The person who was legitimately downvoted had to have something to downvote in the first place, which would be the self vote. You can't unvote and revote the post twice with the free upvote. So the free upvote does not help the attacker in this case.
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You can split your stake into two accounts, post with both, upvote one post with each account, and then use the other account to counter downvotes.
Yeah, this is true. If a large abuser split his votes, he would get a free counter effectively for 100% of his vote. That would be too big of an attack vector for what would be gained; upvote abuse is done much more than any other type of abuse.
In my view absusive downvotes are mostly a problem because there are too few downvotes. As a result, when downvotes do happen they have outsize impact both financial and emotional. The solution to this is not to nerf downvotes, it's actually to make them better. Your suggestion of anonymous downvotes is one such way, but there are probably others. I would actually prefer that all votes (both up and down) be anonymous, as is the case on most centralized sites. Focus would then shift from who is voting and whether that vote is "legitimate" to whether the net payout is appropriate (and if someone who has not voted disagrees, they can vote up or down to express that). That's the right focus.
People should be able to "like" content non-anonymously, a social operation that doesn't affect payouts.
More directly to the point here in your post, I think it would be possible to take the downvote curation reward penalty only from those upvotes chronologically before the downvote, so upvotes to counter the downvote wouldn't be penalized.
If it's possible to make both upvotes and downvotes anonymous, that will take the politics away from voting, and we would get a more accurate picture of what a post is truly worth. It would make the single biggest impact for PoB in a good way IMO. I'm sure many will see a post; think that's a bit overvalued, but don't want to downvote even a small amount due to having their name plastered up for all to see; it can turn tribal. I'm not sure how we would do that without taking voting off the base layer, but I don't think that's a good idea as anything to do with HIVE should be as secure as possible.
The last point you made on downvote curation is clever and accomplishes the same thing without the negative side effects. I'm in favor of doing it that way.
Regarding the latter thing, there would be some edge cases and possibly implementation issues to work out (but it might be easy, I'm just not sure). I do think it would be an improvement over the status quo, but how much of a difference it would make in practice I don't know. Without getting more downvotes deployed somehow as well, probably not much.
Regarding how to do anonymous voting, yes likely some sort of zero knowledge rollup type thing as you suggested but with proper auditing should still be secure. I don't see us being resourced to undertake that sort of development at the moment but with 5 million USD in DAO and growing, perhaps we'll get there.
Frontends could experiment with a 'like' system. Both up and down, separate from votes. From there someone could have a better idea if something should be downvoted or not.
On centralized systems, the downvote or thumbs down is typically used to adjust further suggested content. Vast majority doesn't touch it. Only rarely are they used as a form of genuine expression. When the numbers are higher than average, that's often due to outside contributing factors. For instance, the cancel culture types. They're bringing feelings from the past to anything new. The tallied up downvotes are not highlighting poor quality content. People will apply politics as well in order to help create the illusion of unpopular opinion. Due to the anonymity on the surface, people can act nefariously and get away with creating an illusion. The anonymity is an illusion in itself though. The system or platform knows exactly which accounts are doing what. That data is valuable to them. Creating the illusion of anonymity encourages people to act 'honestly', but what's honest in society isn't always clean or pure. It can be dark and disturbing.
Facebook has the angry emoji. But what's interesting/peculiar about that product is how some content shows up to intentionally piss people off. It's placing certain subject matter in front of those who will disagree in order to help create the illusion an idea is unpopular.
The more I think about this, the less I want to see anonymity applied to voting. For instance, anyone offering a donation on Youtube superchat takes center stage for a moment. The names of accounts donating will even flash across the screen during twitch streams.
Donations are completely different from voting. If you want to spend your own money, then it's up to you whether you want to take credit or not, and you're certainly entitled to do so.
Voting in this context is allocating a shared pool that only really makes sense to exist at all to the extent it is allocated efficiently to increase the value of Hive. For that you need people to be able to both upvote and downvote without harassment or retaliation.
Why does it have to be his stake, what about the DAO?