There are reasons why I don't like anonymous downvoting. It is very confusing to new members. It doesn't encourage people to stay. It isn't helping to make this site not 'beta.' I understand that there is a reasonable concern about one or few time posters getting carried away, spam and so on. I'd prefer a flag, like in the comments. The flag could have reasons like in the review section for things like: spam, off-topic, inappropriate language or, not a question. I think this would be far more inviting and helpful. It would teach in a non-threatening way.
Downvotes matter. Privileges on site are 'bought' with votes. So having anyone be able to downvote without a reason, makes new members confused and feel unwelcomed. Hey, I am a newbie. I know that is how I felt.
ON EDIT Jan 22/17: I have been here since early December/late November. It still irks me. For example, someone downvoted this question. Probably they did not like it. I think not upvoting is enough to say you did not like the question. I have no clue whatsoever why a question that was honest and respectful would get a downvote. It taught me nothing more than someone either doesn't like me -- well okay -- or they felt threatened by the question. I (finally) have enough reputation to not worry about downvotes, but I think that newbies, and particularly people whose first language is not English, do not feel welcomed. Sure a few idiots get through and try to stir the pot. We have mods for that. I can flag a post if I have a concern and know that a mod will decide. I've done no harm. I can be wrong about a flag and the OP has no worry -- an experienced mod will decide.
So I still think that downvoting without a comment is bullpucky. Ha! I am stubborn, I know.