Thanks for mentioning me here, fascinating conversations still happening on this post which I think is amazing.
I wanted to chip in my 2 sbdcents since you mentioned my post, what my current ideas are surrounding it.
What is interesting to note is that in my post, the conclusion that I come to is actually regardless of n^2 or linear or even anything in-between or around, it's nicely summarized in the following quote:
While the Bitcoin system is proactive in that the transaction will be rejected immediately, right now, the only system we have is retroactive. The only way to reject value going towards a double spend, is for the community to retroactively remove the value on that transaction. This is a round-about way of saying that the post must be downvoted to remove the reward. Upon this, the transaction in a sense was not rejected, but rather simply not rewarded.
I have been thinking a lot about this recently with the current situation on Steem, and I think that this is the most important facet to getting "proof of brain" to work right. I don't think you can simply change the reward distribution and hope to solve the problems, no, I think we must reject things that do not satisfy 'proof of brain'.
I have been a strong proponent of separate voting power pools for upvotes and downvotes, because this mentally removes the opportunity cost of downvoting something (as it currently 'costs' an upvote). You would have your pool of upvotes for incentivizing good behaviour, and your pool of downvotes for disincentivizing bad behaviour. They should not be mixed pools, as both are needed.
I think if people started freely downvoting these super bid-botty trash posts, economic incentives will have to find a new equilibrium. People who bid-bot garbage might very well lose out when 'proof of brain' starts working, and brainless posts are rejected -- and if they spent money and got nothing due to being downvoted and rejected, it's an even more direct influence on their behaviour.
I'm glad you felt compelled to participate. I really enjoyed that post of yours.
Like I said, under linear reward, even if we downvote everyone who doesn't engage in proof-of-brain, then all the reward are returned to the pool for other abusers to take.
Pushing this logic to its limit, 50% of stake will down vote 50% of the rest and the pool will still be full and the pool control by dust accounts.
Sure it won't happen but the problem remains the same, it's infinitely less costly to abuse than it is to police. Create a bot, comment 10 times votes those 10 comments, hope nobody flags you. The more people do it the less chance of being single out and flagged.
Yes, what @teamsteem mentioned. What you have in mind is part of the plan, but it likely can't be the only change. The other changes required are preventative in nature and promotes better behaviour with the most minimum amount of work imaginable when it comes to voting on Steem, which is supporting the greater good. It has to be the path of least resistance. But it's not possible when one can just sell their votes for so much returns compared to the proof-of-brain stuff. The economy should at least place curation and vote trading on more or less equal grounds, if not favouring the former.
The suggestion / proposal which also includes the separate downvote pool can be found here: https://steemit.com/steem/@kevinwong/the-number-one-fix-to-improve-steem-s-chances-for-mainstream-adoption
But of course, we may also not want to be so confident, so any simple iteration is better than none at this point. I just think that some of us have debated and reasoned this out well enough to merit the full implementation..