Analysis
Under the terms of the proposed amendment, were the U.S. population to have been below 3 million, each state would have had one Representative in the United States House of Representatives for every 30,000 persons.
Were the U.S. population to have reached 3 million with the amendment in force, the total number of Representatives would have been recalculated. To reach the minimum of 100 representatives, Congress would initially have had to keep the district size at 30,000 per representative.
As the population would have approached 8 million, Congress could have gradually increased the size of districts from 30,000 to 40,000 and still meet the minimum of 100 representatives. This would have been allowed by the amendment, as it says "...there shall be not less than one hundred Representatives, nor less than one Representative for every forty thousand persons, until the number of Representatives shall amount to two hundred; ...".
However, even at a district size of 40,000, the number of representatives would inevitably have grown to 200 when the population would have reached 8 million, thus triggering the final clause. It would have been impossible to satisfy with a population between 8 and 10 million, as it says "...there shall not be less than two hundred Representatives, nor more than one Representative for every fifty thousand persons". For a population of 8 million, a district size of one per at least 50,000 yields at most 160 representatives, below the minimum of 200.
The final clause's conditions would have been satisfied only by a population size of 10 million or above. The clause stipulates a minimum district size of 50,000, and at that minimum size, a population of 10 million would have yielded the minimum of 200 representatives. As the final clause only stipulates a minimum district size, it would thereafter have allowed for any number of representatives between 200 and the current population divided by 50,000. At the approximate current U.S. population of 310,000,000, this would yield a House of Representatives with 200 to 6,200 members, depending on the district size.
The cause of this failure was a "scrivener's error" in Beckley's instructions to the engrossing clerks for transcribing Senator Ellsworth's handwritten report to the engrossed "copies". The change as voted was to have taken place "in the last line but one", that is, in the second clause from the end. Beckley incorrectly instructed the clerks that the voted last minute change was to take place "in the last place of the last line". The apparently intended correct version effectively set both a floor of 40,000 and a ceiling of 50,000 persons per representative. As transcribed, the last clause, with the incorrect placement of the word "more", defeats the original purpose of the Article, which was to have provided for district sizes of at most (not at least) 50,000 when the population would have reached 8 million. See the following table for a summary of the preceding analysis:
| population | number of representatives | district size |
|---|---|---|
| < 3,000,000 | < 100 | 30,000 |
| 3,000,000 to 8,000,000 | 100 to 200 | 30,000 to 40,000 |
| 8,000,000 to 10,000,000 | impossible to satisfy conflicting conditions | ≥ 50,000 |
| ≥ 10,000,000 | ≥ 200 | ≥ 50,000 |
However, had the "more" that was actually changed from "less" by the "scrivener's error" remained unchanged, another impossible situation would have resulted when the population would have reached 3,000,000. Summary:
| population | number of representatives | district size |
|---|---|---|
| < 3,000,000 | < 100 | 30,000 |
| 3,000,000 to 4,000,000 | impossible to satisfy conflicting conditions | ≥ 40,000 |
| > 4,000,000 | ≥ 100 | ≥ 40,000 |
| Note: had the first clause remained unchanged from the original intention, with the word "more" unchanged, the number of representatives need never have grown above 100; the district sizes could simply have been increased to the current population divided by 100. The minimum size of population where the switchover to the conditions of the final clause could have been done would have been 10,000,000, and this would have required Congress to have increased the district size to at least 50,000 by that point to avoid an internal conflict between the final clause's conditions. The last row assumes the foregoing. Again, the number of representatives need never have grown above the minimum specified by the clause, this time 200. | ||
| ≥ 10,000,000 | ≥ 200 | ≤ 50,000 |
The only sane version of the proposed amendment would have had both the words in question be "less", as on this version:
Article the first... After the first enumeration required by the first article of the Constitution, there shall be one Representative for every thirty thousand, until the number shall amount to one hundred, after which the proportion shall be so regulated by Congress, that there shall be not less than one hundred Representatives, nor less than one Representative for every forty thousand persons, until the number of Representatives shall amount to two hundred; after which the proportion shall be so regulated by Congress, that there shall not be less than two hundred Representatives, nor less than one Representative for every fifty thousand persons. (emphasis added)- which would have resulted in this:
| population | number of representatives | district size |
|---|---|---|
| < 3,000,000 | < 100 | 30,000 |
| 3,000,000 to 8,000,000 | 100 to 200 | ≤ 40,000 |
| > 8,000,000 | ≥ 200 | ≤ 50,000 |
It is also possible to view the amendment as an algorithm that adds 100 seats to congress each time the district size grows by 10,000. The first ten steps, and from 288M-399M, are given in the table below.
| population | number of representatives | district size |
|---|---|---|
| < 3,000,000 | < 100 | 30,000 |
| 3,000,000 to 4,000,000 | 100 | 30,000~40,000 |
| 4,000,000 to 8,000,000 | 100~200 | 40,000 |
| 8,000,000 to 10,000,000 | 200 | 40,000~50,000 |
| 10,000,000 to 15,000,000 | 200~300 | 50,000 |
| 15,000,000 to 18,000,000 | 300 | 50,000~60,000 |
| 18,000,000 to 24,000,000 | 300~400 | 60,000 |
| 24,000,000 to 28,000,000 | 400 | 60,000~70,000 |
| 28,000,000 to 35,000,000 | 400~500 | 70,000 |
| 35,000,000 to 40,000,000 | 500 | 70,000~80,000 |
| ... | ... | ... |
| 1,000,000s(s+2) to 1,000,000s(s+3) | 100s | 10,000(s+2) ~ 10,000(s+3) |
| 1,000,000d(d-3) to 1,000,000d(d-2) | 100(d-3) ~ 100(d-2) | 10,000d |
| ... | ... | ... |
| 288,000,000 to 304,000,000 | 1600 | 180,000~190,000 |
| 304,000,000 to 323,000,000 | 1600~1700 | 190,000 |
| 323,000,000 to 340,000,000 | 1700 | 190,000~200,000 |
| 340,000,000 to 360,000,000 | 1700~1800 | 200,000 |
| 360,000,000 to 378,000,000 | 1800 | 200,000~210,000 |
| 378,000,000 to 399,000,000 | 1800~1900 | 210,000 |
For a population of 308,745,538 in the 2010 census we would have roughly 1625 districts of size 190,000. Wyoming, the least populous state, would have three representatives.
Read more about this topic: Article The First
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