> I had to wonder if a multidimensional system (tags like "answers question" and "general context" etc.) would work better.

Same for HN. You're supposed to vote based on "contributes to the discussion" but if someone posts something that's false, that can be a common misconception that others will have as well and is explained in replies. Does it need to be downvoted for a honest mistake? You know people will.

There's a bunch of dimensions you could vote for but something close to "I disagree with this" is what people mostly use. If that were a separate metric from "contributes to the conversation", they could each affect ranking/grayness appropriately

Another forum I'm on lets you classify posts from "troll" (-1) through "irrelevant" to "fine", "good", and "exceptional" (+3). It then takes the median value of all votes, biasing/tie-breaking towards "fine". There is no limit on how many posts you're allowed to mark as exceptionally good, but if you abuse it, your voting rights are taken away. It's far from perfect (if you have behind-the-scenes knowledge of something, you can see where the hive mind goes wrong) but I like it better than what HN does, also because it's public and you can filter for the exceptionally good replies. They're most often by people who post additional sources and information that the article could/should have had. On HN, the only time we get to see vote count is when something gets grayed out for being super bad...