistent with not much flow.

Based on the 5-year ACS, the 122K is an outlier (or alternatively, the other 4 years were on the low side.  105, 104, 108, 114, 122 could represent an upward trend, an exaggerated upward trend, or an outlier in the 5th year.

The Census Bureau reports a lot more data about inward flows, since the question asked is whether the person lived in a different residence 1-year ago, and if not where you lived. This gets reported as: same house, same county, same state, not in the US.

Some counties with high interstate movers as percentage of population are Dale and Russell, which are likely tied to Fort Rucker and Fort Benning. Russell will get "interstate" movers who simply crossed the state line from Columbus.

Others include Lee and Tuscaloosa. The Census Bureau considers college students living in dorms to be residing at that location, and the same would be true for students living off campus. Freshmen would report that they had moved in the last year. Upper-classmen might, depending on how they interpreted the question. There may be procedural differences as well. Group quarters at college campuses are only surveyed in January-April, and September-December. The Census Bureau really has no way of knowing whether an apartment is occupied by a seasonal student, or a permanent resident.

There may be biases introduced. If a student does not complete college, they are somewhat likely to return to their hometown. If they are living at their parent's home, Mom when she fills out the census form may not remember that Johnny was "residing" at Auburn 12 months previously.

And the skipping of the summer months may have a bias. Let's say those who would have been surveyed in July were shifted to September/October; August to November/December; May to January/February; and June to March/April. Those who would have been surveyed in July and August, will be surveyed after they have arrived on campus. Those who would have left by May and June, will be surveyed before they have left.

This sort of shifting would also happen for Alabamians who go out of state, but the student flow might be towards Alabama. Where a parent attended school may influence the choice of school for their children. If you graduated from Auburn and lived in Atlanta, you might be willing to pay out-of-state tuition to Auburn, particularly if you viewed Athens as too liberal, and if your child wanted to go to Clemson, you might not only refuse to pay their tuition, you would probably disinherit them. There are likely more Alabama and Auburn graduates in Atlanta, than UGA grads in Birmingham.

Other counties with high domestic inflows are Lauderdale, on the state boundary, and probably with more jobs than adjacent areas of Tennessee or Mississippi; Madison, where Huntsville will actually attract college-educated persons; and Baldwin, next to Pensacola, and actually has a coastline, which would be attractive to retirees. Far southern Alabama may be attractive to retirees who want a warm climate with low housing costs.

If you take the states north from Virginia, Kentucky, Missouri, and Kansas, only ME, NH, DE, SD, and ND had domestic inflows cumulative over the the estimate period. Of the remaining states in the southeast and west, only MS, LA, NM, WY, AK, and HI had domestic outflows. Alabama barely makes it into the positive side because it is in the southeast, and better off than Mississippi and Louisiana.

[jimrtex]

Do you have or know of a spreadsheet where one could input population numbers to determine the overall seat apportionment?

Column A(2:51): State Names
Column B(2:51): Populations (leave out DC and PR, unless you want to experiment)
A52: Cell with number of representatives, set to 435, but you can vary.
B52: Quota =SUM(B2:B51)/A52
Column C(2:51): Estimate. =B2/$B$52, etc.
Column D(2:51): Minimum number of seats. =MAX(INT(C2),1), etc, ensures all states get one representative, and avoids division by zero.
D52: Minimum seats = SUM(D2:D51)
Column E(2:51): Divisor for next seat:

Huntington-Hill: =SQRT(D2*(D2+1)), etc. (Geometric mean of n and n+1)
Webster's = D2 + 0.5 (Arithmetic mean of n and n+1)
Dean's = D2*(D2+1)*2/(D2+D2+1)  (Harmonic mean)
Jefferson's = D2+1
Adams's = D2

Webster's is same as St.Lague, Jefferson's the same ad D'Hondt

Column F(2:F51): Quotient = B2/E2, etc. May also use C2/E2, etc.
Column G(2:G51): Quotient Rank = RANK(F2,F$2:F$51), etc.
G52 extra seats to apportion A52-D52

Column H(2:H51):= D2 + IF(G2 <= $G$52, 1, 0), etc. add one for largest quotients.
H52 total apportionment = SUM(H2:H51), should match A52

I just lost a whole lot of what I had composed here online, but your method caps the number of seats each state has between its integer "floor" and its integer "ceiling" (or just the "ceiling" for a state with a fractional quota of less than 1, which is correct of course), while these methods, when interpreted as divisor methods rather than fixed ratio methods some of them started out as, don't.  I was starting to explain the virtues of each when my web browser closed down for me for some reason.

