I’ve run into this question frequently. It is used, almost exclusively, to trip up an argument, because from the antagonist’s point of view, nothing you say will be right. It is a cheap way of breaking momentum and knocking you off your game.
The other night at my Play, The People’s Republic of Edward Snowden, after the talk back, a very nice older woman-old enough to have gone to Prom with James Garfield, and dripped wealth- drew me aside to remind me that America is “Not a democracy, but a representative republic.” I have pondered both the question and answer carefully for some time, and have a clear and succinct, and accurate answer to all those smart-asses attempting to stifle cogent arguments by tripping their counterpart on meaningless details.
I said in a kindly manner that it was both, because our representative republic is only renewed through the democracy of people voting, and that policy should, and often is a mixture of the three branches of the republic and the pressure of citizens through activism, engagement and protest.
So, in fact, it is both, if we do it correctly.