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Analysis of “Article the first...” 




a. Introduction 
The purpose of this section is to summarize the analyses of the three versions of Article the first: the original House version, the Senate version and the final version that was proposed in 1789 as part of the Bill of Rights. A complete analysis is provided by the TTO report entitled: “The Minimum and Maximum Size of the U. S. House of Representatives” (download at this link).
The original intent of this amendment was to provide a formula for determining the minimum size of the House of Representatives. The maximum size was already defined by the Constitution: “The Number of Representatives shall not exceed one for every thirty Thousand…”.

There are really three versions of Article the first that must be considered:

The original version drafted by the House of Representatives on August 24, 1789.
 The version drafted by the Senate on September 2, 1989.

The final version produced by a HouseSenate conference committee on September 24, 1789.
The House and final versions are identical except for the change of one single word which, in effect, made the final version defective. How this revision came about is explained in the sidebar to the right (and further in The History of the First — and Now Forgotten — First Amendment).
Section b (below) provides the full text of the two versions. After that, Section c translates and parses the dense prose so that it may be more easily comprehended.


Text below excerpted from: The Bill of Rights:
Creation and Reconstruction
by Akhil Reed Amar
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 pastejob 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’ proposed amendments.
© Yale University Press (1998) 
 


b. The House and Final Versions: More or Less the Same 
Both versions of this amendment (shown below) are identical except for the word “less” — in the last sentence of the original House version (left) — was replaced by the word “more” in the final version (right).


Because this amendment consists of rather dense prose, a translation is provided in the next section. 

c. The House and Senate Versions: Translated & Parsed 
This section translates & parses the original text of the amendments in order to contrast them and to explain the threetier approach utilized by both versions. 
Passed by the
House of Representatives
August 24, 1789

Proposed by
Congress
September 25, 1789 
The first tier is the same for both versions:
“...there shall be one Representative for every thirty thousand, until the number shall amount to one hundred...”
Meaning: there will be exactly one Representative for every 30,000 people
until the total U.S. population reaches 3,000,000. 
The second tier is the same for both versions:
“...after which...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...”
Meaning: after the total population exceeds 3,000,000,
and until
it reaches 8,000,000,
there shall be at least
one Representative
for every 40,000 people
(but no less than 100 Representatives).

The third tier of
the House version:
“...after which...there shall not be less than two hundred Representatives, nor less than one Representative for every fifty thousand persons...”
Meaning: after the total population reaches 8,000,000 there shall be at least one Representative for every fifty thousand persons. 
The third tier of
the final version:
“...after which...there shall not be less than two hundred Representatives, nor more than one Representative for every fifty thousand persons...”
Meaning: after the total population reaches 8,000,000 there shall be no more than one Representative for every fifty thousand persons.


By changing a single word, the joint HouseSenate committee created these three problems:
 A Redundant Maximum
It imposed (in the third tier) a new formula for determining the maximum size of the House. This was clearly unnecessary given that the Constitution (drafted only two years earlier) already provided the method for determining the maximum size (“shall not exceed one for every thirty Thousand”).
Moreover, the new and more restrictive maximum (of one representative per 50,000) would not be activated until the total population reached 8 million, at which point a significant & discontinuous reduction in the maximum size of the House becomes imposed.
 An Irresolvable Math Error
It incorporated an internally contradictory math error in that — for a given population range — the required maximum would be below the required minimum. (This is explained in the next section.)
 Failed to Maintain a Proportionate Minimum
Though the amendment proposed a proportionate minimum size as long as the total population remained below 8 million, beyond that number it effectively abandoned the need to define a minimum. This reversed the original intent of the amendment by eliminating the guidance for determining a minimum size for the House that would have been proportionally commensurate with our nation’s total population.


d. Comparison of All Three Versions 
The table below summarizes all three versions of Article the first. 
Number of Representatives (R) 
House Version
(Aug. 24, 1789) 
Senate Version
(Sep. 2, 1789) 
Final Version
(Sep. 25, 1789) 
Tier 1
(R ≤ 100) 
Ceiling 
P ÷ 30,000 
Floor 
Tier 2
(100 < R ≤ 200) 
Ceiling 
P ÷ 30,000 
P ÷ 40,000 
P ÷ 30,000 
Floor 
P ÷ 40,000 
P ÷ 40,000 
Tier 3
(200 < R) 
Ceiling 
P ÷ 30,000 
P ÷ 60,000 
P ÷ 50,000 
Floor 
P ÷ 50,000 
200 
P = Population 

The important point to note here is that the Senate’s version would have produced results nearly equivalent to that of the House’s version in that it would have mandated that the total number of Representatives increase proportionately with the population.
For a total population level up to 25 million, the three formulations are graphically illustrated in the chart below. 

As identified in the chart above, the light yellow area illustrates the range — between the minimum and maximum number of Representatives — that would have been permitted by the House version of Article the first.
The single red line indicates the number of Representatives that would have been required by the Senate version.
The range permitted by the final version of Article the first is illustrated by the lower area (shaded in red). The two important points to note regarding the final version is that:
 For a population range between eight and ten million, the maximum number of Representatives allowed would have been less than the minimum number permitted. This mathematical defect was introduced inexplicably at the last minute by the joint HouseSenate committee;
 The principle of maintaining proportionally minimal number of representatives — which was the entire raison d’etre of Article the first — has been eliminated.
All three formulations are illustrated for a population range up to 300 million in the chart below. 

The chart above further illustrates that either the House or the Senate versions would have mandated that the size of the House grow proportionately with the population, whereas the final version would have mandated a relatively meaningless absolute minimum of 200.
A thorough analysis of all three versions of Article the first is provided by the TTO report entitled: “The Minimum and Maximum Size of the U. S. House of Representatives” (download at this link).

“If a nation expects to be ignorant and free ...
it expects what never was and never will be.”
– Thomas Jefferson

Created: 15July2004 

