Commentaries on Representation

The Blog for

Commentaries on Representation

The Blog for

The Rediscovery of Article the first’s Inexplicable Defect

A historical puzzle: Why is it that “the amendment’s intricate mathematical formula made little sense”? A noted scholar struggles to explain how this could have happened.

As explained in Section Two of, the very first amendment proposed for the Bill of Rights contains a fatal defect in its wording, the effect of which was to eventually sabotage its ratification to the Constitution. Thereafter, the very existence of this amendment’s mysterious defect seems to have disappeared into America’s memory hole for two centuries!

So who, in modern scholarship, was the first to rediscover its existence?

I believe that credit goes to Akhil Reed Amar,1Akhil Reed Amar biography. a distinguished professor of law and political science at Yale University. In 1991, Professor Amar published a paper about the Bill of Rights which included a brief examination of the first Article and its defect.2Amar, Akhil Reed. “The Bill of Rights as a Constitution.” The Yale Law Journal 100, no. 5 (1991): 1131–1210. Noting that its formulation “made little sense”, Professor Amar explains its two major problems as follows:

First, the amendment’s intricate mathematical formula made little sense. If the population rose from eight to nine million in a decade, the requirement that there be at least two hundred representatives would be inconsistent with the requirement that there be not more than one representative for every fifty thousand people. In effect, the amendment required the population to jump from eight to at least ten million in a single decade. The mathematical oddness of the text is confirmed by the lean legislative history that does exist. When initially passed by the House of Representatives, the amendment was worded identically to its final version with one exception: its last clause provided for “not . . . less than one Representative for every fifty thousand persons.”  So worded, the proposal was sent to the Senate, along with all the other amendments proposed by the House. When the Senate adopted a Bill of Rights whose wording and substance diverged from the House version, the two chambers convened a joint committee to harmonize the proposed bills.  At this conference, the word “more” was inexplicably substituted for “less”, and the conference paste job was hurriedly adopted by both houses under the shadow of imminent adjournment, apparently without deep deliberation about the substitution’s (poor) fit with the rest of the clause.  Thus it is quite possible that the technical glitches in the First Amendment’s formula became evident only during the later process of ratifying Congress’s proposed amendments.

Second, what the First Amendment promised in the short term—increased congressional size—it took back in the long run. Its final clause established a maximum, not a minimum, on congressional size. Even worse, this maximum was more stringent than that in the existing Constitution.  In effect, the amendment dangled the bait of more “democracy” now in exchange for more “aristocracy” in the future. Some committed democrats may have been wary of snatching that bait. Tellingly, not a single state ratifying convention had proposed a stricter constitutional maximum on the size of the House.

Referring to the “mathematical oddness of the text”, Professor Amar observes that “the amendment required the population to jump from eight to at least ten million in a single decade”, which would have been a patently absurd requirement had it been intentional. He observes that “it is quite possible that the technical glitches in the First Amendment’s formula became evident only during the later process of ratifying Congress’s proposed amendments”. In other words, it is likely that, somehow, absolutely nobody in Congress was aware of the mathematical defect in its language!

This appears to be the very first time in modern history that Article the first (including its defect) was considered in a scholarly way. Several years later, Professor Amar repeats this commentary in his excellent book “The Bill of Rights: Creation and Reconstruction”.3Amar, Akhil Reed. The Bill of Rights: Creation and Reconstruction. New Haven: Yale University Press. 1998. Page 14. Interestingly, all other scholarly references to the proposed first Article that I have found (previous to Professor Amar’s 1991 paper) mischaracterize the defective proposal sent to the states as if it were the intended version.  I don’t believe this is ever done deliberately. Instead, it’s because people naturally tend to construe it in the only way that seems sensible.

In his paper, Professor Amar points out that the “mathematical oddness” of the first Article was created when “the word more was inexplicably substituted for less”.  He hypothesizes that the conference committee made this “inexplicable” substitution with the expectation that the states would accept “more aristocracy” in the longer term in exchange for “more democracy” in the near term (i.e., during the first two tiers of its formulation).  This additional aristocracy refers to the reduction in the maximum size of the House from that permitted by the Constitution (1:30,000) to that stated in the third tier of the defective version (1:50,000).

It should be noted, however, that a maximum House size of one for every fifty thousand is well beyond any limit that would have then been regarded as sufficiently aristocratic, as Madison himself had sought a fixed upper limit of 175 or 200 Representatives.  While those who created this alternate version undoubtedly hoped it would allow aristocratic rule to continue, their primary objective would have been to prevent a populous House dominated by the non-aristocratic members of society, which is what the intended version of the first Article would have certainly accomplished.

Professor Amar’s hypothesis is predicated upon the seemingly reasonable assumption that two-thirds of both Houses wittingly voted to approve the defective proposal that was sent to the states. And, given that, he endeavors to make explicable the formulation that “made little sense”, as he put it.

However, all the available historical information indicates that it is inconceivable that over two-thirds of both chambers would have reversed their previous votes on this matter in order to support such a preposterous revision. And, as the professor notes, “not a single state ratifying convention had proposed a stricter constitutional maximum on the size of the House”.  Therefore, these congressmen would not have expected their states’ legislatures to contradict the recently-ratified Constitution in order to accept a provision they had not sought. Consider also that none of the other proposed amendments contradicted the Constitution in any way, as their stated requirement was to word them in a supplementary manner, so as to not alter the original document itself.

Even if the House had wittingly voted for this alternate version, that would have certainly instigated furious debate in their chamber, and yet none is reported.  Moreover, it is unimaginable that not a single Representative or Senator noticed the absurd mathematical defect contained in this alternate version. It would have taken only one to notice it and bring it to everyone’s attention.

There are numerous reasons to believe that Congress never wittingly voted for this altered version of the first Article.  The one I’ll mention here is that for the first five apportionments, especially the fifth apportionment, Congress conspicuously authorized a total number of Representatives that was compliant with the intended version, and completely disregarded the defective version which was sent to the states. (Explained here: Article the first’s Mysterious Defect.)

The mischaracterization of the defective first Article is so extraordinarily persistent that, even after Professor Amar explained why its formulation “made little sense”, many are still unaware of its inherent absurdity. For example, in a 2010 Press Release, the National Archives describes the defective first Article as if it were the intended version, stating:

Had this been ratified, there would be far more than 435 members of Congress –nearly 6,000.4National Archives Presents the ORIGINAL Bill of Rights – with 12 Amendments!” Press Release · Tuesday, December 7, 2010.

In fact, had this defective version been ratified, it would have only required a minimum of 200 Representatives, not “nearly 6,000” as stated in the press release.  Instead, 6,000 would have been the maximum allowable size, inexplicably contradicting the larger maximum size already specified in the Constitution.  Again, this mischaracterization is most certainly an honest mistake based upon an interpretation of what the first Article would appear to mean, especially given its legislative history as recorded during the summer of 1789.

© [Article published 06/30/22 and updated 07/15/22]

Print Friendly, PDF & Email