There is a "Send private /msg to OP" link associated with each node and available when reading a thread (rather than browsing a section).
However, I suspect most downvoters would ignore such an opportunity even were it more in their face. A vote, up or down, is a quick but fairly blunt way to express approval or disapproval of something. It may have nothing to do with a node's content even. Although a quick perusal or nodes and their votes indicates that random voting is not prevalent.
If you (the reader rather than OP specifically) receive consistent down votes check that you have read the site documentation about posting technique and that you are not being inflamatory in some fashion.
In reply to Re: Optional vote explanation box as an anonymous message sender.
by GrandFather
in thread Optional vote explanation box as an anonymous message sender.
by imp
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