How to interpret the curve in very simple terms.
First things first. Rshares are easy. Posts collect rshares. What you assign to posts is proportional to your SP (for simplicity, assume full voting mana).
Now let’s put the curve on top.
The reward curve assigns a score to each post, based on where they lie on the curve.
The payout distributed proportionally based on the score.
It's as simple as that.
What plotting the derivative of the reward curve gives (as done in the deep dive ) is that it tells you how much additional score you get per rshare if an additional person votes.
Linear is simple, the derivative is flat. No matter where you are in terms of your post score, your score adjusts by the same amount per rshare.
In every other case, you see that the better your post does, the more impact additional rshares have on your score. This is an interesting property that has the following effect for maximizers:
Splitting stake into multiple posts (post farms) is less efficient than consolidating stake into voting a single post, so the preference will be to pile votes into a single post.
Why? It’s very obvious in n^2, but holds true for any reward curve whose derivative is increasing. But as an illustration:
Scenario 1: 10 posts with 10 rshares each : score of 10 * 10^2 = 1000
Scenario 2: 1 post with 100 rshares : score of 100^2 = 10000
And note, your payout is proportional to the score, so scenario 2 is better by a factor of 10!
With n^2/(n+1):
Scenario 1: 10 posts with 10 rshares each: score of 10 * 10^2/(10+1) = 90.9
Scenario 2: 1 post with 100 rshares: score of 100^2 / (100+1) = 99
Here the gap is much less pronounced, in relative terms. Though one thing to note here is that it’s sensitive to the scale. If n here was replaced by n/1000 for example, then we are doing this exercise closer to the ‘quadratic/n^2’ portion of the curve:
Scenario 1: 10 posts with 10 rshares each: score of 10 * (10/1000)^2/(10/1000+1) = 0.00099
Scenario 2: 1 post with 100 rshares: score of (100/1000)^2 / (100/1000+1) = 0.00909
( a factor of 10 again, what do you know )
What this means is, scale is important and can change the system dramatically based on the rshares distribution. If the scale is chosen so that all stakeholders are influencing the earlier, ‘quadratic/n^2’ portions of the curve, then this is really no different than n^2. If the scale is chosen so that all stakeholders can influence on the latter portions of the curve, then this is no different than linear. You can imagine that the scale will be chosen so that we have a gradual transition.
Of course, given the distribution, we know that a handful will be able to push posts rshares to the far right of the curve. (But compare this to the old n^2 system, and just imagine just how much power they had before!)
Anyway, the point is, piling all of one's rshares into few posts is better than massive post farming now. Every post farmer will now need significant stake to escape the quadratic early portion of the curve. Suffice it to say: post farming is now only an option for large stakeholders.
But that's kind of the point of the proposal: as @kevinwong / @trafalgar say (I forgot who said it): bring the rewarded posts out into the light.
And with convergent linear, I'm perfectly happy with it because it doesn't bring them too far out that it's basically at the sun.
There's a downside to this though: it's harder to make money at all at the low end of rshares. Comments may as well not give money at all (except of course if they are exceptional). But I think that's in alignment with how value should be distributed. After these changes it becomes much more important to build your network (which arguably you should be doing now anyway).
So what is the takeaway here? The convergent nonlinear curve looks pretty much like linear except at the low end. The scale needs to be chosen carefully so that it doesn't "curse" too many posts to the quadratic end of the curve. So one need not worry too much about this proposal as long as it is done carefully.
The other good thing about this is that I think the post reward dust threshold (at 2 cents) could even be removed after this curve change and is a less drastic cutoff.
Now… this alone doesn't really do much to address the perceived problems. As mentioned before, self voting without any other change will be for the large stakeholders. Bid bot dynamics is also interesting. Those that use it for promotion will pretty much be operating under the more linear part of the curve. But it will shut out those that are only bidding low total amounts. This again brings "valued posts into the light".
If you continue that quote by the way, I believe it was something like "bring valued posts into the light… …so they can be evaluated further". Meaning, the rest of us can downvote those that are clearly overvalued. Several posts have been made to this effect so I need not explain it further. But requiring varying degrees of free downvotes or increased curation percentage to address various issues.
(Summary: increased curation means increased sniping, which would signal that perhaps the post farmer might opt for doing something else. And more prevalent downvotes will also discourage it further. The same actually applies to bid bots as well, in an indirect manner. )
I hope this can help illuminate a few things regarding this so-called rewards curve.
- PS: downvotes. Downvotes would also be more powerful when the posts are at the higher end of the curve.