Skip to main

Of the People, By the People, For the People

Written by Jake Tawney, November 4, 2024 -

 

Of the People, By the People, For the People

In the summer of 1787, the very future of the country was hanging in the balance. It had been widely accepted that the Articles of Confederation approved a decade earlier were insufficient as governing principles for the American experiment. Delegates from every state gathered in Philadelphia beginning in May for a convention to discuss the defects and plot a path forward. As to the delegates, the “high intellectual and moral caliber of the fifty-five men who represented the respective states at the Constitutional Convention is staggering, particularly given how young they were, with an average age of forty-two.”[1] It was perhaps not entirely foreseen that four months later this convention would produce a brand-new Constitution of the United States, causing history to eventually dub the event the “Constitutional Convention,” a term that no one at the time dared to apply.[2]

united states map with author faces

Two of the ideals that guided the construction of the new government laid out in the Constitution were balance of power and the people’s representation. First, the Framers, aware that power has a tendency to corrupt, wanted to ensure that it was distributed in a variety of ways, including between the federal and state levels and between three independent branches: the Legislature, the Executive Branch, and the Judiciary. Second, at the heart of each branch is the other guiding principle: representation of the citizenry. The constituted government was to be, in those future hallowed words spoken at Gettysburg, “of the people, by the people, and for the people.” The Executive Branch was to be headed by a President, elected from among the people. The Judiciary was to be shepherded by justices appointed and confirmed by elected officials. However, the importance of representation was most keenly felt in the formation of the Legislative Branch: a cadre of Americans from every state in the union whose task it is to write the laws that will govern their fellow citizens. In fact, in its purest form, the Legislature is the only branch that is to be creative. The Executive Branch was to enforce laws passed by Congress, and the Judicial Branch was to judge whether the laws were applied as they were written in particular cases.[3] The power to create laws rests entirely with the Legislature. This is perhaps why representation from every state was seen as so critical in forming this body and why getting the particulars of this representation evoked so much passion from the Framers.

At the Constitutional Convention, the passion turned into a heated dispute and threatened the ratification of the Constitution itself. Large states argued for James Madison’s Virginia Plan. In this plan, Congress was to have two houses: a lower house elected by popular vote and an upper house chosen by the lower house from among each state legislature. At the heart of the Virginia Plan was the idea that each citizen should be represented equally, so states with larger population numbers would have greater representation. Small states, concerned that this would inevitably deprive them of any national influence, argued for William Patterson’s New Jersey Plan, which like the Articles of Confederation called for one house of Congress and gave each state the same representation regardless of size.

This clash was a question not only of contending powers but of competing principles. Representation by state, in which each state had equal representation, seemed to violate the very principle of democracy itself, rendering the votes of those in the populous states less valuable than those in the small states…. But representation by population had its problems, too, for it violated the principle that the country was, as its name implied, a unity of states, in which the states remained the fundamental unit upon which the national polity was built.[4]

These were not the only two positions. Some delegates wanted representation to be based on economic realities, such as the amount of federal tax dollars a state was contributing.[5] With advocates from all sides refusing to ratify the Constitution unless the Legislature was set up in the way they deemed fair, the document and the founding government itself was saved by a compromise proposed by Roger Sherman from the state of Connecticut. Like the Virginia Plan, there were to be two houses in the Legislature. Unlike the Virginia Plan, one would have membership consisting of the same number of representatives per state regardless of population, thereby satisfying the small states. The second house would have membership based on the population of each state, thereby satisfying the larger states. The word “satisfying” may be too strong, for opposition still reigned. On July 16, as “American unity hung by a thread when Washington called the roll,”[6] it took two absent states (New Hampshire and Rhode Island), a state with a lack of quorum (New York), and a state with divided delegates (Massachusetts) to pass Sherman’s motion in a narrow 5-4 vote of the remaining nine states. Even so, the Connecticut Compromise was one of the most clever and important political moves in the history of our country. While certainly a political compromise, it also produced a legislative system that was better than either alternative.[7]

The Constitution of the United States sets out the construction of the Senate, the “small state” house, in Article I, Section 3:

The Senate of the United States shall be composed of two Senators from each State, chosen by the Legislature thereof, for six Years; and each Senator shall have one Vote.[8]

The House of Representatives, the “large state” house, is described in Article I, Section 2:

The House of Representatives shall be composed of Members chosen every second Year by the People of the several States.… Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers…. The actual Enumeration shall be made within three Years after the first Meeting of the Congress of the United States, and within every subsequent Term of ten Years, in such Manner as they shall by Law direct. The Number of Representatives shall not exceed one for every thirty Thousand, but each State shall have at Least one Representative.[9]

While membership in the Senate is clear, the language about membership in the House of Representatives is less clear. First, the Constitution does not give a total number of House seats or even a way of calculating it. In contrast, the size of the Senate is always to be twice the number of states. For the House of Representatives the Constitution only gives an upper bound: not exceeding “one for every thirty Thousand.” For example, the population of the United State in 1787 was 3,615,920.[10] This would put the maximum House size at 120.[11] While the actual size of the House is not specified by the Constitution, the way in which it is determined is. The responsibility lies with Congress. They have the power to determine the total number of seats by an act of legislation (“as they shall by Law direct”) along with the power to determine how many seats each state receives (the “actual Enumeration”). According to the Constitution, Congress must pass such a law within three years of their first meeting, which was March 4, 1789, in New York City’s Federal Hall. Congress will then reapportion the House every ten years.[12] The reapportionment of the House following a census each decade serves the purpose of keeping the fair representation current. This was a significant departure from other representative governments at the time, namely Great Britain, where the number of seats in Parliament was a result of historical precedence rather than up-to-date population numbers.[13] While the first census and subsequent apportionment was not to occur until 1790, the Constitution specifically lists the initial number of seats for each state.

