On April 5, 1792, George Washington vetoed an apportionment bill entitled: “An Act for an apportionment of Representatives among the several States according to the first enumeration.” An account of this event can be found at The Papers of George Washington web site (at the University of Virginia).

President Washington vetoed the amendment on constitutional grounds and — given that he presided over the Constitutional Convention — his opinions on this subject should be considered. Besides being historically noteworthy, President Washington’s rationale for his veto also raises questions about the constitutionality of the current apportionment scheme.

His primary objection to the proposed amendment was that “there is no one proportion or divisor which, applied to the respective numbers of the States will yield the number and allotment of representatives proposed by the Bill.”  The relevance of this today is that the “number and allotment” that results from the current fixed allocation of 435 seats does not pass the test established by President Washington. In other words, there is “no one proportion or divisor” which would yield the current allotment of representatives (as shown in Section V).

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On March 6^th, 1792, the Second Congress passed “An Act for an apportionment of Representatives among the several States according to the first enumeration.” This is summarized in the table below.

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After the initial apportionment bill (above) was vetoed, the Congress proposed one which was ultimately signed into law by President Washington. This one is described below.
 

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There are three important points to take away from the veto of the first apportionment bill and the approval of the second.

First, this was the first application of the apportionment process required by the Constitution. Many of the people involved in the decision, especially the President and his advisors, were key participants in the creation of the Constitution itself, which had taken place only five years earlier.

Second, the approved apportionment is in accordance with the one-divisor principle (with a target divisor of 33,000). A common-divisor is necessary to achieve what is now known as the one-person-one-vote principle.

Third, the approved act includes language (not present in the initial bill) that explicitly affirms this apportionment methodology: “the House of Representatives shall be composed of members elected agreeably to a ratio of one member for every thirty-three thousand persons in each state, computed according to the rule proscribed by the constitution...”

Below is a table summarizing both of the apportionment proposals described above.

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Looking at these two apportionments — the vetoed vs. the approved version — the practical difference is not readily apparent; i.e., why is the approved apportionment better than the one which was vetoed? A mathematical analysis of these provide the answer, along with a possible benchmark against which subsequent apportionments may be compared.

This is provided in this section for the estimated 15 people in the world (including the author) who would be interested in such an analysis.

In the table above (in section d), the “size” columns (C & E) are the actual resulting size per district (in that state) for the proposed apportionment. Column C is the state’s representative population (A) divided by the proposed number of representatives (B). Similarly, E=(A÷D).

At the bottom of the two “size” columns (in the table above) are the actual average sizes for each option. This is calculated by dividing the total population by the total number of representatives, as follows:
Vetoed apportionment: 3,615,920 ÷ 120 = 30,133
Approved apportionment: 3,615,920 ÷ 105 = 34,437

For each state, the resulting size is compared with the average size to determine the percentage difference.
 

To evaluate the deviations above against the current standard used for the one-person-one-vote principle, every deviation greater than 5% is highlighted in red. The total number of these is shown in the last row above.

The vetoed apportionment would have created six deviations greater than 5%; the approved apportionment creates only two. Though this is a simplistic analysis, it is the one currently being used to determine compliance with the one-person-one-vote principle. In any case, it is probably not dissimilar from the analysis that would have been made in 1792 (prior to the application of modern statistical methods).