I'd support having such a log for administrators, although I find it likely there already exists such a thing as LW does keep track of every upvote and downvote of every user on every post/comment they up/downvote.

I would only want them to take "appropriate action" if appropriate means announcing clearly any new policy and preferably automating that policy. I do not think an unannounced one off "you are a bad person because you downvoted whoever 7 times thursday so we are X'ing you" without putting some automation and/or warning in place is appropriate.