The correct answer to this open question is the following.
The enlightenment thinkers' ideas that seemed especially compatible with representative democracy were the following.
First, the idea of natural rights. Those universal and inalienable rights that humans have. Another important idea was the will of the people, the right of the people to elect their representatives. Another one was the definite separation of the church from the state. Finally, a very important idea that influenced many countries was the separation of powers.
Great Enlightenment thinkers such as Jean-Jaques Rosseau, Baron of Montesquiou, Jhon Locke, and Thomas Hobbes, created great ideas that years later influenced important independence movements such as the American Revolutionary War and the French Revolution.