To be more specific the blockchain currently keeps `total_reward_shares2` (total vshares for active posts) and computes payout using `total_reward_fund_steem*vshares[post]/total_reward_shares2`. We'd need to replace that with `total_reward_shares` (not squared) and add `active_posts` (counter).

Post payout would then be `total_reward_fund_steem*max(vshares[post]-total_reward_shares/(active_posts*N),0)/total_reward_shares` (N here sets the threshold; 20% would be N=5)

EDIT: unfortunately this won't work to allocate the entire reward pool at the correct rate. More refinement needed.

Credit goes to @anonymint who mentioned it on bitcointalk i think.

Standard deviation is going to be a lot harder to calculate on the blockchain but variance would work. In my proposal it is the bottom 20% by stake votes (or equivalently reward pool), not by post count. I don't think sock puppet voting that way is effective. However, just flooding the system with empty posts will reduce the average, so you are right some further refinement on it is needed.

>  Standard deviation is just the square root of variance.

Blockchains need to produce 100% deterministic repeatable results. Most practical implementations of floating point math functions such as square root have allowable rounding error that depends on the implementation. It is possible a deterministic approximation of square root could be used, but mostly the practice in blockchain code is to just avoid anything that is floating point (Steem currently uses none afaik). Similar problems exist for the suggestion to use n^1.2 or n^1.5.  n log n works well because floor(log_2) (or some variant) can be used for 'log' and that is an easy integer function.

>>Someone with a large stake could split up his account and upvote and get consensus no? Do you know the exact calculation formula?

No.  Someone with a large stake doesn't need consensus.  The idea at the time seems to have been that large stake users would police each other, and smaller stake users would have votes so weak that they couldnt abuse the system significantly on their own.

nesting

Consensus is based on steem power, not the total number of accounts using it (which is part of the problem with n^2).  So if i have 10K steem power and you have 30K steem power, your vote is worth 9 times more than mine, because you have more consensus.  You don't have to split your account into 3 10K accounts to get the bonus its already there.

Because voting on something that no one else votes for results in a much smaller reward, both content reward and curation reward.

If you look at the universe of posts, some with consensus voting from many stakeholders and some with just self-voting, the ones with consensus voting will earn the predominant portion of the reward pool under a superlinear curve. Self voting will still earn something, but it isn't much. Under a linear system, self-voting earns _proportionately_ a lot more.

[nesting]
> Yeah but someone who wants to vote for himself is by definition not going to vote for anyone else so how does this curve encourage someone to change his behavior and stop upvoting himself? Still don't get it. Sorry

Harm reduction

There is nothing inherently wrong with voting for yourself. In fact the system autovotes by default whenever you post! The idea is to minimize rewards for anyone who does this and doesn't get other votes.

[nesting]
>  How is consensus voting calculated ? Wouldn't someone with intention to self upvote just create lots of sockpuppets to upvote too?

It is stake weighted to splitting up stake changes nothing.

> I don't really think this feature is useful to be honest as users who self vote themselves without consensus are very easy to spot and downvote.

Fair point, although as the system gets large there is a reasonable argument that no one is really going to invest in doing that enormous amount of work. Sites like Facebook pay teams of people dedicated to handling hardcore abuse (such as posting child porn). Adding self-voting reward abuse to the task makes it even more challenging. In Steem there is no incentive to do any of this downvoting work. It is somewhat viable now with 1000 posts/day but with millions or billions of posts per day who is going to do it?