Is this possible on SO? Similar to Facebook where you can see who "Liked" something.
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I don't believe this is possibe, primarily for the fear of negative consequences (a downvoted user returning down-votes, for example). Requests for the feature typically meet with a status-bydesign (or similar) fate.
For reference: Can I tell who downvoted one of my answers?
It's also worth looking at the minor-compromise effort that Jeff implemented ( Encouraging people to explain downvotes ) which, in theory, encourages first-time down-voters to suggest ways in which the question/answer they're down-voting can be improved. And then hopes they remember in future.