USA 2020 Census Results Thread (Release: Today, 26 April)

[jimrtex]

Count imputation rates (= guesstimates of people not counted) will be similar to previous Censuses (ca. 0.5%):



Which means about 1.7 million people were not counted properly either by self-response, by a census taker (which includes info received from a landlord or neighbour), or by using administrative records.

The error due to count imputation will be much smaller. The Census Bureau assigns the count from a nearby housing unit . So some units with an actual count of two might be assigned a count of one, and some with an actual count of one might be assigned a count of three.

They may be able to compensate for systematic bias. That is, there may be demographic characteristics that are associated with housing units that had to be imputed.

Why did no one self-respond, why was no one able to be located during NRFU, why was no proxy identified, why were there no administrative records?

In the case of duplicate responses, the cause may be that no one assigned the housing unit to NRFU because they believed that they had a self-response. Perhaps someone responded in April in one location, and in July in another, and so it is unknown who lived at the second address in April.

[jimrtex]

For the first time ever, military members (stationed abroad) were counted in their current/last base of deployment on the mainland - not where they privately live:

https://www.npr.org/2021/04/22/989938913/potential-changes-from-census-changing-how-it-counted-deployed-u-s-troops-in-202

This will boost states with a lot/big military bases.

You have garbled some things.

Military personnel have a duty station. This may be either in the United States or overseas. They may also be deployed for a shorter time to some other location.

US military who are stationed in the United States are counted in their place of residence. Since most military personnel in the US live in private quarters, often with dependents, they are counted the same way as civilians. The exceptions are those living in barracks who are counted as living in group quarters, similar to students living in dormitories.

Those who are stationed overseas (places such as Germany, Britain, Japan, Korea) and their dependents living with them are counted at their "home of record". It is not clear what state the DOD uses. Military personnel have a residence from which they enlisted, but they may also establish a different residence during their career, which they would inform the DOD. This is no different than 2010.

Those who are deployed overseas (places such as Afghanistan or Iraq) will in 2020 will be counted based on their duty station stateside. In 2010 they were counted as if they were stationed overseas. Dependents generally do not deploy overseas, so they will likely be counted where they are/were living near the duty station.

The number deployed overseas in 2020 was about 97,000.

In 2010 Census, the overseas population was just over 1 million, 96% of that military affiliated, and 60% of that dependents.

In 2020, this number may be halved.

[jimrtex]

For the first time ever, military members (stationed abroad) were counted in their current/last base of deployment on the mainland - not where they privately live:

https://www.npr.org/2021/04/22/989938913/potential-changes-from-census-changing-how-it-counted-deployed-u-s-troops-in-202

This will boost states with a lot/big military bases.

You have garbled some things.

Military personnel have a duty station. This may be either in the United States or overseas. They may also be deployed for a shorter time to some other location.

US military who are stationed in the United States are counted in their place of residence. Since most military personnel in the US live in private quarters, often with dependents, they are counted the same way as civilians. The exceptions are those living in barracks who are counted as living in group quarters, similar to students living in dormitories.

Those who are stationed overseas (places such as Germany, Britain, Japan, Korea) and their dependents living with them are counted at their "home of record". It is not clear what state the DOD uses. Military personnel have a residence from which they enlisted, but they may also establish a different residence during their career, which they would inform the DOD. This is no different than 2010.

Those who are deployed overseas (places such as Afghanistan or Iraq) will in 2020 will be counted based on their duty station stateside. In 2010 they were counted as if they were stationed overseas. Dependents generally do not deploy overseas, so they will likely be counted where they are/were living near the duty station.

The number deployed overseas in 2020 was about 97,000.

In 2010 Census, the overseas population was just over 1 million, 96% of that military affiliated, and 60% of that dependents.

In 2020, this number may be halved.

If it indeed was halved, the 0.5 million extra population went from the apportionment population to the resident population.

Which states would benefit most if military members/their families went back from overseas to their home states ?

Or is it pretty uniform ?

Some of it is due to reduction in the overall size of the military. There is probably a bias towards southern states with military bases, especially for those with long service, who met their spouse while serving. They may have developed connections to those states, especially if they have children. But that movement from military to civilian should already be factored in to the population estimates.

Those stationed overseas will apparently be treated the same as in 2010. The Census includes dependents living with the service members overseas. These persons may be attributed to the wrong state, and in particular a different state than where they vote. That is because the DOD keeps records of where the service member was living when they enlisted.

