There are several issues here so I shall address each in-turn.
1. Maturity - almost certainly varies dramatically depending on the species. There is a 3-part fanfic series about Seven of Nine that posited that she, although she was very obviously chronologically older than the standard 18 years old that most countries on Earth treated as being an adult, but that the Mulari goddess decided that because of her life experiences she was still a teenager and therefore not considered an adult. I suspect it wouldn't just matter about age or species but with individuals. In this case, it's perfectly possible that this might be the same with the age of consent as an example. Certainly what is clear is that the criterion a person must meet to qualify will certainly have been the same or very similar indeed.
2. The Nature of the Federationís Democracy itself
a. The Make-up of the Federation - how are we to know that the Federation isn't something like the UN? We elect Member Parliaments and the Head of Government for the Member State may well nominate an individual and the Parliament confirms that candidate and sends them to San Francisco. Out of that group you have the Federation's Legislature and then the Federation Council might well be the Security Council, with the big members, Earth, Vulcan, Andoria serving on a permanent basis and a few others with rotating members joining on a non-permanent basis. The Legislature might well do the electing for the President or there might well be an electoral college system. It certainly seems a very a-partisan environment.
b. Partisanship - The issue of partisanship has been mentioned in above posts, as well as, arguably demonstrated in 'A Journey to Babel'. Had their been a lot of political parties getting together into voting blocs, wouldn't one have been willing to hand Kirk over to the Klingons in the aftermath of the Genesis incident in-order to preserve the peace? To sacrifice one rogue commander for galactic peace might not seem too bad to some politicians. Perhaps Roddenberry might have been looking to the initial phase of the American Republic, before the existence of Jefferson and Madison's Democratic-Republican party, the period between the end of the Revolutionary War and the First Party System
. George Washington's second Presidential term was very rancorous, not through his fault, but the Federalist and Democratic-Republican movements were really trying to take shape. Perhaps there might be more of an Expansionist, pro-Starfleet as the Military grouping with the Andorians in the lead and a Domestic, Peace-party grouping, with say the Vulcan presence at the core. Quite possibly there is a strong, central-government versus limited Member-focused government debate, which is basically what the Federalists and the Democratic-Republicans where so passionately debating about in-reality. Does the Council just focus on Foreign Policy, Foreign Trade, Defence, the ways to fund these and Constitutional matters?
c. The Role of the President - I would expect, based on the way that we have seen the President thus far, as an office under-siege. Is the President a strong figure? A President in the American sense of the term? Is not the Federation too big for that? Perhaps what we should look at it as a combination of the role of Commander-in-Chief, Chief Diplomat, Managing Director of the Federation Government, protector of the Constitution and perhaps President of the Council as well. In this case is the President of the Twelve Colonies
on Battlestar Galactica
not a more considered definition? It is clear that much of BSG comes out of Ron Mooreís thoughts about and criticisms of Star Trek, quite possibly rooted just as deeply in the final months of his personal Trek, his personally difficult time aboard Voyager. Laura Roslin is the only President we see in any detail and her acts and circumstances are in no way typical, she is terrifically expansionist about her powers, sheís making things up as she goes along and probably, although never expressly said to be, her own Minister of Defence. Sheís a Churchill or a Roosevelt, not a Woodrow Wilson. But we can assume that the office itself, which is confirmed in her balancing act with the Quorum, a body she uses when convenient.
d. Participation - the other issue of course actual participation. A contented culture tends not to vote, this is borne out in voter turnout
analysis. It doesnít matter the manner you vote in, although itís guaranteed to be completely technological in the Federation. I suspect that the concerns that normally lead cultures to vote in droves, the financial instabilities, austerity measures, tax hikes etc, donít appear to apply. It would also be difficult to vote if you were in Starfleet. I suspect that you would probably vote at a local or provincial level or possibly at a Member planet-level, but Iím not convinced that you necessarily would feel a great deal of need to vote in an election for a President? How do you mount a campaign on that scale? How do you make people feel connected to the leadership on Earth? If Obama, Bill Clinton and Ronald Reagan, the great recent communicators in the White House have to/had to really work hard to communicate and reach out and seem relevant. I donít think you can on this kind of scale. I might be wrong, but the Federation seems to be a culture that is comfortable with the culture of professional public servants, you can make it into that if you want to, but there isnít necessarily the traditional American commitment to local public office and perhaps too comfortable with Starfleet, who should be the experts, having a considerable influence about the stateís priorities. It takes something extreme for people to shake themselves out of this trend i.e. how Human colonists naively allowed themselves to be handed to the Cardassians and then started fighting back when their stupidity became obvious, or probably after the Dominion War when foreign policy and Starfleetís struggles to defend the Federation despite what is probably an enormous portion of the central budget. But you have to shake the tree to get people interested rather than merely observant.
I could of course be completely wrong....