Confederation Congress
The three-fifths ratio originated with a 1783 amendment proposed to the Articles of Confederation. The amendment was to have changed the basis for determining the wealth of each state, and hence its tax obligations, from real estate to population, as a measure of ability to produce wealth. The proposal by a committee of the Congress had suggested that taxes "shall be supplied by the several colonies in proportion to the number of inhabitants of every age, sex, and quality, except Indians not paying taxes". The South immediately objected to this formula since it would include slaves, who were viewed primarily as property, in calculating the amount of taxes to be paid. As Thomas Jefferson wrote in his notes on the debates, the southern states would be taxed "according to their numbers and their wealth conjunctly, while the northern would be taxed on numbers only".
After proposed compromises of one-half by Benjamin Harrison of Virginia and three-fourths by several New Englanders failed to gain sufficient support, Congress finally settled on the three-fifths ratio proposed by James Madison. But this amendment ultimately failed, falling two states short of the unanimous approval required for amending the Articles of Confederation (only New Hampshire and New York were opposed).
Constitutional Convention
The Convention had unanimously accepted the principle that representation in the House of Representatives would be in proportion to the relative state populations. However, since slaves could not vote, leaders in slave states would thus have the benefit of increased representation in the House and the Electoral College. Delegates opposed to slavery proposed that only free inhabitants of each state be counted for apportionment purposes, while delegates supportive of slavery, on the other hand, opposed the proposal, wanting slaves to count in their actual numbers.
The proposal was debated on July 11th and initially, the concept of counting by a three-fifths ratio was voted down by the members present at the Convention. A few southern delegates, seeing an opportunity, then proposed full representation for their slave population. Seeing that the states could not remain united without some sort of compromise measure, the ratio of three fifths was brought back to the table and agreed to.
Compromise and enactment
After a contentious debate, the compromise that was finally agreed upon—of counting "all other persons" as only three-fifths of their actual numbers—reduced the representation of the slave states relative to the original proposals, but improved it over the Northern position. An inducement for slave states to accept the Compromise was its tie to taxation in the same ratio, so that the burden of taxation on the slave states was also reduced.
The Three-Fifths Compromise is found in Article 1, Section 2, Clause 3 of the United States Constitution, which reads:
Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons.
A contentious issue at the 1787 Constitutional Convention was whether slaves would be counted as part of the population in determining representation of the states in the Congress or would instead be considered property and, as such, not be considered for purposes of representation. Delegates from states with a large population of slaves argued that slaves should be considered persons in determining representation, but as property if the new government were to levy taxes on the states on the basis of population. Delegates from states where slavery had become rare argued that slaves should be included in taxation, but not in determining representation.
The proposed ratio was, however, a ready solution to the impasse that arose during the Constitutional Convention. In that situation, the alignment of the contending forces was the reverse of what had been obtained under the Articles of Confederation in 1783. In amending the Articles, the North wanted slaves to count for more than the South did because the objective was to determine taxes paid by the states to the federal government. In the Constitutional Convention, the more important issue was representation in Congress, so the South wanted slaves to count for more than the North did.
Much has been said of the impropriety of representing men who have no will of their own.... They are men, though degraded to the condition of slavery. They are persons known to the municipal laws of the states which they inhabit, as well as to the laws of nature. But representation and taxation go together.... Would it be just to impose a singular burden, without conferring some adequate advantage?— Alexander Hamilton