If they were previously stationed in the US prior to the transfer to Germany, etc., they would have been recorded where they were stationed but for the transfer to the foreign duty station. That is, they were living in North Carolina towards the end of March 2020, and transferred to Germany in early April 2021. They might be attributed to North Carolina, New York, or Germany based on the transfer date.

The change in the deployment rules will have the most net effect on those states that had deployments in 2010.

[jimrtex]

Imagine my disappointment when I looked down at the time on my computer and it read 4/26 and I thought that I had missed the live announcement by an hour and a half.

[jimrtex]

If NY had 89 more people, it wouldn't have lost seats?? This is crazy

MN is #435

Cuomo single-handedly cost New York a seat.

[jimrtex]

New York was 89 people away from not losing any seats?

What.

I guess when those people were declaring "I'm leaving New York!" they actually meant leaving Manhattan for Westchester or LI.

Or barely anyone other than a few self-important pundits actually left cities?

Anyway, this is good but CA losing while so many other places don't is just disgusting.

Oh there were definitely people who left cities, just 1) not as much as the media portrayed it, and 2) not as far from major cities as the media also portrayed--people moved from Manhattan to Jersey City/Westchester, or from DC to Arlington/Alexandria

The answer was incorrect in terms of the intent of the question. By my calculation NY needed 3,056 more people to overtake MN. The spread in the proportional value for the seat was less than 100. I'll post the bubble seats with their proportional value shortly so you can judge how close states were to the threshold.

I think
89 is the correct answer.

Quotient for Minnesota is 5,709,752 / sqrt (7*8) = 762998

New York would need a population of 762998 * sqrt (26*27) = 20,215,840

New York change needed is 20,215,840 - 20,215,751 = 89

[jimrtex]

Puerto Rico lost 11.8% of it's population since 2010 and hasn't had this few people on the island since the 1980s.

Here’s a big part of your explanation for those NY/NJ undercounts.

This is probably wrong but I assume it's harder to count PR-born residents since they can move freely to the US? It'd be like tracking inter-state movements.

Possibly, some consider themselves to be visiting relatives in Florida or New York. The flight is not that expensive. You can stay at your cousin's. You can find a service job through family connections. You don't need a green card and can legally work, unlike someone who is here on a tourist visa.

You might return to Puerto Rico in the winter. Your visits might become longer and longer. At some point you might decide that you are resident, but even then do you consider yourself a New Yorker, or Floridian? Maybe your child who graduates from CUNY or UCF does.

The Census Bureau estimates for interstate migration are based largely on IRS and SSA records (they don't get the 1040s, but name-address records). Someone who is seasonally in the USA might continue to file in Puerto Rico.

So it may be harder to track Puerto Rico to the mainland migration than it is interstate migration.

[jimrtex]

If NY had 89 more people, it wouldn't have lost seats?? This is crazy

MN is #435

Cuomo single-handedly cost New York a seat.

Who cost Texas its third?

RI, AL, MN

cost AZ, TX, FL

The 2020 Census was about 1% higher than an estimate based on the July 2020 estimates interpolated to April 1, 2020.

TX and FL were not quite that high, while AZ was lower than the estimate.

RI was much higher than the estimate - the census estimate for RI was among the worst for some reason. This is pretty odd since there is not much migration to/from Rhode Island and birth/deaths are easier to track. TX, AZ, and FL are harder to estimate because of large scale migration, both interstate and international.

TX gained enough for an increase of 2.8, but it was from 35.6 to 38.4 (they just barely got 36, and didn't quite get 39. They are quite likely to get +3 in 2030, with a chance of +4 with a small uptick.

[jimrtex]

New York was 89 people away from not losing any seats?

What.

I guess when those people were declaring "I'm leaving New York!" they actually meant leaving Manhattan for Westchester or LI.

Or barely anyone other than a few self-important pundits actually left cities?

Anyway, this is good but CA losing while so many other places don't is just disgusting.

Oh there were definitely people who left cities, just 1) not as much as the media portrayed it, and 2) not as far from major cities as the media also portrayed--people moved from Manhattan to Jersey City/Westchester, or from DC to Arlington/Alexandria

The answer was incorrect in terms of the intent of the question. By my calculation NY needed 3,056 more people to overtake MN. The spread in the proportional value for the seat was less than 100. I'll post the bubble seats with their proportional value shortly so you can judge how close states were to the threshold.

I think
89 is the correct answer.