I forgot a caveat and a limitation.

The short cut I used assumes there will not be quota violations, where a state would not be apportioned either n or n+1 districts when:

n/435 <= P_state / P_USA < (n+1)/435

This is estimated to be about a 1/1600 occurrence for the USA (the probability is based on the distribution of state populations, that is effectively random, and can only be simulated). For other uses, such as the apportionment of the British Parliament it is quite likely.

While the shortcut could be regarded as a defect in my implementation, the fact that a quota violation could occur, should be considered a defect of the divisor methods.

The limitation of my method is that it does not identify all the seats near the 435th seat. California should be apportioned roughly every 8th seat. While its quotients will be quite regular and periodic, other states will have different periods, so the rankings will not be periodic. My method will identify the ranking for California's 53rd seat, but not its 54th or 52nd, etc. And some of the rankings of other states will be in error because of this (but not, barring quota violations, whether or not they will be apportioned a particular number of seats).

To generate a full ranking with a spreadsheet requires more of a brute force approach. For example, one could generate, say the first 63 divisors, and calculate the quotients for all 50 states for each divisor. This would produce the top 500 or so rankings.

500/435 * 53 = 60.92 is an estimate of California's representation in a 500 member House. 63 is a fudge of 60.92, to make sure that California's rankings in the top 500 are generated. This method would also produce a lot of extraneous results quotients (e.g that for Wyoming's 63rd seat).

[jimrtex]

If it was desired that 100% of districts be within 5% of the mean, this could be done with a House of 3031. The final piece is Vermont six seats being underpopulated to above 95% of the average of  109,328 persons. CA would have 368 seats, TX 269, FL 201. NY, PA, IL, OH would each have 100+; 15 others (down to CO and MN) would have 50+; 13 others (down to KS) would have 20+; 9 others (down to MT, RI) would have 10+. The final six would be DE 9, SD 8, ND 7, AK 7, VT 6, and WY 5. DC would have 7 electoral votes. 3031 + 50x2 + 7 = 3138 electoral votes. A speculators might want to acquire 3138.com.

[jimrtex]

If it was desired that 100% of districts be within 5% of the mean, this could be done with a House of 3031. The final piece is Vermont six seats being underpopulated to above 95% of the average of  109,328 persons. CA would have 368 seats, TX 269, FL 201. NY, PA, IL, OH would each have 100+; 15 others (down to CO and MN) would have 50+; 13 others (down to KS) would have 20+; 9 others (down to MT, RI) would have 10+. The final six would be DE 9, SD 8, ND 7, AK 7, VT 6, and WY 5. DC would have 7 electoral votes. 3031 + 50x2 + 7 = 3138 electoral votes. A speculators might want to acquire 3138.com.

That is a real website; its a Chinese Chess website.

It appears to be a game development company. If only other companies had similar press releases:

"Volkswagen is not a liar..."

"Enron - Some friends and relatives are worried about their initial investment..."

[jimrtex]

Do you have or know of a spreadsheet where one could input population numbers to determine the overall seat apportionment?

