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The Minimum and Maximum Size
of the
U. S. House of Representatives

Per the Constitution
and pursuant to all three versions
of the proposed “Article the first”

Published: April 5, 2007
Revised: June 24, 2007

Quantitative Historical Analysis #4

How many Representatives shall we have in Congress? Though the Constitution explicitly sets the size of the Senate at two per state, there is no corresponding formulation for determining the size of the House of Representatives. In 1789, this omission was considered to be a significant deficiency that needed to be corrected. As a result, the very first amendment ever proposed by Congress would have mandated a minimum number of Representatives as a function of the population. That proposal is the subject of this report; but first, the reader is encouraged to carefully examine the amendment which was proposed in the twelve Bills of Rights as 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 more than one Representative for every fifty thousand persons.

Does this amendment appear to be easy to understand? If so, then how obvious is the mathematical defect that renders it inexecutable at certain population levels? How apparent is the spectacularly illogical discontinuity in its formulation? As shown in this report, these significant deficiencies have generally been ignored, if not undetected, for over two centuries.

After providing a thorough analysis of Article the first, this report argues that most of the state legislators who voted on that amendment did not actually understand it. The hypothesis proposed is that this amendment initially was mistaken for the original House version which it clearly resembles; more specifically, the legislators could not have easily detected the subtle last-minute alteration that had been made in the haste of an adjourning Congress. To the extent that any legislators did understand the amendment’s anomalies, then there were a variety of reasons for them to allow the prevailing misperception to persist.

(This report provides analytical support for this same analysis that was initially published in this web pamphlet in 2004. )
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