If I am not mistaken anyone can change their score on a story by going to the upper right of the first page, directly under the author's username, where it says "score" and if you click on the "change" word right under that you are allowed to change your score. I have done that in the past.
At least, it works to change a score upward. I'm not sure about using it to lower a score. I've not done that.
There may be some consistency glitch with the vote change option, as we do get requests from members who can't get the 'vote change' option to work for them.
this is probably the best place to pose a question i've had for awhile: why am i able to see in my activity feed (on my profile) when someone changes a vote? this really surprised me because i have it set to where my friend's votes are hidden.
i ask because i have one friend who changed their vote on a story more than once. i'm quite sure they're friends with the author and that the author had it mentioned on their profile each time it was altered. this concerns me because it is a breach of privacy and has the potential to cause drama.