The principles of these papers are meant to stand apart from the old Federalist papers, and though you're right that they do not deal specifically with Federalism, democracies today are built from strong central governments, so the connection exists there. In any event, it's the name of the papers, you may take them with a grain of salt.

Now, as to your distinctions between groups and society etc., I don't personally find it useful to discuss the distinctions between such terms. What the group is in front of you is secondary to the larger issue of how an elected leader is chosen to represent them. That remains the case whether we are talking about a group of folks who want to elect a student body leader, a new governor, or the President.

I agree that how the leader should be chosen should depend on what the position is. But in the context of democratic elections, one person one vote should, I argue, be the default and norm.

NATO is an alliance and non-governing body, not a democracy, so my logic doesn't really apply to that sort of institution. Points all taken though, and I appreciate your candor.