Quotient for Minnesota is 5,709,752 / sqrt (7* = 762998

New York would need a population of 762998 * sqrt (26*27) = 20,215,840

New York change needed is 20,215,840 - 20,215,751 = 89

I agree with this. I relied on the table in Tender's original link, and that turned out to not include overseas population. That cut the shortage from over 3K to under 100. Given all the uncertainty in the Census collection and given that the pandemic was most prominent in NYC on Census Day, I would not be surprised to see a lawsuit to address the NY situation.

Utah's lawsuit over the 2000 Census was based on a significantly larger differential, wasn't it? I seem to recall they lost out on their fourth seat to North Carolina based on a few hundred people at least. Of course, they ultimately lost their suit, too, but I think it did result in some shifts in the numbers, maybe even enough to make a difference for New York this time if the same changes applied.

The Census Bureau included this table showing the gap by decade.

Additional Apportionment Population Needed for First Runner-Up State to Gain Another Congressional Seat: 1940 to 2020 (PDF)

The difference in quotient between Minnesota and New York was only 4. The expected gap average gap is around 1800. This census was easily in the 99th percentile for closeness.

New York could conceivably demand a recount.

They might also sue over exclusion of non-resident civilians. The apportionment population is used to determine the number of representatives in Congress. Congress requires that civilians residing overseas be permitted to vote for those representatives, but excludes them in determining how many there are. This would seem to violate equal protection.

With New York having a very large immigrant population, it also a large number of persons who return to their birth country, even if they were naturalized.

[jimrtex]

The house size needs to be expanded. The undercount is so obvious here

If just nineteen seats were added to the house, no states would lose any seats this redistricting cycle (I believe WV-3 is the 454th seat). You’d have thought that some representative from a state that’s losing out would want to put forward a bill to expand the house a bit so they can keep their seat...

This was what was done after the 1910 Census and also the 1870 Census.

In 1910, the effects of large-scale immigration to the industrializing northeast, rather than the homesteading west. Remember, Iowa was tenth largest in 1900.

So rather than reducing representation in states that had never lost representatives they expanded the House to 433 members (435 after NM and AZ entered the Union in 1912, and this was provided for in the Apportionment Act).

One reason no apportionment was done after the 1920 Census was a reluctance to repeat that process every decade. This led to the decision before the 1930 Census to fix the size of the Congress, and use a mathematical calculation. The law doesn't actually say "435" but rather says the current number of representatives.

When Alaska and Hawaii joined the Union just before the 1960 Census, two representatives were added to temporarily increase the House to 437, but the statute provided for reversion to the previous number at the next Census.

The apportionment law for the 1930 Census provided for using both Huntington-Hill and Webster's method. It did not matter in 1930.

It did matter after the 1940 Census. Huntington-Hill is more favorable to smaller states, and Huntington-Hill would switch a representative from Michigan to Arkansas. Given that the representative from Arkansas was certain to be a Democrat, and from Michigan likely to be a Republican, the decision was made to use Huntington-Hill.

I am almost certain that Webster's method would flip the seat from Minnesota to New York.  

It would make more sense to use independent rounding.

If a state had between n.5 / 435 and (n+1).5 / 435 of the population then it would receive n+1 representatives.

The total size of the House would vary a bit from Congress to Congress but that really doesn't matter.

[jimrtex]

The house size needs to be expanded. The undercount is so obvious here

If just nineteen seats were added to the house, no states would lose any seats this redistricting cycle (I believe WV-3 is the 454th seat). You’d have thought that some representative from a state that’s losing out would want to put forward a bill to expand the house a bit so they can keep their seat...

It also has the potential to change close presidential election outcomes.  2000 flips by roughly doubling the size of the House and 1916 would have flipped with a stadium-size House roughly 60X the current size!

Oddly enough, the 2000 election would have only flipped because they were using a decade-old obsolete apportionment at the time. The 2000 population of Bush states was infinitesimally smaller than the 2000 population of Gore states. Bush would have maintained an electoral college lead based on the number of states that Bush won even if the House were expanded by 1000s.

[jimrtex]

In the media focus on NY ending up 89 people short, they miss the fact that had MN counted 26 fewer people they would have lost the seat to NY. The asymmetry of the differences is due to the size of sqrt(26*27) in NY compared to sqrt(7* in MN.

Extra credit algebra problem:

How many persons would have to move from MN to NY to flip the seat.

If Minnesota would have lost the seat it would illustrate a flaw in Huntington-Hill (and all divisor methods):

A state that had increased its share of the population would have decreased its share of representation.

[jimrtex]

I am almost certain that Webster's method would flip the seat from Minnesota to New York.

