That is probably the biggest part of our disconnect on this.
I agree.
We know that under linear rewards the system can devolve into simple interest (ignoring downvotes, so somewhat unrealistic). I have said this before and I've never gotten an answer: How bad is that?
Then it should be made simple interest on SP. Steem shouldn't say proof-of-brain increase the value of Steem when people engage in it if it only decreases the reward of those who actually engage in it.
Did it help create a very effective system of content discovery? Did it reliably reward new unknown users with valuable contributions as a way of encouraging rapid viral growth? The answer to all of these questions is "No".)
I mostly agree but I'm convinced under n2 and over time the answer would have been yes.
Fair enough, or just reduced/disabled (SP already has some interest, so it probably isn't necessary to add more). One reason I encourage stakeholders to vote for @burnpost because it accomplishes similar things with less load on the blockchain than a lot of self-voting (also supporting otherwise-unincentiveized downvoting of explicit abuse and helping to stabilize the value of SBD).
Sure, but n^2 did too, at least with only 25% curation rewards (to my knowledge no one has looked closely at comparing 25% with 50% or some other number under the n^2 system). The most rewarded were those with large stake engaging in self-voting (or "friend" voting), which in turn means the others not doing that were less rewarded (i.e. "decreased reward"). If n^2 or some other system actually rewarded people more for voting in a proof-of-brain manner I might support it more, but it didn't. More downvoting to provide an input measure consensus between stakeholders (rather than just concentration of stake, whether multiple stakeholders or not) could possibly do this, but it could do it with n as well as n^2, or other curves.
It is impossible to completely rule out any hypothetical but the other problems with n^2 made it unsustainable therefore unsuitable. For similar reasons, it also isn't coming back. Possibly other approaches can be tried.
BTW, why n^2 rather than n^9999 or n^1.1? Clearly n^9999 has obvious problems with too much concentration, and possibly n^1.1 might not be non-linear enough to accomplish what you are trying to accomplish. But how do you know that n^2 was not also subject to either (or both!) of these major problems? I guess if it is just your opinion, that is okay, but I don't see a strong conceptual or theoretical reason to conclude this.
I also always wondered why ^2 and not something else. What you pointed out gave me a possible hint at why, which was the simple, less computer intensive integer to implement without going unnecessarily too high.
I could be wrong about ^2 overall but I feel like it's better than linear for the reasons I pointed out or tried to point out.
True there were some abuses and I was very well aware of many but I feel like the free market would have regulated it over time.