Is there a way to see the entire history of up and down votes of a post? That is, not only the current aggregate number of votes, but rather distribution of how many up votes and how many down votes.
Every post has a hidden timeline to it, which has detailed info regarding the votes a post has aggregated each day, with links in the form of
http://[sitename].stackexchange.com/posts/[postID]/timeline. (But obviously not the info about who voted)
For instance, the timeline link for this question is https://meta.stackexchange.com/posts/290708/timeline.
You need the established user privilege to see the breakdown of votes though, and without it, you will only see the total score (upvotes−downvotes) for each day.
As animuson points out in a comment, it's only a sum of votes a post has gained each day, but it's the analysis with the most details about votes that you can get.
It is part of the Established User privilege.
You get this when you reach 1,000 reputation on launched sites - and when you get it, clicking on the score of a post you will see the breakdown.
, sum(case when votetypeid = 1 then 1 else 0 end) accept
, sum(case when votetypeid = 2 then 1 else 0 end) upvote
, sum(case when votetypeid = 3 then 1 else 0 end) downvote
where postid = ##postid##
group by creationdate
order by creationdate
You'll notice that you'll only get dates for the votes, not the exact time the vote was casted. This is done to ensure anonymity of voting
Keep in mind this data is refreshed weekly on sunday.