Actually, under Webster's method (or rather Major Fractions as used in 1910 and 1930, having a fixed House size rather than having a fixed ratio as was done in the beginning of our country's history (with a largest remainder method with a bunch of paradoxes in between fixed ratio and fixed House size divisor methods)), Minnesota would still have 8 seats but seats would have "moved" from Montana and Rhode Island to New York and Ohio.  Minnesota would have lost a seat under the Harmonic Mean ("Dean") divisor method to Idaho (which would have gained a 3rd seat), interestingly enough.

There is probably a value of p in the generalized or power mean between 0 (geometric mean; equal proportions) and 1 (arithmetic mean; major fractions) that would just flip a seat from Minnesota to New York, but I haven't tested that yet.  Montana got the second-to-last seat IRL so I can't be sure it wouldn't lose one before Minnesota without checking.

1 / 2.000006951 would tie the two.

The quotients using the square root for Minnesota and New York are only 4 apart while Montana is 4501 greater than Minnesota.

Using 1 / 2.000006951 would reduce the gap between Montana and Minnesota-New York to 4497.

Ranking methods and a fixed house size are fundamentally flawed. If Minnesota had lost the seat it would have increased its share of the USA population while simultaneously reducing it share of the USA representation.

[jimrtex]

Census put out at least 2 blog posts about the quality of the count that we might find interesting:

https://www.census.gov/newsroom/blogs/random-samplings/2021/04/examining-operational-metrics.html

https://www.census.gov/newsroom/blogs/random-samplings/2021/04/comparisons-to-benchmarks-as-a-measure-of-quality.html

Some takeaways for the tl;dr crowd:

-65.28% of census addresses were resolved by self-response, vs 61.05% in 2010.
-Only 55.48% of non-response follow up households “were enumerated with a household member; 26.07% were resolved with a proxy respondent, such as a neighbor, building manager or landlord; and 18.44% were enumerated using high-quality administrative records. The use of administrative records was new to the 2020 Census, but the proxy rate is comparable to the 2010 Census, in which 24.71% of occupied households in Nonresponse Followup were enumerated by a neighbor or other knowledgeable person. The proportion enumerated by a household member was 74.88% in 2010.”

In other words, 19% fewer NRFU responses were from a knowledgeable person. Could this have had an effect on the unduplication efforts? Maybe. Census reported a few days ago that there were more duplicates this year than in 2010, and they took additional steps to try to resolve them:

https://www.census.gov/newsroom/blogs/random-samplings/2021/04/how_we_unduplicated.html

Any other thoughts from those more knowledgeable than me?

Nothing really stands out on these metrics, you can compare state to state or state to USA etc. Perhaps if you got them in a spreadsheet you could try to identify outliers.

https://www.census.gov/library/visualizations/interactive/2020-census-operational-quality-metrics.html

Something I had not realized that most of the proxy responses were either that the housing unit was vacant or deleted (did not exist). The Census Bureau in 2020 identified bunches of hypothetical housing units (around 150 million total, even though the ACS number is closer to 130 million). If you are looking for a sample, you can skip locations that are only 2% likely to have anyone living in them. If you want a complete count you check whether they exist.

Lots of "vacant" housing units are vacation/summer homes. Persons per housing unit in Hamilton County NY is under 1 per HU. There may be non-rentable apartments in New York, and even more in other cities such as Detroit.

Unresolved housing units were highest in several distinct areas:

New Mexico
Black Belt: Louisiana to Georgia
West Virginia
Northeast, including New York, Massachusetts, and Vermont

There must be economic reasons for the first three. I don't know what it is for the Northeast. Perhaps there are more dual use areas (rooms behind or above stores) that are less likely to occur in the West and South where residential and commercial areas are more distinct.

New York and other northeast states had distinctly low self-response rates during the initial census period, undoubtedly related to Covid19. Areas in the West and South had lower rates, but that is because they had not received census forms in the mail, and Update/Leave was delayed.

You could do Self Response without receiving a form, but it was somewhat harder to do.

Later, during Update/Leave and NRFU, New York did catch up some in self response. One could self respond even if it was because an enumerator had pushed you to do it. "I mailed it last week. It will probably arrive in the next week. Or two." (after enumerator leaves)
"Do you remember where we put the census forms?" "It is in the pizza box with the insurance policies, car registration, and lottery tickets. If it is not there, it is probably in the clothes hamper."

