When a user has the established user privilege, they can click on the post score to see the individual counts for upvotes and downvotes.
When a user doesn't have this privilege this functionality isn't present, except after loading newly added answers without refreshing the page. After clicking the "new answers to this question" link the click functionality to view vote counts is added to all posts, though actually clicking on it results in a dialog stating that an error occurred (I'd assume due to not having the required reputation).
May be related to the fix for this previous bug report: Vote count breakdown is unavailable on "new answers to this question" loaded after page load