How did the delegates to the constitutional convention balance competing interests?

The Delegates to the Constitutional Convention balance the competing interests by establishing a bicameral legislature or two-house legislature.
The 3/5 rule for the counting of slaves census purposes was a compromise between the anti-slavery and pro-slavery factions. The House of Representatives wanted by the large population states, while the Senate wanted by the small population's states. It also involves the Federalism, the great compromise, separation of powers and social contracts theory.

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