Outreach might be more successful in NYC. There will be persons who can not be reached in any other way. Someone from Chad might only respond if someone from the New York Chadean Culture Center (or whatever it is known as in French) helps them to respond. It is possible that these assistant push to report persons who would otherwise not be reported.  It might be the cousin who was visiting, and the assistant assures the respondent that the Census Bureau will sort it out, and that it won't be reported to ICE.

New Yorkers may be less willing to admit too much knowledge about a neighbor. Some of these housing units may be imputed as occupied, when they were actually vacant.

[jimrtex]

Here's census' Operational data state spreadsheet:

https://www2.census.gov/programs-surveys/decennial/2020/data/operational-quality-metrics/census-operational-quality-metrics-release_1.xlsx

FAQs:
https://www2.census.gov/programs-surveys/decennial/2020/data/operational-quality-metrics/operational-quality-metrics-faqs_release-1.pdf

And technical documentation:
https://www2.census.gov/programs-surveys/decennial/2020/data/operational-quality-metrics/operational-quality-metrics-technical-documentation_release-1.pdf

I'm still not entirely sure what all this means, but New York was number 1 in the Unresolved, person unduplication category, which I think means they removed the most duplicates from NYS. NYS was about average in the makeup of NFUR method - 55% interview/27% Proxy/19% Administrative Record. It has the 10th highest percentage of households considered occupied using administrative records, but was 45th in administrative record vacancies.

Edit: now, I realize this is just the underlying data behind the data viz you linked.

The app with the statistics was slow and kept resetting so I appreciate the spreadsheets. I was going to note that Louisiana had the highest non-resolution, but saw that you had specifically noted unresolved due to unduplication for New York.

In Louisiana the unresolved addresses were due to the inability to determine which pile of lumber was the former house, or even get into the hurricane areas.

New York was also a bit high in the Other Occupied. "Other" includes Rural Alaska and Update Enumerate, so Alaska was high in those categories. Rural Alaska was when enumerators started going out to the bush in January, when they hoped to catch people before they started moving around after the sun comes up. Update Enumerate was only used in Alaska and extreme Northern Maine. Unlike Update Leave, where the enumerator leaves the census form, in Update Enumerator does the enumeration on the first visit.

So for the other 48 States, "Other" incorporates "SRQA" and "Cov Imp". I assume SRQA is Self-Response Quality Assurance, and "Cov Imp" is coverage imputation. I don't know what this implies for New York.

If they receive a self response from an address, it is going to be assumed that the address exists and somebody lives there. It would be taken off the NRFU workload. There are conditions that could kick it back out, but the whole idea is that these don't need to be scrubbed down, and they can concentrate there efforts on the 30% to 40% or more which they don't have.

It is interesting that they got some vacant/delete from self response. I suppose this would be from people who control the mailbox, who responded that nobody lived there, or in some rare cases that the building no longer exists.

If they get another response for the same people from a different address, they first half to determine/guess which is the correct one. Since this was after field operations they might not be able to check back (or maybe they can?). So does unresolved mean that they are pretty sure, but not 100% sure that the other address was vacant on April 1.

[jimrtex]

I am almost certain that Webster's method would flip the seat from Minnesota to New York.

Actually, under Webster's method (or rather Major Fractions as used in 1910 and 1930, having a fixed House size rather than having a fixed ratio as was done in the beginning of our country's history (with a largest remainder method with a bunch of paradoxes in between fixed ratio and fixed House size divisor methods)), Minnesota would still have 8 seats but seats would have "moved" from Montana and Rhode Island to New York and Ohio.  Minnesota would have lost a seat under the Harmonic Mean ("Dean") divisor method to Idaho (which would have gained a 3rd seat), interestingly enough.

There is probably a value of p in the generalized or power mean between 0 (geometric mean; equal proportions) and 1 (arithmetic mean; major fractions) that would just flip a seat from Minnesota to New York, but I haven't tested that yet.  Montana got the second-to-last seat IRL so I can't be sure it wouldn't lose one before Minnesota without checking.

1 / 2.000006951 would tie the two.

The quotients using the square root for Minnesota and New York are only 4 apart while Montana is 4501 greater than Minnesota.

Using 1 / 2.000006951 would reduce the gap between Montana and Minnesota-New York to 4497.

I didn't understand quite what you were saying here.  Some slight weight to the geometric mean, perhaps?  Feel free to answer "offline" if you wish (it might be of limited interest, even among those who frequent apportionment discussions on this forum).

Maybe I don't know what the power mean is.

We know that if the divisors for Minnesota and New York were

(7*8) ^1/2  and  (26*27) ^1/2

resulted in Minnesota's quotient being approximately four greater than New York's.

