The founders and the "ratio of representation"
Constitutional representation fueled the well-named Spirit of ‘76. One of the most popular slogans during the revolution was “No Taxation Without Representation.” Patrick Henry declared the common sentiment in simple terms – “Taxation without Representation is Tyranny.”
However, as the Constitutional Convention began in Philadelphia on 25 May 1787, such revolutionary slogans had fallen aside and into disuse. Instead there was an unease and even pessimism of revolutions. After winning one, the founders wanted things to calm down, and taxation without representation became a necessity - the country was too big for a true democracy, where all vote for all. What was needed was a new way.
This new way was developed at the Constitutional Convention. The gathering in Philadelphia took a turn that some thought too much. Instead of working on “fixing” or reforming the current government – The Articles of Confederation and Perpetual Union – the mood and momentum turned toward a new form of government altogether. You can see this change in the records from the meeting: it began on 25 May, and by 11 June the first major change was underway. That was when the founders first passed a resolution on changing from the old system, equal representation and one state, one vote, to a new system and the “ratio of representation”:
"Resolved that the right of suffrage in the first branch of the national Legislature ought not to be according to the rule established in the articles of confederation; but according to some equitable ratio of representation."
The resolution passed. Seven states were for the change, three against, and the Maryland delegation divided. (That accounts for 11 of the 13 votes – as Rhode Island and New Hampshire did not have delegates present on this day.) In less than three weeks, the founders had made a fundamental change in the distribution of power: the new government would be based on “some equitable ratio of representation.” Today, this equitable ratio of representation is found in Article 1 of the US Constitution: "The Number of Representatives shall not exceed one for every thirty Thousand".
This was not the first time a ratio had been proposed in the colonies for representation. On 7 October 1777, the Continental Congress, discussing the terms of the Articles of Confederation, had voted against two proposed representation ratios. One proposed ratio was one representative for every 50,000 inhabitants; the other was one for every 30,000 inhabitants. At that time, the newly independent states agreed to a third proposal for representation – the one state, one vote compromise – with only Virginia in dissent. So the concept of a ratio for representation was familiar to the founders by the time of the Constitutional Convention in 1787.
Two other votes of interest from 11 June 1787 included one on ‘who was to be counted and how?’ as well as ‘what to do with the second branch of the national legislature?’ On the first question – Who counted and how? – The founders passed a resolution stating, “that the right of suffrage in the first branch be according to the whole number of white and three fifths of the other inhabitants.” Thus, slavery and representation were paired together at the beginning.
On the second question – How to represent the second branch? – They voted for a resolution making the right of suffrage in the second branch just like the first – based on an equitable ratio. The equitable ratio for the second branch, the future Senate, became the one we are familiar with – two Senators per each state in the Union.
*Excerpt from chapter 2, Representation and our Constitution, in Article the first of the Bill of Rights (2006), by Bryan W. Brickner.
 Farrand’s Records, 1:192. Italics added.
 See Alfred de Grazia, Public and Republic: Political Representation in America (1951), p. 84.