On the issue of how long it takes to tabulate the vote, it amazes me that people assume that this is automatically an electronic process.
The Federation by its very nature is an amalgam of multiple species and worlds with varying cultures and traditions. For all we know there are multiples ways that one might cast a vote in an a Federation election. Just to use the US as an example, all elections are locally organized and rules and voting procedures vary from state to state. Some states only do paper ballots, some do electronic, some do mail in only.
In a multi species Federation, that process could be even more varied. There is NO reasons that elections have to be done on computers. For instance, Bajor might have cultural/historical reasons for deciding that all votes be done on paper. Some worlds might do the equivalent of a door to door census. Others might hold something like a caucus process with elaborate ceremonies that take days to complete. The hive mind on the Bynar home world might decided to take days to consider all of the potential outcomes of selecting who they as a species will vote for. Hell, for all we know, even on Earth there may be places that uses paper ballots. In a civilzation that truly respects infinite diversity in infinite combinations, voting might really be a long drawn out process.
Just because the Federation COULD have push button electronic voting does not mean that that is what it in fact does or is the only way. Remember, even today, in most developed countries, voting COULD be done electronically from your home or office via the internet. However, for a number of perfectly valid reasons, almost no nation does that and electronic voting has proven controversial.