But if the divisors were:

(7*8) ^{1/2.000006951}   and  (26*27) ^{1/2.000006951}

they would have been tied.

The value of p in the power mean of (# of seats a state already has been "awarded") and (# of seats a state is "going for") where Minnesota and New York would be tied for the last seat is p ≈ 0.0021.  Minnesota and Montana would be tied for the last seat at p ≈ 0.1017.  Minnesota oscillates between 7 and 8 seats several times as p increases from −∞ to ∞ (or decreases from ∞ to −∞).

Just indicating that I read this, but don't understand. I glanced at the power mean reference, and saw that there was a "cubic mean", and decided I could use any power.

Ranking methods and a fixed house size are fundamentally flawed. If Minnesota had lost the seat it would have increased its share of the USA population while simultaneously reducing it share of the USA representation.

All in the eye of the beholder.  Scholarly works will sometimes talk of divisor methods with a fixed house size (or at least fixed as far as that being the "key number" and not the ratio) as being the gold standard.  It doesn't have some of the paradoxes that largest remainder methods have.

Perhaps I should have written ranking methods with a fixed house size are fundamentally flawed.

Webster's method applied to the apportionment of the British Parliament is a quota violation generator, because the apportionment is between only four countries, and England is so dominant. A person moving from Scotland to Wales can cause Northern Ireland to gain or lose a seat. But this is only because the Parliament size was fixed at 500.

If you simply calculate a quota (total electorate/500), and divide that quota into the electorate of each country, you are calculate how many 500ths of the electorate is in each country.

A country with between n.5 and (n+1).5 /500ths of the electorate should have n+1 MPs. It does not matter that this results in 501 or 499, or even 502 or 498 MPs in Parliament.

[jimrtex]

Webster's method applied to the apportionment of the British Parliament is a quota violation generator, because the apportionment is between only four countries, and England is so dominant. A person moving from Scotland to Wales can cause Northern Ireland to gain or lose a seat. But this is only because the Parliament size was fixed at 500.

Well, Paul LePage gained a Governor's seat in 2010 in part because some people (including me) voted two weeks early for Libby Mitchell and couldn't pivot to Elliot Cutler (the equivalent of the Andromeda Galaxy gaining a seat because people couldn't get visas to leave the U.S.S.R. for say... Denmark in time for the Local Group census, so how is your above example that different?  :)

I don't understand your counter-example. :(:

As you likely know, heretofore Britain has used independent quotas for redistricting the four countries, though in exchange for creation of a Scottish Parliament, the Scottish quota was reset to that of England.

The Tories proposed reducing the size of Parliament to 600 and using a common quota across the four countries - or alternatively, apportioning the members of parliament among the four countries on the basis of their population (or more precisely on the basis of their electorate).

They use Ste. Lague, but for our purposes we can refer to it as Webster's method.

See Rule 8

The boundary review provided for by the 2011 statute was never put into effect. There is just now a new boundary review to take effect in 2023.

2023 Review

The apportionment formula is retained, but the size of Parliament is increased to 650.

It is difficult if not impossible to determine the probability of quota violations, because that requires assumptions about the distribution of population. But we can vary the "fixed" size of parliament. A size of 651 is no less or more arbitrary than one of 650.

As we vary the size of the parliament a lot of cases of quota violations occur.

You of course understand why polling results rounded to the nearest percentile do not total 100.

If Candidate A has 45.39%, Candidate B has 39.20%, and Candidate C has 15.41%, a poll might show A at 45%, B at 39%, C at 15% and include a note that says that the results do not total to 100 due to rounding.

Your copy editor looks at your results, and changes the results to

A 45%, B 39%, C 16%, and eliminates the results.

You seethe at the editor's innumeracy and meander off into the Alabama paradox and Hamilton's method, and perhaps suggest that it should be

A 46%, B 39%, C 15%.

But is that really better?

46, 39, 15 is arguably better than 45, 39, 16 but is it better than

45, 39, 15?

Isn't column 2 a fairer more accurate representation of the actual results of the poll.

45.39%  45.45%  46.00%
39.20%  39.39%  39.00%
15.41%  15.15%  15.00%

The same applies when apportioning 600 or 650 MPs, or 435 representatives.

[jimrtex]

The Census Bureau didn't publish how many numerical people each state was from displacing Minnesota or New York (assuming no other states gained/lost seats), so I calculated the 10 closest states to gaining and losing seats.

