1) Your browser caches some info and doesn't update until you take action to force update the vote count (and one of the ways to do that is upvoting/downvoting yourself). Dr_Jerrone mentioned something along the lines; the upvote/downvote isn't a live display but sometimes delayed.
2) I have no idea about the code, but maybe there's actually a built-in spam protection that delays the display of other people's upvotes/downvotes. It's a similar reason why some websites don't display this (for example, Reddit doesn't display vote count until a post is one hour old).
In any case, it's a display issue on your side. Whether it's your browser messing with you or intended by the devs as a spam protection, I don't know. But I can tell you that we can see every individual upvote/downvote and some more info. This helps us to identify vote fraud - and for the obvious reasons (to not give those people any hints on how to fool us and hide their vote fraud) we can't reveal any more details. But rest assured, every upvote/downvote is registered and it's tied to one user account, so whatever is happening is most likely a browser or display issue, but no flaw in the system. "It's not a bug, it's a feature".
After observing votes, likes, follows, and all this kind of Internet karma bullshit developing for the past 10+ years, I wish we just would get rid of it once and for all. It just brings out the worst in people and it doesn't stand for quality. Just look at Reddit: A Diablo 3 troll post gets 1000 upvotes within an hour. Useful guides rarely get over 100 upvotes and often fall off the main page just because someone doesn't like their name or remembers one single bad action of said person in the past.