I've never downvoted anyone so far and don't want to. Got my first downvote today which was a surprise but was told it was just someone nasty who downvotes all the time. It does concern me though that I can get downvoted for no reason at all by anyone nasty enough to do it. Not sure I like the downvote button, but I guess it must do some good if it stops things happening that are not good for steemit...
Recently some changes were made to the Steem blockchain that allow people to do about 2 or 3 downvotes a day without using the Voting Power that is better spent on upvotes. The main reason is to prevent abuse. I wouldn't worry about getting small downvotes worth less than $0.01, the people doing that are just trolling. Chances are your post is worth so much anyway, the net effect of these small downvotes is nil. If you actually do something considered 'abuse', the backlash will be severe and obvious.