Once there was n^2
Once upon a time, rewards on Steem were calculated by factoring in the voting accounts SP according to the follwoing function:
effective_voting_sp = (actual_sp) ^ 2
This describes how much SP you effectively had when you vote. So while your SP would remain unchanged during a vote, it was used exponentially proportional.
Then there was n^1, AKA n
n^2 is gives quite greater voting power, to those holding higher amounts of SP. This made the gulf between free accounts (so-called "red fish") and whale accounts much more massive than even the direct SP proportion assuming a straight (linear) comparison.
For example, a whale account of 90k SP has x1800 more SP than a red-fish account with 50 SP. Under n^2 the comparison becomes 8.1 billion to 2.5k, giving the whale effectively 3.24 million times the voting power.
n^2 compared with n^1
However there were some good reasons behind n^2 that are completely lost under n^1. These are concentration of SP and pain / gain in powering down / up.
Concentration of SP
Under n^2 it was more effective to keep all of your SP in one account.
Alice has X SP and she splits it up evenly into Xa and Xb such that Xa = Xb = X / 2. Her effective SP unsplit is X^2 whereas her split SP is
Xa^2 + Xb^2
= (X / 2)^2 + (X / 2)^2
= (X^2 / 2^2) + (X^2 / 2^2)
= 2(X^2 / 4)
= X^2 / 2
So in the case where Alice splits her SP evenly into two alt accounts, she has half the effective SP! That's a lot, and it gets worse the more she splits it up.
Thus n^2 becomes an incentive to SP concentration and puts a cost on alt accounts. This was part of the original design to discourage alternate accounts which would make the social aspects of the blockchain harder to be effective, encouraging a one human one account bias.
Pain / gain in powering down / up
There is a similar effect to powering up, in that the voting power increase is more than the amount you put it, and powering down, where the amount of voting power you lose is also more.
Despite all the changes to the system in the years it has been up, a singular fact remains that it's in the interest of the chain to have a large amount of Steem tokens powered up into Steem Power. n^2 created a simple incentive for that.
Why I propose n^1.2
The change to n^1 was arguably very good for accounts holding smaller amounts of SP. Their votes became small instead of meaningless. This was incredibly good for morale and making sure that very high stakeholders do not unfathomably dwarf smaller accounts.
However the above explained incentives are still important and I think it's time to reintroduce them with an adjustment to the curve which would make it n^1.2
In the first example of 90k vs 50 SP, the higher SP account has about 8000 times more effective SP, far less than 3.24 million times under n^2 and only about 4.5 more than under the current n^1.
Alice splitting up her account under the current n^1 system doesn't impose any penalty. She has the same amount of effective voting SP to use. We saw that under n^2 she had half as much. However under n^1.2 she has approximately X^1.2 / 1.29739671 to use. That's still a sizeable penalty for account splitting.
To put some numbers in there, if she was the 90k SP holding whale and split that up she would have about 881k effective SP in a single account but about 679k if split evenly in to accounts, a loss of nearly 23%.
To put it into perspective for the red fish, if the 50 SP account holder (with effective SP of about 109 SP) decided to add only 100 SP to their account they would have effectively 4 times as much (effective SP of about 408 SP) instead of only 3 times as much.
Whales and their discontents
There is the widespread impression that whales, those stakeholders with exceptionally large stake, make up a separate class. This leads to inheriting the concepts and language of class division and even class war. I've heard that the whales should not be trusted, should be stopped, etc.
This stems from the fact that they have far more voting power. This is true under any system which does not actively discourage SP ownership, something which is obviously counter to any goal of the system. Whether under n^1, n^2 or n^1.2, whales have more. The only thing that the reward curve does is set how much more proportionally when compared with users of different (in this case almost always lower) SP.
By weighting votes by SP we are making a simple statement. Owning (/ controlling) more SP gives you more of a say in who to reward, and who runs the network. This is fundamental. Changing this would make Steem something completely different and I have not once seen a credible proposal for changing this.
While I agree that n^2 reward curve made the gulf between low and high SP holders far too large, under any reward curve with exponent (the 2, 1 or 1.2 number) greater or equal to 1, we have a sizeable gulf. It is very much by design. If you want more of a say buy in. If you're powering down it should hurt your ability to vote. In losing super-linearity we have lost some powerful incentives against multiple accounts and powering up / down SP.
I would like to see those incentives returned.
HF20 deducted 1.2 steem from accounts before applying rshares when you upvoted.
So there now is a cost to splitting up accounts into alts. Before, if you split 1000 SP into 10 accounts of 100SP each, there was no penalty. Now there is a penalty of (1.2 SP x 10) = 12SP. It's a small deterrance to splitting accounts.
I don't really see this as a necessity or a benefit of superlinear. Alts can be made just the same. Yes, they can't split stake across them but that didn't give an advantage in linear anyway.
There's already an incentive for that. Power up to participate and also get part of the inflation automatically. Do we really need more and do we really expect more to do so with a bump like this?
You already get more say the more you stake. Powering down does reduce voting ability. I see you want the cost to be greater, but I don't really see it doing much.
That's because many of them are acting greedily without the interest of the platform. But mind you, not all of them are doing so. Yes they are entitled to do what they want with their stake, but if it's hurting the long term prospects of the platform they really have to take a good look in the mirror at some point. I also heard the line "well they already made enough by buying in early, whatever they get in addition is just gravy". Not sure how much truth there is there but it could explain quite a bit.
On a separate note, doesn't this also encourage a group of people to delegate all to one giant account for more influence? (And find a way to split the result appropriately)
Yes, it's about adjusting the cost / benefit curve. It doesn't do a whole lot but it's better. It's good for things to be better, even if not by much. It perplexes me why people are not willing to make some steps in the right direction, instead insisting on doing the whole journey in one go.