Column A(2:51): State Names
Column B(2:51): Populations (leave out DC and PR, unless you want to experiment)
A52: Cell with number of representatives, set to 435, but you can vary.
B52: Quota =SUM(B2:B51)/A52
Column C(2:51): Estimate. =B2/$B$52, etc.
Column D(2:51): Minimum number of seats. =MAX(INT(C2),1), etc, ensures all states get one representative, and avoids division by zero.
D52: Minimum seats = SUM(D2:D51)
Column E(2:51): Divisor for next seat:

Huntington-Hill: =SQRT(D2*(D2+1)), etc. (Geometric mean of n and n+1)
Webster's = D2 + 0.5 (Arithmetic mean of n and n+1)
Dean's = D2*(D2+1)*2/(D2+D2+1)  (Harmonic mean)
Jefferson's = D2+1
Adams's = D2

Webster's is same as St.Lague, Jefferson's the same ad D'Hondt

Column F(2:F51): Quotient = B2/E2, etc. May also use C2/E2, etc.
Column G(2:G51): Quotient Rank = RANK(F2,F$2:F$51), etc.
G52 extra seats to apportion A52-D52

Column H(2:H51):= D2 + IF(G2 <= $G$52, 1, 0), etc. add one for largest quotients.
H52 total apportionment = SUM(H2:H51), should match A52

I just lost a whole lot of what I had composed here online, but your method caps the number of seats each state has between its integer "floor" and its integer "ceiling" (or just the "ceiling" for a state with a fractional quota of less than 1, which is correct of course), while these methods, when interpreted as divisor methods rather than fixed ratio methods some of them started out as, don't.  I was starting to explain the virtues of each when my web browser closed down for me for some reason.

I forgot a caveat and a limitation.

The short cut I used assumes there will not be quota violations, where a state would not be apportioned either n or n+1 districts when:

n/435 <= P_state / P_USA < (n+1)/435

This is estimated to be about a 1/1600 occurrence for the USA (the probability is based on the distribution of state populations, that is effectively random, and can only be simulated). For other uses, such as the apportionment of the British Parliament it is quite likely.

While the shortcut could be regarded as a defect in my implementation, the fact that a quota violation could occur, should be considered a defect of the divisor methods.

The limitation of my method is that it does not identify all the seats near the 435th seat. California should be apportioned roughly every 8th seat. While its quotients will be quite regular and periodic, other states will have different periods, so the rankings will not be periodic. My method will identify the ranking for California's 53rd seat, but not its 54th or 52nd, etc. And some of the rankings of other states will be in error because of this (but not, barring quota violations, whether or not they will be apportioned a particular number of seats).

To generate a full ranking with a spreadsheet requires more of a brute force approach. For example, one could generate, say the first 63 divisors, and calculate the quotients for all 50 states for each divisor. This would produce the top 500 or so rankings.

500/435 * 53 = 60.92 is an estimate of California's representation in a 500 member House. 63 is a fudge of 60.92, to make sure that California's rankings in the top 500 are generated. This method would also produce a lot of extraneous results quotients (e.g that for Wyoming's 63rd seat).

California, with 52.53/435 of the United States's apportionment population as of and according to the 2010 census, would have had 55 seats under Jefferson's method and 50 seats under Adams's.  Texas and New York must also have had quota violations in one or both of those methods as the difference in the apportionment between the them is 3 for Texas and 2 for New York (it would be 2 for Florida if not for the guarantee of 1 seat for each state, which gives Vermont and Wyoming seats that would otherwise go to Florida and Washington).

I messed up. Jefferson's method would give two extra seats to California, and one extra to TX, NY, IL, OH, NC, and NJ; and take one from WA, MN, SC, WV, NE, ME, NH, RI; compared to Huntington-Hill (based on 2010 population).

Huntington-Hill, Webster's, and Dean's method often give the same result. After Congress failed to make an apportionment in 1920, they came up with the current procedure of using a divisor method, and fixing the size of the House, such that Congress could do what it does best, do nothing. But they did not make a decision between Huntington-Hill and Webster's methods. Under the 1930 apportionment they gave the same results. In 1940, there was a different result, with Arkansas gaining a seventh representative at the expense of Michigan. Since Arkansas was a reliable Democratic state at the time, Congress adopted Huntington-Hill on a party line vote (except Democrats from Michigan) and Huntington-Hill has been used ever since.

Huntington-Hill is estimated to have quota violations quite rarely (perhaps once in 1600 apportionments over 16000 years for USA-like population distributions), and I had conflated this to include Jefferson and Adams methods.

