What made them settle on 3/5, not 2/5, 1/2, etc? Why 3/5 in particular?
Hi, not discouraging new answers here, but while you're waiting, check out some earlier responses
/u/sowser in In colonial America, why was 3/5 chosen as the value of a slave when counting population?
/u/FireRavenLord in Was the 3/5ths compromise a true compromise? What were the compromises and who got the better end of the deal?
/u/AnAmenableAnemone in Why were slaves considered 3/5 a person?
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First, it's important to clarify what's meant by "black people were counted as 3/5 of a person." The three-fifths compromise refers to a clause in the constitution relating to how states were both represented and taxed. Basically, larger, more populous states were meant to both pay more to the federal government and be better represented in the federal government. This meant that a populous state like Massachusetts would have 8 representatives, while a less populous state like Rhode Island would have only 1. Specifically, states received 1 rep per 30,000 residents.
The sticking point was that some southern states had large slave populations. Virginia alone had almost 300,000 in 1790. The compromise decided that these 300,000 slaves would give Virginia 6 seats in congress, rather than 10. It's important to remember that slave owners wanted slaves to be counted the same as a free man and it was abolitionists (or at least people without slaves) wanted slaves to count for less or nothing at all. Many people find this counter-intuitive.
As for your actual question, there was a precedent. Prior to the Constitution , the United States was organized under the Articles of Confederation for roughly a decade after independence. A proposed 1783 amendment to the articles would have allowed the federal government to collect taxes from each state based off how many people lived in each state. Southerners, such as Thomas Jefferson, balked at this amendment, as they considered slaves to be property, rather than people. The Virginia delegation proposed counting slaves as 1/2 while several New England states pushed for 3/4. Future president James Madison convinced them to compromise at 3/5. Then the whole amendment was thrown out, because the articles made for an extremely weak federal government.
When the constitution was being written 5 years later, the debate over how to count slaves was revived, but with everyone switching sides. In short, slave owners had not wanted slaves to be counted when it would result in a tax, but did want them to be counted when it resulted in political representation. They eventually settled on the same compromise ratio and it was justified in Federalist No. 54. So in short, there is nothing particularly special about 3/5, except that it was acceptable to both slave states and "free" states (most northern states still had relatively small slave populations).