I am aware that the various Trek novels are non-canon, but nonetheless, I'd like to know how much our perception of the Federation's government would change if they were, so to speak. For example, is there any definite description of democracy or the precise system of legislature given by any author? Freedom of speech? Any elaboration on the economy? And so on.
The Federation President is directly elected by popular vote, or something akin to that. Each planet has a Federation Council seat; additionally, if I'm remembering right, the Federation Cabinet is put together in similar fashion to a Westminster system, with members of the Federation Council being given ministerial posts, as opposed to the US where they are appointed by the President and are not drawn from the legislature. Though some posts are by Presidential appointment IIRC.
Nan Bacco was not even a Federation-level official; she was the Governor of Cestus III who made a splash following some Gorn attack/occupation of Cestus during the Dominion War (another novel, or graphic novel, depicted these events - Trek written fiction is starting to gain a fairly coherent continuity from what I've seen). Spoiler
Of course, there are still issues. Like, oh, Starfleet forcing the prior President, the Bolian Min Zife, to resign after a botched Dominion War-era plot forces Starfleet into a bloody occupation of a crappy planet and opened the potential for war with the Klingon Empire, after which Section 31 assassinated Zife, his Chief of Staff, and his intelligence advisor. Later Bacco does find out about this and Ross feels obligated to fall on his sword and claim sole responsibility because he feared if Bacco learned of Section 31 they'd assassinate her too.
Edit: Forgot to note that this is all from the recent novels, including "Articles of the Federation", though Bacco's introduction - and her successful presidential campaign - came from the last book of the "A Time to..." series, "A Time for War, A Time for Peace". According to the novels' timelines, the events of Star Trek Nemesis fell between the last chapter of ATfW,ATfP and the epilogue of that novel, with "Articles of the Federation" occurring immediately thereafter.
I would also highly recommend Articles, it was a good book and is the kind of look at the Federation's political and social life that the franchise has been begging for since, well, Day 1 really.