Perhaps contributing to this was a recollection of the 1790 apportionment. The initial apportionment based on Webster's method was vetoed, by President Washington, the first ever presidential veto. He did so on the basis of the advice of Secretary of State Thomas Jefferson, who pointed out that some States would have more than one representative per 30,000 persons.

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The Constitution is ambiguous. One reading is that the total number of representatives for the United States may not be greater than one per 30,000 - this was the interpretation by Congress. The other was that of Jefferson, which was adopted by Washington, that the limit was on a per state basis. Congress was unwilling to challenge George Washington, who was revered, on so important a subject as the interpretation of the Constitution.

But what they did was to use Jefferson's method, but chose a quota so that it would produce only minimal changes from Webster's method (one representative from Delaware to Virginia).

For my short cut method to work, an estimate of the number of representative to which a state is entitled must be made.

Let w = P_state/quota, where quota = P_USA/435

Then for Webster's: est = w

For Huntington-Hill: est = sqrt( w² + 1/4 )

For Dean's: est = ( w + sqrt ( w² + 1) ) / 2

For Jefferson's: est = w - 1/2

For Adam's: est = w + 1/2

But for all nethod's other than Webster's the estimates would sum to something other than 435.

So we need to adjust the quota. This can be done in an iterative manner:

Where quota₁ is the quota from above, and estusa is the total representation for the USA based on a particular quota.

quota_n+1 = quota_n * estusa(quota_n) /435

Convergence is quite fast for Huntington-Hill with estusa ~= 435.000 after two iterations. About 4 iterations are needed for Jefferson's and Adam's methods.

For the 2010 Census (disregarding overseas population) the quota for Webster's method is 708,405; for Huntington-Hill is 711,428; and for Jefferson's method 669,906. Calculate the estimates using these adjusted quotas to to in the form n.xxx. The state will get n or n+1 seats by that method.

[jimrtex]

As of the July 2017 estimates:

87 counties now have population sufficient for a congressional district (1/435 of the national population). This is up from 83 in 2010. The new giants are Cobb and DeKalb in Georgia, and Denton and Fort Bend in Texas. None have dropped, though Monroe in New York is perilously close.

53 of the giants are gaining at a faster rate than the country as a whole, 34 are losing ground.

6 are losing in absolute numbers: New Haven, CT; Wayne, MI; St. Louis (County), MO; Suffolk, NY; Cuyahoga, OH; and Allegheny, PA.

[jimrtex]

As of the July 2017 estimates:

87 counties now have population sufficient for a congressional district (1/435 of the national population). This is up from 83 in 2010. The new giants are Cobb and DeKalb in Georgia, and Denton and Fort Bend in Texas. None have dropped, though Monroe in New York is perilously close.

53 of the giants are gaining at a faster rate than the country as a whole, 34 are losing ground.

6 are losing in absolute numbers: New Haven, CT; Wayne, MI; St. Louis (County), MO; Suffolk, NY; Cuyahoga, OH; and Allegheny, PA.

18 are gaining at more than twice the national rate: Maricopa, AZ; Hollsborough, FL; Orange, FL; Palm Beach, FL; Fulton, GA; Gwinnett, GA; Clark, NV; Mecklenburg, NC; Wake, NC; Bexar, TX; Collin, TX; Denton, TX; Fort Bend, TX; Harris, TX; Tarrant, TX; Travis, TX; King, WA; and Snohomish, WA.

[jimrtex]

22 counties have gained more than 1/10 of a congressional district since 2010:

Harris, TX 0.450
Maricopa, AZ 0.376
King, WA 0.203
Bexar, TX 0.201
Fort Bend, TX 0.197
Travis, TX 0.196
Tarrant, TX 0.196
Clark, NV 0.195
Collin, TX 0.193
Orange, FL 0.188
Denton, TX 0.182
Wake, NC 0.163
Dallas, TX 0.161
Miami-Dade, FL 0.159
Riverside, CA 0.152
Hillsborough, FL 0.150
Mecklenburg, NC 0.141
Williamson, TX 0.136
Broward, FL 0.123
Montgomery, TX 0.121
Lee, FL 0.116
Palm Beach, FL 0.105

5 counties have lost more than 1/10 of a district since 2010.