Gaining (Farthest to Closest)
Texas - 189,645
Florida - 171,561
Utah - 136,978
Virginia - 111,635
Delaware - 88,205
Arizona - 79,509
West Virginia - 73,911
Idaho - 27,579
Ohio - 11,462
New York - 89

Losing (Closest to Farthest)
 Minnesota - -26
 Montana - -6,371
 Rhode Island - -19,127
 Oregon - -62,408
 Colorado - -72,445
 Alabama - -85,285
 Nebraska - -94,387
 North Carolina - -160,592
 South Carolina - -179,944
 Wisconsin - -187,747

Wait a damn minute, South Carolina could have lost a seat? All the time people in the state brag about having some of the fastest growing areas (Horry, Charleston, Greenville) and we could’ve lost one?

In 2010, South Carolina was entitled to 6.528 seats. In 2020, this has increased to 6.722. So South Carolina is still somewhat close to 6.5, but further away than it was in 2010.

We can back of the envelope estimate that South Carolina will be close to 7.5 in 2060 when it might gain an 8th seat (assuming current trends continue).

Alternatively, South Carolina gained 10.4% over the decade, while the USA gained 7.1%. South Carolina grew 3.1% faster   (1.104/107.1) = 103.1

South Carolina's representation should also grow by 3.1%. 3.1% of 7 is 0.217.

As long as South Carolina continues to grow faster than the USA as a whole it won't lose representation.

[jimrtex]

So hopefully you can see that just changing the root or power of the product doesn't really "work", at least not for something that can be described as a continuum of means or a continuum of divisor methods based on a continuum of means.

Why does a divisor method have to be based on a continuum of means?

Is it just because the power means for an exponent of -infinity, -1, 0, 1, and +infinity have other properties?

As long as the series of divisors exhibit monotonicity, x > y => f(x) > f(y), why can't it be used?

Where does Imperiali fit into this scheme?

For p = 1, the raising of exponents or taking of roots doesn't change anything, so you're left with the the arithmetic mean.  For p = -1, the negative 1st power (or negative first root) of a number is the reciprocal of that number, so you get the reciprocal of the arithmetic mean of the reciprocal of those two numbers.  The cubic mean you alluded to (p = 3, the cube root of the arithmetic mean of the cubes of those numbers) is actually on the "larger number side" (or the greatest divisors/D'Hondt/Jefferson "side") of the arithmetic mean (or major fractions/Webster), which itself is on the D'Hondt side of equal proportions, while you maybe thought it was somewhere on the smallest divisors/Adams "side" of equal proportions.

Since I was trying to switch the representative to New York, I was trying to choose something on the Jefferson side, but that was not so far as Webster's which you pointed out would also flip Montana and Rhode Island.

Does that explanation help at all?

I do appreciate the explanation.

My understanding of Adam's, Dean's, Huntington-Hill, Webster's, and Jefferson's method are more based on the properties of each.

[jimrtex]

The Census Bureau has agreed to release the PL 94-171 redistricting data to Ohio by August 16.

[jimrtex]

While not official. If anybody is interested the 2020 estimates for incorporated places are out.

https://www.census.gov/programs-surveys/popest/technical-documentation/research/evaluation-estimates.html

Texas now has 41 cities over 100K including 12 new performers:

Round Rock
Odessa
Pearland
Richardson
College Station
Sugar Land
Lewisville
Allen
League City
Tyler
Edinburg
San Angelo

[jimrtex]

Given the makeup of the Supreme Court, this could be the last census in which imputation can be used:

Conservatives aim at Census' method for uncounted households

When U.S. Census Bureau workers couldn't find out any information about some households after repeatedly mailing them questionnaire reminders and sending census takers to knock on their doors, the statisticians turned to an obscure, last-resort statistical technique known as “imputation.”

Less than 1% of households were counted using the technique during the 2020 census. But some conservative political groups are questioning it, potentially laying a foundation for legal challenges to the data that will ultimately be used for drawing congressional and legislative districts.

Imputation involves using information about neighbors with similar characteristics to fill in head counts or demographic characteristics for households lacking data. For instance, a rowhouse with no information may be counted as having two people if a neighboring rowhouse is occupied by two people. The technique tends to be utilized in hard-to-count places, often with racial and ethnic minorities, where people haven’t answered the census questionnaire and could otherwise go uncounted.

“It makes the overall dataset — or census in this case — more accurate than leaving the gaps blank," Pat Cantwell, a bureau official, said in a blog post earlier this year. “By using imputation, we fill in what we don’t know, using information we do know."

