Unfortunately your definition is only part of our full definition.
http://stephendpalmer.com/american-form-government/
[h=1]What is the American Form of Government?[/h] May 18, 2008
The most common — and grossly incorrect — answer to this question is that we are a democracy.
The right — albeit simplistic — answer is that we are a republic.
A more sophisticated answer is that we are a constitutional republic.
The most thorough answer comes from selections of the
Federalist Papers: an Extended Limited Commercial Federal Democratic Republic.
“Extended” refers to geography — never before in history has there been a republic that covered so much territory.
“Limited” refers to the fact that the Constitution expressly defines what the government can and cannot do.
“Commercial” refers to our national character.
The Founders said that there were three main national characters: martial, religious, and commercial. Rome had a martial character, as does China. Ancient Israel had a religious character.
Since religious and martial-character nations tend toward tyranny, the Founders chose commercial.
By “federal,” Madison meant as much power as possible was preserved with the People, and that the federal government only existed for specific and limited purposes.
The idea of federalism is that the closer one gets to the People the more power there is, while the closer one gets to the federal government, the less power one finds.
“Democratic” refers to the idea that we are a social democracy, although not a governmental democracy.
Social democracy is the concept that intrinsic in our culture is the understanding that all men and women are created equal, that no individual is better than another, and that everyone has equal opportunity to succeed.
(As an interesting side note,
Oliver DeMille gives an updated version of Madison’s lengthy label. He says that we are now an “Internationalist, Sometimes Constitutional (Except Where Prohibited By Law), Extended (Globally), Increasingly Commercial, National, Representative/Virtual/Popular Democracy, With a Technocratic Supremacist Court.” But that’s a conversation for another day…)