What is "a democracy"? It's not among the types of government currently in existence. We have republics (with and without constitutionality), which limit democracy by channeling it through representation, and we have constitutional monarchies, which do the same but also limit monarchy through representation. We then have various other systems where democracy is even further limited by giving the voter a limited access to choosing the representation. But we have no system where representation would be bypassed the old Greek way and actual voting influence over issues granted to the general population. The last nation-sized true democracy probably died back when nations grew to be larger than ten thousand people in size...
KIRK: There are other Vulcans aboard.
Agreed that this probably refers to the delegates, as many a Spock-centric episode previously hinged on Spock being unique.