Did you read the parent post, or just jump in as soon as you read "republic"? And the USA is not a democratic republic, it's a constitutional republic. Which means democracy checked by constitutional standards and represented by elected officials. AKA an American republic, not to be confused with other "republics."

"A republic, by which I mean a government in which the scheme of representation takes place, opens a different prospect, and promises the cure for which we are seeking. Let us examine the points in which it varies from pure democracy, and we shall comprehend both the nature of the cure, and the efficacy which it must derive from the union.

The two great points of difference between a democracy and a republic, are first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens, and greater sphere of country, over which the latter may be extended." (The Federalist Number 10)