The alts situation is important in my opinion. Of course you can always create alts, as many as you want if you're willing to pay. That was allowed unfettered in the blockchain design because of the stake splitting cost.
Concentrating SP into an account by delegation would be more effective without an additional rule change, that's true. I guess in effect it would make bid bots even more attractive. There could be a supplementary rule with this change, delegated SP does not get the n^1.2 bump in voting, it stays at n^1. It should be remembered in this context that stake delegation did not exist in the original incarnation of the algorithms and so additional balancing may be appropriate.
There are lots of additional and alternative possibilities. What's clear to me is that something fundamentally beneficial was lost in moving from n^2 to n^1
There's admittedly something attractive about penalizing stake splitting in terms of ease of tracking, but it also seems that we are pretty good at figuring out which alts are likely to be together due to how they act. In the end stake being split or not we can judge each alt independently as well. But I think we will likely agree to disagree about whether the alt splitting is truly a problem or not.
Yes if 1.2 goes, I agree we should penalized delegated stake. Might be a little awkward to implement though. Or more likely just to remove it altogether... I see, good that we never had delegations with n^2 in the past.
I would like to know more about this. Were more people staking? And back then how was it in comparison to the market? I suppose the market wasn't super exciting then.
I understand that trending and most payouts were more or less in control by large stakeholders. Curated posts that made it were supposedly higher quality. There were no bid bots but I can't imagine that they would go away if we brought the rules back. At least one whale serves to benefit from passively running one off their own stake. Is the reason there were no bid bots that nobody set one up or that it really made more sense to collude into curation agreements (I am hearing that was happening and was beneficial but I don't know much about the math there even though I was trying to work out how the stacking might work)?
Another question is that back in n^2 times, there were much fewer people also right? Would it still "work" with many more small stake people in the platform?
Agreed, superlinear can avoid alts and bidbots (to a large degree), which we currently see everywhere on Steem. Linear simply won't work, we all see that in the past year.
thanks for putting a little bit of light to this subject. I'm here for 10 months and I still didn't understand the difference on reward curve. Your examples made it clear for me.
However while everyone free to do whatever they what with their stakes. They would just find a way to adjust to it to maximize their ROI so I doubt that changing it wouldn't change a thing in the end.
I didn't wanna spam with this 11 accounts voting pattern, but if you have time just take a look, changing curve to something else is just make to share the SP on less or more accounts. Result wouldn't change.
eonwarped said, "That's because many of them(whales) are acting greedily without the interest of the platform. But mind you, not all of them are doing so."
When majority acting greedily, it's too hard to spot the other ones. So giving stake-holders a higher hand is not something attractive for newcomers & investors. While mentioning investors we should also take a look how much does it cost to be a whale today and what ROI it proposes.
Not whales even orca's start to focus on curation rewards which is one of the not many options of a red-fish to grow. So while this greed is around it's hard to fix it with some code.
Indeed, but the point of aligning incentives is to achieve the situation whereby participants following their self interest (maximizing ROI might be the strongest of that category) the system benefits from the actions they take. That's the goal in applying game theory.
Making it in a whale's (and everyone else's) self interest to keep their SP in one place has the effect of highlighting their actions more clearly and opening them up to scrutiny. This scrutiny is one of the best features of this blockchain and an often unacknowledged reason why things are the way they are. Implementing n^1.2 implements a cost for whales who want to disguise their activities in obscure alt accounts.
Regarding rewards, I'm a firm proponent of rewarding those with stake or who are able to appeal to those with stake. Any other system is not Steem, it's some kind of welfare.
Oh, but dont you know, smt's will fix all that at some unreliable date in the future?
Until then we should all just pay to play because that is the what the community decided when we all voted to go linear.
All hail, stinc, et al!
Unfortunately you are exactly correct, changing anything like this will be practically incredibly hard because of the still quite hazy promise of SMTs. I've been told this more or less directly by members of STINC I will not here name when I brought up similar ideas before 😔
Still, one must go on.
Yep, dead in the water until friendly coders get it in gear.
It’s a pity that the only truly valid argument for n^1.2 is barely ever made.
Barely ever made because it isn’t an economic argument. Yet it is a totally valid argument to be considered.
But, when keeping in mind how people try to maximize curation rewards with low powered alt accounts and the fact that such alt accounts need only little SP and get only little profit from their thousands of votes... I prefer that struggle to deal with over the inconvenience anything nothing linear imposes on the largest classes and makes their struggles to level up harder.
As for the larger stakeholders... remember that anything obtained too easily is valued less. As such that will have an impact on the token value. STEEM is already one of the worst performing tokens year over year. Let’s not further erode it.
What argument is that? You've neglected to add it.
The struggle to level up is in fact easier with superlinear curve when compared with your peers, not when compared with those with far more SP. You are discounting that the effect is greater when powering up the same amount of n^1.2 when compared with the current n^1
This is not a society of classes.
It’s the one you just made here. The only one which doesn’t have a fully economic argumentation.
Why do you refer to this (not) being a case of class society? Doesn’t your post mention red fish and whales, aren’t those classifications?
A reality is that many in this beautiful and potentially disruptive technology will often not power up because the platform actually drives livelihoods of people. More than beautiful matrices. As such, I don’t discount that effect but find it negligible an argument. That also because it gives additional, and thus too easily obtained, (virtual) stake.
Oh, then I guess it's a compliment, thanks!
By class I'm obviously referring to class as the term is meant in society, I find it hard to believe you did not read that as such. Class-ification, is a broader more general term, you could also say category or type.
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