I can't agree with this. One problem with anonymous actions is that people tend to become psychologically more distant from those actions. It's much easier to throw away the junk mail from a homeless charity than it is to refuse a homeless person pleading with you in the street.
Another is that without oversight, arbitrary decisions flourish. There's no culpability, and no protection from abuse. I think this is a serious problem with question deletions, which are technically public, but only to a tiny minority of Stack Overflow.
Requiring multiple votes helps a little, but there is a clear herd effect that works against this. It's much easier to add your vote to a few existing ones, than it is to cast the first vote, or actively oppose a decision.
The request seems to be about dealing with the presumably serious problem of serial downvotes. I don't know much about your closing style, or why you have been attacked, but I do know that
- In 11 months, I've never been serial downvoted on SO, where I regularly close questions, argue about reopens, edit other people's stuff, and tell people off for abuse of the system.
- Even if I was, it would make a completely negligible difference to my reputation. And on SO, I've got 20,000 less rep than you!
- There are already systems in place to handle serial downvoting.
- I absolutely want all my actions to be public and accountable.
Ultimately, it boils down to something pretty simple: If you are willing to take an action, then you should take responsibility for that action. If you are going to take the step of actively trying to close someone's question, the least you can do is stand by that action, as you refuse their appeal for help.