In the sweltering heat of Philadelphia, during the fateful days of July 5 and 6, 1787, an extraordinary event took place, but one that is hardly mentioned anymore by anyone.
As I’ve written in an earlier article in this series, even before the echo from the gavel had subsided, divisions had emerged between large and small states regarding the structure of the legislative branch. James Madison, the intellectual beacon of the gathering, championed the idea of proportional representation, while William Paterson ardently defended the rights of smaller states through the New Jersey Plan.
Amid this heated controversy, a significant breakthrough occurred on July 2 as Roger Sherman and Oliver Ellsworth of Connecticut proposed the Great Compromise, a brilliant synthesis that would resolve the contentious issue of representation. This pivotal compromise incorporated elements of both the Virginia and New Jersey Plans, establishing a bicameral legislature consisting of a House of Representatives based on population and a Senate with equal representation for all states.
On July 6, a special committee of the Compromise Committee presented its report on a motion made earlier by Benjamin Franklin setting the ratio of votes in the House of Representatives at one representative for every 40,000 inhabitants.
As anyone can read in the U.S. Constitution, eventually the convention settled the matter in Article I, Section 2, which reads (in relevant part):
The number of Representatives shall not exceed one for every thirty Thousand….
Notice the nuanced changes made to Franklin’s motion regarding the ratio of representation. Franklin set a firm ratio: every 40,000 inhabitants of a state will have one representative in the House of Representatives. The ratio that made its way into the final form of the U.S. Constitution is really no ratio — no firm ratio — at all! The plain language of that clause simply caps the number of representatives at one for every 30,000 inhabitants. Do you see the difference?
Why does this apparently arcane arithmetic matter at all?
It matters because representation is the keystone of republican government. As James Madison explained in The Federalist No. 10, a republic is a form of government in which “the scheme of representation takes place.”
Additionally, Article IV, Section 4 of the Constitution guarantees to each state a “republican form of government.” In other words, the Constitution guarantees that government in each state will be one in which the will of the people will be carried out through a smaller group of people elected to represent the whole.
I know that I didn’t warn you that there would be a math question in the article, but let’s solve a couple of very easy division problems.
First, let’s look at how many members of the House of Representatives there would be if Benjamin Franklin’s motion (a motion that passed, by the way) had become part of the final text of the Constitution.
According to the U.S. Census Bureau, in 2022, the total voting-age population in the United States was 255,457,000 people. Divide that number by 40,000 — the maximum number of people that should be represented by each member of the House according to the Franklin proposal — and you get just a little under 6,387.
That’s right. If Ben Franklin’s motion had become part of the Constitution, the House of Representatives would have at least 6,387 members! Keep that number in mind.
Now, let’s look at the non-binding ratio that is included in the Constitution: one for every 30,000 inhabitants.
A quick note: I know it says “inhabitants” and not “people of voting age,” but I did this to be simple and to be a bit more realistic. The sums are different, but the surprise is the same!
Time for the second division problem: We take that 255,457,000 and divide it by 30,000 and we get a little over 8,515. So, under the limits set out in Article I, Section 2 of the Constitution, there should be no more than 8,516 (we round up because there’s no such thing as .2 people) members of the House of Representatives.
Today, there are 435 members of the House of Representatives. That is 8,081 members fewer than allowed by the Constitution. Even under Common Core math, that’s a big difference!
One last math problem: Let’s take the 255,457,000 voting-age population in the United States and divide that by the actual number of members of the House of Representatives, 435. The answer: just under 587,258.
Now let’s put the three numbers together in a way that paints a troubling picture.
Under the representation ratio approved by Benjamin Franklin (and a majority of the delegates present on July 6, 1787), each member of the House of Representatives would represent no more than 40,000 people. Obviously, the delegates at the convention considered that sufficient representation to qualify as republican government.
Under the limit in size set out in Article I, Section 2 of the Constitution, the size of the House of Representatives — in order to pass constitutional muster — would be capped at 8,516, or, one representative for every 30,000 voters. Again, in light of the guarantee of a republican form of government for the states, the delegates at the convention obviously considered that number of representatives sufficient to qualify as republican.
But we don’t have 6,387 members of the House of Representatives, and we don’t have 8,516 members of the House of Representatives. We have 435 members of the House of Representatives.
So as to not violate the guarantee made in Article IV, Section 4, the question that we must ask ourselves is: Knowing that the numbers proposed and passed by the Founding Fathers present at the Constitutional Convention of 1787 were acceptable to them as qualifying as republican representation, would they think the same thing of 435 representatives? Would they think that number qualified as republican representation?
I’ll let you decide the answer, but I will conclude this recap of the events of July 6, 1787 with two quotations from the The Federalist. First, from The Federalist No. 49, written by James Madison:
The members of the legislative department … are numerous. They are distributed and dwell among the people at large. Their connections of blood, of friendship, and of acquaintance embrace a great proportion of the most influential part of the society … they are more immediately the confidential guardians of their rights and liberties.
And finally, from The Federalist No. 57, likewise written by Madison:
The house of representatives … can make no law which will not have its full operation on themselves and their friends, as well as the great mass of society. This has always been deemed one of the strongest bonds by which human policy can connect the rulers and the people together. It creates between them that communion of interest, and sympathy of sentiments, of which few governments have furnished examples; but without which every government degenerates into tyranny.
