What reasons for anonymity of voting overcome the following objection?
A down-vote fails to communicate what is thought to be wrong. Suppose I post a question that says "Doesn't the fact that $2+3=5$ mean that $2\cdot3$ must also be $5$?". Someone down-votes it. It may be that they down-voted it because they thought I was mistaken in thinking that addition is the same thing as multiplication. But I may have had doubts about whether the number $3$ exists and I may suspect it was down-voted because of my confused and erroneous belief that that number exists. Or I may mistakenly think it was down-voted because it's not research-level math, despite the fact that most mathematicians know that the proposition that $2\cdot3=5$ is one of the great unproved conjectures. Or I may suspect someone down-voted it because he thought I'm having an affair with his wife. A simple verbal statement saying "It is well known, having been proved by Paul Erdős in 1939, that multiplication is not the same thing as addition." would make it clear what the objection is. A non-anonymous downvote would make it possible for me to ask the person specifically what the objection is. A system that communicates the fact that there is an objection but withholds all information about what it is cannot indicate in what direction content should be altered to make it appropriate.