Question

Why did the Great Compromise and the Three-Fifths Compromise involve so much debate and discussion?

Answer 1

Because they couldn't decide on whether slaves counted as a person at all or not.

Answer 2

Answer:  Because each state was looking out for its own interests in regard to representation in Congress.

Details:

The Great Compromise and the Three-Fifths Compromise both focused on  the representation of states in Congress.   Both of these compromises were devised during the United States Constitutional Convention in 1787.  

• The Great Compromise resolved a dispute between small population states and large population states.  The large population states wanted representation in Congress to be based on a state's population size.  The smaller states feared this would lead to unchecked dominance by the big states; they wanted all states to receive the same amount of representation.  The Great Compromise created a bicameral (two-chamber) legislature.  Representation in the House of Representatives would be based on population.  In the Senate, all states would have the same amount of representation, by two Senators.
• The Three-Fifths Compromise was a way of accounting (somewhat) for the population of slaves in states that permitted slavery.  For taxation and representation purposes, the question was whether slaves should count in the population figures.  (They were not considered voting citizens at that time.)   The Three-Fifths Compromise said that three out of every five slaves could be counted when determining a state's population size for determining how many seats that state would receive in the House of Representatives.