Our nation has been a democratic republic since at least 1790; in fact the first two political parties were the Federalists and the Democratic Republicans. However in the early decades of the nation the voting franchise in presidential elections at least, though left up to the states, was almost universally extended to only about 5% of the population, landed white males; 2% actually voted for the president. Voting rights were gradually extended by Constitutional amendment to include all adults, although local "Jim Crow" laws, poll taxes and so forth effectively took away the franchise from many Constitutionally qualified people.  The 2008 presidential election saw the highest ever voter participation with about 43% of the total population voting. (Wiki) However many of those voters were effectively disenfranchised by voter discouragement, gerrymandered districts, and the electoral college, which disempowers large states relative to small states.

(cont'd)