Re: Did we ever see anyone vote in the Federation?
I could see it taking several days for the entire vote count to be finished. While communication might be pretty much instantaneous on one planet, or between nearby planets, we have seen repeatedly that it can still take quite a while for messages to get from one side of the Federation to the other. Not to mention the fact that there would probably be votes come in from outposts and ships that aren't even in the Federation at the time.
Then there is the fact that the person you're electing will become one of the most powerful beings in the entire galaxy. When you're making such a huge decision I can see where it would be a good idea to take you're time and make sure that your results are accurate.
They say a little knowledge is a dangerous thing, but it is not one half so bad as a lot of ignorance. - Terry Pratchett, Equal Rites