In preparation for the next hard fork our team has been working on an alternative to the N^2 reward curve that results in the top posts making significantly more than everyone else.
n log(n) curve and blue representing the n curve.
We found it was easier to understand these curves by taking the derivative, which is what we graphed.
Ideal Curve
In a world with honest people who don't vote on themselves to get "free money for nothing", a simple linear curve, aka n would produce a 1 share 1 vote proportional payout. This is the blue line and shows the ideal situation.
Realistic Curve
Unfortunately, we live in a world where people will attempt to game the system by voting for themselves. If everyone voted for themselves then the result would be simple interest payments and have no economic impact. We believe that groups are more honest in aggregate than individuals. We also believe that whales (accounts with over $500K Steem Power) have more to lose and are easier to police than the multitude of smaller accounts.
The green line, n^2 / (1 + n), shows a blend between n^2 and n where for small numbers of votes the reward schedule is closer to n^2 and for larger values it approaches n.
With these curves, any single whale in the top 20 will have the power to vote with n weight such that the reward is 75% linear. If two or more of the top 20 whales concur the the final result is over 90% linear. For all content on the top of steemit.com today the reward payout would be 99% linear under this curve.
n log(n) Alternative
In the past we suggested something closer to n log(n), but as you can see from the graph, it takes longer to reach a linear approximation and then it overshoots and remains biased toward concentration of votes.
Deployment Proposal
We propose to role out the new curve for the comments only because comments do not have curation rewards in the next release. If it is successful for comments, then we will have to derive a new curation reward equation based upon this curve before we can adopt this curve to top level posts.
All equations shown are normalized by removing constants we will scale by.
Please give your feedback and let us know what you think.