What did the three fifths compromise at the constitutional convention determine

That a slave is 3/5 of a man.

Explanation:

Just because they're considered as this. An exchange.

social contract theory basically says that all individuals are born equal, and provided a god given right to consent to be governed. american government is based of this

thomas hobbes and john locke said that we are selfish, individualistic, and constantly at war with each other, therefore we need to be controlled. 

government is defined as the legitimate use of force to control human behavior within territorial boundaries, here comes in hobbes and locke.

hobbes takes the part about controlling human behavior. while locke takes the part of legitimate use of force, since force is not legitimate unless there is consent of the people. 

there are basically 3 goals of the government: 1) maintain order by protecting life and property. 2) providing public goods, those which are typically not provided by the public sector, such as roads and education. 3) promote equality be it political, opportunist or outcome equality.