Cook, IL -0.359
Los Angeles, CA -0.259
Wayne, MI -0.223
Cuyahoga, OH -0.136
Suffolk, NY -0.110

[jimrtex]

I threw 2017 estimates into an apportionment calculator and displayed the changes. Note that the total seats calculated was 436, one more than the total.

Why the increase to 436, unless it's to give one to DC?

The extra seat is NY (-1).

[jimrtex]

Does anyone know when this month the City and Town (incorporated places and I believe all census-designated "county subdivisions", which are generally the same thing in New England) estimates for July 1, 2017 will be released?

It is incorporated places and (some) minor civil divisions. Technically, estimates are made for the "estimates universe county subdivisions" which means the county subdivisions that the Census Bureau makes estimates for.

In practice these are the minor civil divisions in 20 of the 21 states in the Northeast and Midwest divisions (all except Iowa). These are the areas where minor civil divisions (towns and townships) typically have functioning governments.

There are another eight states where there are minor civil divisions recognized by the Census Bureau (and delineated by the state). In some cases, these are used because there are advantages when applying for federal grants.

In another 20 states, the Census Bureau has defined Census County Divisions, which permits the census bureau to present some data at a level equivalent to MCD in other states. Through 1950, the Census Bureau treated all counties as having MCD, though these were often temporary such as election precincts, or electoral districts. CCD are a way to provide statistical consistency from decade to decade, but in practical terms are useless.

In Alaska, the Census Bureau has defined Census Areas and Census Subareas in areas of the state with no local government (the Unorganized Borough). These serve as county equivalents and county subdivisions.

[jimrtex]

In practice these are the minor civil divisions in 20 of the 21 states in the Northeast and Midwest divisions (all except Iowa). These are the areas where minor civil divisions (towns and townships) typically have functioning governments.

There are another eight states where there are minor civil divisions recognized by the Census Bureau (and delineated by the state). In some cases, these are used because there are advantages when applying for federal grants.

In another 20 states, the Census Bureau has defined Census County Divisions, which permits the census bureau to present some data at a level equivalent to MCD in other states. Through 1950, the Census Bureau treated all counties as having MCD, though these were often temporary such as election precincts, or electoral districts. CCD are a way to provide statistical consistency from decade to decade, but in practical terms are useless.

In Alaska, the Census Bureau has defined Census Areas and Census Subareas in areas of the state with no local government (the Unorganized Borough). These serve as county equivalents and county subdivisions.

20 + 8 + 20 + 1 (Alaska) = 49.  Is Iowa in with the 8 or the 20, and if so was it included in your tally?

Iowa is not with the 8 or the 20.

Northeast (9) + Midwest (12) + Southeast (8) = Minor Civil Division (29)
Southeast (8) + West (12) = Census County Division (20)
Wesr (1, Alaska) = Census Subarea (1)

Census Estimates: Northeast(9) + Midwest (11, all bu Iowa) = Estimates (20)

[jimrtex]

Something I just figured out, if a state or federal prison opens in a county after the 2010 census, then it doesn't get incorporated into census estimates for the rest of the decade.  It's easy to see the demographic impact prisons have on small counties like Gilmer and Summers, WV and Bland, VA and since those prisons existed in the 2010 Census they're captured going forward, but for prisons opened in McDowell WV and Grayson VA after the 2010 census they never show up in Census estimates or American Community Survey data until I guess the Official 2020 Census.

I think that they do. The new unit in Grayson VA opened in September 2013. The estimates are as of July 1. There were population drops before 2014, and after 2014 that makes it look constant.

In a rural area, a prison might not attract workers into the county, since they can easily commute.

Census 2010   15533
Estimate 2010   15498
Estimate 2011   15366
Estimate 2012   15143
Estimate 2013   15131
Estimate 2014   15921
Estimate 2015   15953
Estimate 2016   15869
Estimate 2017   15665

[jimrtex]

Something I just figured out, if a state or federal prison opens in a county after the 2010 census, then it doesn't get incorporated into census estimates for the rest of the decade.  It's easy to see the demographic impact prisons have on small counties like Gilmer and Summers, WV and Bland, VA and since those prisons existed in the 2010 Census they're captured going forward, but for prisons opened in McDowell WV and Grayson VA after the 2010 census they never show up in Census estimates or American Community Survey data until I guess the Official 2020 Census.