[U]ntil such enumeration shall be made, the State of New Hampshire shall be entitled to chuse three, Massachusetts eight, Rhode-Island and Providence Plantations one, Connecticut five, New-York six, New Jersey four, Pennsylvania eight, Delaware one, Maryland six, Virginia ten, North Carolina five, South Carolina five, and Georgia three.[14]

There is a further problem with the Constitutional language concerning House membership. While the document indicates that the representatives shall be apportioned proportionally among the states (“according to their respective Numbers”), it does not indicate how this should be done. The idea of proportional representation seems relatively straightforward. If a state has ten percent of the nation’s population, then that state should receive ten percent of the seats in the House of Representatives.

What is to happen though when proportionality gives a state 13.4 seats? Should that state receive 13 or 14 seats? If the state is given 13, it will rightfully claim underrepresentation from a constitutional perspective. If they receive 14 delegates, then other states will cry foul, also citing the Constitution. Of course, something must be done. We cannot give a state a fraction of a delegate. One would think that this simple mathematical problem would produce a simple mathematical solution. One possibility could be to round to the nearest seat. As we will soon see, such simple solutions produce plenty of paradoxes. The early statesmen of our country, the likes of Washington, Jefferson, Hamilton, Webster, John Quincy Adams, and others, were fully aware of the problem of fractional seats. Even though they were not professional mathematicians, they were aware that conventional rounding was not without controversy and contradiction. What’s more, many of these men developed their own mathematical techniques for dealing with the problem of fractional seats. This political problem is relatively unknown to today’s average American. What is more familiar are the controversies of drawing fair Congressional lines. However, prior to 1941, the political problem was to determine how many seats each state should receive following the census. Every ten years from 1790 until 1940, Congress found itself situated in a very human drama that stands at the crossroads of mathematics and politics. This drama contains the first presidential veto in American history, situations where a state mysteriously stands to lose a seat when all logic suggests to the contrary, and a presidential election that hinged upon a particular apportionment method, extraneous House seats, and contested electoral college votes, and was so contentious that days before the scheduled inauguration, Congress could not agree on the electoral winner.

Politics and mathematics – what could such a subjective art and an objective science have to do with one another? The apportionment of the House of Representatives is the collision story of these two very human fields, a story that begins in the earliest years of the United States of America and extends nearly two hundred years.


[1] McClay, Wilfred M., Land of Hope: An Invitation to the Great American Story (2019), page 64.

[2] McDougal, Walter A., Freedom Just Around the Corner: A New Documentary History 1585–1828 (2004), page 297.

[3] In the landmark case Marbury versus Madison, the power of the Supreme Court was extended to judicial review, giving the judiciary the ability to determine whether laws passed by the Congress violated the Constitution, and if so to strike those laws down.

[4] Land of Hope, page 67.

[5] Young, H.P., “Fairness in Apportionment,” Johns Hopkins University and the Brookings Institution, 2004.

[6] McDougal, pages 299-300.

[7] Land of Hope, page 68.

[8] Constitution of the United States, Article I, Section 3

[9] Constitution of the United States, Article I, Sections 1 and 3. Note that the language in Section 3 includes who is to be counted as part of the population for the purposes of representation. The Fourteenth Amendment, Section 2, changes that definition. “Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed. But when the right to vote at any election for the choice of electors for President and Vice President of the United States, Representatives in Congress, the Executive and Judicial officers of a State, or the members of the Legislature thereof, is denied to any of the male inhabitants of such State, being twenty-one years of age, and citizens of the United States, or in any way abridged, except for participation in rebellion, or other crime, the basis of representation therein shall be reduced in the proportion which the number of such male citizens shall bear to the whole number of male citizens twenty-one years of age in such State.”

[10] Young, H.P., “Fairness in Apportionment,” Johns Hopkins University and the Brookings Institution, 2004.

[11] With a House size of 240, the representation would be two per thirty-thousand, exceeding the constitutional “one for every thirty Thousand.” The population of the United States as of the 2010 census was 309.3 million, which would create a maximum House size of 10,310. The size of the House of Representatives is currently much less than that at 435.

[12] Actually, it is “within every subsequent term of ten years,” which means Congress can reapportion the House sooner than ten year since the last apportionment. We will see later that Congress will conduct a census at the start of every decade, mostly recently 2020, and then conduct the reapportionment following that using the new census data.

[13] Young, H.P., “Fairness in Apportionment,” Johns Hopkins University and the Brookings Institution, 2004.

[14] Constitution of the United States, Article I, Section 2