Make users' votes on stories public. Presumably, the purpose of upvotes is to indicate that a story will be of value to other readers. If that's the case, users should be willing to put their names behind their suggestion. Users will theoretically be less willing to vote for stories that other people won't find useful.

This solution doesn't scale, but it's quicker to implement than giving a higher weight to the votes of people who have voted for editor-selected good stories in the past. I don't like downvotes on anything.