I think that they do. The new unit in Grayson VA opened in September 2013. The estimates are as of July 1. There were population drops before 2014, and after 2014 that makes it look constant.

In a rural area, a prison might not attract workers into the county, since they can easily commute.

Census 2010   15533
Estimate 2010   15498
Estimate 2011   15366
Estimate 2012   15143
Estimate 2013   15131
Estimate 2014   15921
Estimate 2015   15953
Estimate 2016   15869
Estimate 2017   15665

Well, I've been using American Fact Finder, specifically via this link

https://business.wvu.edu/centers/bureau-of-business-and-economic-research/data/population-data

And then under the annual estimates of WV counties, I'll click on option 3 or 4 which gives me year by year table with gender or race options.  To look at another states counties I'll just use the add geographies button.  The population estimates for Grayson don't match the ones you have listed and as far as gender is concerned there not the sudden addition of 1000 males at any point.  Same for McDowell.

Also, if I use US census quickfacts it gives me a 2016 estimate of 15107 for Grayson and a 15665 estimate for 2017 (which is an odd increase)

https://www.census.gov/quickfacts/fact/table/graysoncountyvirginia,blandcountyvirginia,gilmercountywestvirginia,mcdowellcountywestvirginia,WV,US/RHI225216

Why are our databases not matching?

For Grayson, the 2015 and 2017 estimates (but not the 2016 vintage) show the step up in 2014.

The components of change are issued each year. They include births and deaths, which have reasonable reporting - but may be misattributed based on place of birth or death being in a different county. Migration is inferred based on Social Security and IRS records. But these don't work for prison populations, since inmates may not have tax liabilities. And while they might show up as moving into a different county after release, it won't show up in the prison county.

I don't know how they handle estimates for institutional population. Probably not that well because it would require a lot of individualized handling (you can's simply feed the IRS and Social Security data into the estimates).

The ACS for Grayson does show an increase in group quarters. The ACS is based on a sample over 5-years. Housing units are assigned to 5 groups so that no household will be surveyed twice in a 5-year period. Each year, roughly one in six housing units for that year's group will be selected randomly, and assigned to one month. Over a five-year period, about 1/6 pf housing units will be surveyed, sufficient for statistically meaningful estimates for block groups. The next year, they throw out the results from the first year, and add in the results for the next year.

When the Census Bureau becomes aware of new housing units they are added in.

For group quarters, they survey chunks of 15 residents. Let's say a prison has 600 inmates, then it will have 40 chunks of 15 (the chunk of 15 does not correspond to any individual inmate or cell). The 40 chunks would be assigned to the 5 year groups (8 per year). Then the number of chunks to be surveyed each year would be determined and assigned to a month. When they make a survey, they get a list of inmates, and randomly select 15.

Under the best of circumstances the ACS will lag population growth since it assumes that there is no change over time, and there were zero population for some of the years in the average.

For McDowell, and the Federal Correctional Institution there has been a definite increase in the group quarters population, and it also shows up in one census tract and city data for Welch (the prison is inside the city limits)..

For Grayson, it only shows up for 2015 and 2016. The 2016 has the correct census tract. It is possible that the Census Bureau was not aware of the prison. This might have to be relayed through some state bureaucracies. River North did not open until fall of 2013. It would not be surprising if a prison opened with lots of guards and few inmates. Rookie guards would not be able to handle the ordinary number of inmates, and you might not want to move a full prison population. If an average sentence is five years (made up number), you could just let the prison fill with new offenders over time.

[jimrtex]

These yearly estimates don't seem to even account all of the regular housing. for example based on this article, Bloomingburg, NY must have about doubled in population, but the census bureau shows no change.

It is not clear that this actually happened. Google Earth photo from 2016 shows a lot of what looks like empty buildings.