We have never seen it happen - but Kirk, in a bout of righteous patrioticsm in "Errand of Mercy", claims that democracy is what separates the UFP from the Klingon Empire. And the context is one of deciding who gets to rule over Organia, the democrats or the imperialists, so it is basically a sales pitch for UFP exports.Does the federation export democracy?
That's the only time democracy is quoted as a UFP value, AFAIK. To be sure, Kirk wouldn't let facts come in the way of his praise of the UFP system on this occasion, but OTOH there is no pressing need to assume he was telling the exact opposite of truth, either. So we might just as well assume that the UFP (at least at the time of TOS) meets the 23rd century human criteria for democracy, but doesn't make much noise about it and has nothing particular against authoritarian or incompletely representative types of rule.Kirk: "We're nothing like you. We're a democratic body."
Kor: "Come now. I'm not referring to minor ideological differences."
Timo Saloniemi