Final answer:
The delegates to the Constitutional Convention established republics with mixed governments to avoid 'mob rule' and ensure separation of powers, hence creating a balance between safeguarding individual liberties and maintaining social order and government integrity.
Step-by-step explanation:
During the Constitutional Convention, the delegates implemented a new distinction between democracy and republicanism. They agreed on the formation of republican governments based on the consent of the governed but were cautious of majority rule and feared the potential for 'mob rule'. To address these concerns, they pursued the creation of mixed governments with a separation of powers among a legislature, an executive, and a judiciary system. This design intended to prevent government abuse while still safeguarding individual liberties. In the states, various approaches to representation and voting rights reflected tensions between democratic ideals and concerns over too much democracy leading to instability or the undermining of elite interests.