It's true that James Madison was deeply concerned with a tyranny of the majority supplanting core constitutional rights, a flaw in democracy first identified by Aristotle.

> In a letter to Thomas Jefferson in October 1788 James Madison expresses lukewarm support for the idea of a bill of rights since “repeated violations of these parchment barriers have been committed by overbearing majorities in every State.”

> [...]

> He continues to believe that the real threat to liberty will come from “the majority of the Community” and not from “acts of Government”.

To say that the United State's purpose is to protect the minority is way off base. After all, the country was born as an opposition to the idea of people not being represented by its government and instead at the behest of a very small minority of royalty and aristocrats.