The focus for conservatives is on how this technique was applied to college dorms, nursing homes, prisons and other places where people live in groups. These residents were particularly difficult to count during the 2020 census because the pandemic sent college students fleeing campuses and put nursing homes in lockdown. In response, the Census Bureau unexpectedly decided to use the technique for group housing, where about 3% of the U.S. population lives.

There is likely a systemic bias in which housing units must be (or are) imputed. Apartments and other more transient housing are more likely to not return a form, or unable to be contacted, or locate a proxy who knows who lived in that apartment five months ago.

In areas of single family homes, it is more likely that the occupants were still there during NRFU or that neighbors would be more able to know the number of former occupants.

Count imputation should have smaller errors, though there may still be systemic biases. Households with a single person may be more likely to require imputation than those with families - or it could be the other way around. If the Census Bureau knew why they were imputing for a particular housing unit, they wouldn't need to impute.

But assigning a count of 2 or 3 would likely be more likely to be accurate than assigning a zero.

Imputing for group quarters seems much more dicey.

The comment in the story about deduplicating did not make sense. The Census Bureau does not impute actual persons.

[jimrtex]

The comment in the story about deduplicating did not make sense. The Census Bureau does not impute actual persons.

Isn't that the point, though - because Census doesn't impute actual persons, they can't be deduplicated. Thus, some people can be counted in 2 places or states.

I was reacting to the following quote:

Conservatives aim at Census' method for uncounted households

The initial batch of Fair Lines documents included a slideshow that indicated the Census used the statistical technique to get a head count in 43,000 separate group housing facilities. That included 5,500 college housing units, which Torchinsky said were a special concern given the number of students who relocated last year. They could have been double-counted at their parents' homes and in the dorms through imputation, he said, though the Census Bureau says it eliminates duplicate responses during the numbers-crunching phase of the 2020 census.

I interpreted "though the Census Bureau says it eliminates duplicate responses during the numbers-crunching phase of the 2020 census" as being the reporters words. While "they could have been double-counted at their parents' homes and in the dorms through imputation" was a paraphrase of Torchinsky.

[jimrtex]

For anyone who wants to see the full list of cities with over 100k without having to download an excel chart:
https://en.wikipedia.org/wiki/List_of_United_States_cities_by_population

Half of the 317 are in five states: CA, TX, FL, CO, and AZ.

Five have none: DE, ME, VT, WV, and WY.

DE had one, but probably won't ever again. WY may have one in the distant future.

[jimrtex]

Something I realized is that the July 1, 2020 estimate for Austin's population puts it at 995,484.

Considering the city's rapid growth, and considering it's been almost a year since that estimate, I think it's safe to say that Austin has now surpassed 1 million people in its city limits, making its northern Texas neighbor Fort Worth the largest city in the United States to have less than 1 million people (which it should surpass by 2025). That now means that 11 cities in the USA now have 1 million people or more.

By the 2030 census, besides Austin and Fort Worth, I would expect the following cities to surpass 1 million people:

Jacksonville, Florida
Columbus, Ohio
Charlotte, North Carolina

This would make 15 cities with a population of 1 million or more, and based on growth trends, Seattle would likely become the largest city in the country to have less than 1 million people, as it (along with possibly Denver as well) would likely surpass Indianapolis and San Francisco in population.

Also to add-on, Texas is now the state with the most cities with 1 million people or greater, with 4 cities (Houston, San Antonio, Dallas, Austin) compared to California with only 3 (Los Angeles, San Diego, San Jose).

Is Columbus' growth that rapid? I would've thought most of the growth would be outside the city limits.

Columbus has had a very aggressive annexation policy. In Ohio, cities can annex with agreement of landowners. Columbus makes deals with landowners to provide water and sewage in exchange for being annexed. If you are developing a tract of land for a shopping center, or an office park, or warehouses, or apartments or single-family residences, you are going to need reliable infrastructure - water, sewage, and roads. The developer will be expected to put in the sewer and water lines and internal roads, but they need to connect to trunk lines. The roads will need to connect to major arterials, so the developer might also pay for stop lights and intersection expansion. But all of this will benefit the developer since people will be able to get to the shopping center or office park or out of the residence. So Columbus has lots of develop-able land.

Ohio also has adopted restrictions on creation of new cities. It used to be easier to incorporate residential areas which would incorporate and block expansion of Cleveland and Cincinnati. There are now minimum population requirements at least around major cities. While there has been some effort to contain Columbus it hasn't been wholly successful.

This shows the Columbus city limits. Incorporated cities, including Columbus are shown with a gray tint. Be sure to zoom in.

Columbus zoning map