Argument against (completely) proportionally linear effective voting Steem Power

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.