In my last post, i described some criticisms i had of Snowflakes plan to change the Steemit curation system.  In this post, i would like to share some of my own ideas.  I should mention at the start that my default assumption is that people on steemit will vote in the future pretty much the same way they vote now.

Is it possible that strong incentives and disincentives either way will effect voting behavior.  But in the real world, the magnitude and specifics of such effects are difficult to predict.  Also, in order to have the desired effect, such incentives and disincentives must be so strong as to frequently appear heavy handed.  A complicated pulley-based system of carrots and sticks is just as likely to fall over as to produce the desired results.
http://img.sparknotes.com/figures/5/58d0bf8a567f329cbfb0d18f70e6be77/y=x%5E2.gif
# What is exponential weighting?
On steemit, the blogging reward pool is allocated according to vote weight on an n^2 curve.  This means that if one user has X times as much steem power as another user, his vote on a brand new post is worth X * X as much as the other user's vote.  So, for example, if i have 1000 steem power, and you have 2000 steem power, your vote is not worth twice as much as mine, it is worth (2 * 2 =) 4 times as much as mine.  If i have 1000 steem power and you have 10,000 steem power, your vote is worth 100 times as much as mine is.

# The F-word and the C-word
A mathematical equation is not good or bad in a vaccuum. Its a way to figure something out.  Some equations are more appropriate for figuring certain things out than others.  In my opinion, the n^2 curve has two significant factors that work against it being a good way to determine reward distribution
http://2r38u4bq49o1ys1ldz1hpxnb.wpengine.netdna-cdn.com/files/2008/12/curse1.jpg
### F is for Fairness
There is a notion that's widespread on steemit about the concept of fairness.  We're told that life isn't fair, and that people who want a system to be fair are whiners, babies, or just generally out of touch with the way reality, business, the internet, or crypto currency works.

However, I believe that there is a reality of public perception deeper than this superficial, hip cynicism.  Most people simply don't want to be a part of a system that they perceive to be unfair.  Even if that system is unfair in a way that is neutral to them.    A set of rules that acts to magnify an already significant advantage that the 'rich' have over the poor offends most people's sense of right and wrong.  I think most of the general public understands percentage ownership as a concept because of things like stocks.  I think most people are fine with the guy who owns 1% of the company getting one percent of the say.  But when you tell them that the guy with 1% ownership gets only .01% of the say, thats when they say "fair is fair.  Give that guy what he paid for"

It is beyond the scope of this post to discuss whether these notions of right, wrong, and fairness are useful, reasonable  or "morally correct".  But i do post to those reading this that (at least in my opinion) they are out there -- they do exist.  If steemit has enough utility or appeal, many might be willing to participate in it despite not conforming these notions of right and wrong... However, we should ask outselves, is overcoming potential users fundamental notions about fairnesss really a hill we want to make ourselves climb?  Isn't it better to avoid some obstacles.

### C is for Concentration
Steem was initially mined by a very few early participants.  Some of them were steemit inc employees.  Others were just those fortunate enough to get in on the action early.  The result of this is that there is a significant concentration of stake.  There are many reasons why this concentration is an impediment to growth.  Many potential investors might be hesitant to invest in a currency platform where a very large percentage of the coin is held by a very small number of people.  They might be afraid of getting dumped on.  Or they might be afraid (in a POS system) of rules unfavorable to smaller investors being adopted in hardforks.

Also, if contemplating a sizable investment, they might be concerned that even their sizable investment will not make them a "big fish in a little pond" that it might elsewhere.  Even the guy who dumps 50 grand into steem, at this point, is still goign to have a very limited amount of influence compared to those who mined early.

I have seen many users, whale and non whale alike refer to stake concentration as the single biggest problem facing steem.  And personally, I am inclined to agree.  

So how is this relvant to the n^2 distribution?  Simply speaking, the n^2 distribution serves to magnify the effect of the already existant cocentration of stake in an important part of the platform.  If anything, it is desirable (to the extent fair play would allow) to ameliorate the effects of this concentration.  But at the very least, we should try to magnify it as little as possible.

# The N Word
### N if for necessity
And necessity beats everything.  If there is some reason we need n^2 to make the platform viable, then things like fairness and mitigating the effects of stake concentration are just luxuries we cannot afford.  So why do we have n^2?  Do we really need it?

The whitepaper gives a pretty good explanation of this, which ill summarize.  One of the problems with letting users vote on the distribution of rewards is the potential for abusive self-voting.  That is to say, if everyone just posts X times a day where X is the vote regeneration number, and upvotes their own posts and no one elses, steemit would be more of an anti-social network than a social network.  The whitepaper description is below.

>The naive voting process creates a Prisoner's Dilemma whereby each individual voter has
incentive to vote for themselves at the expense of the larger community goal. If every voter
defects by voting for themselves then no currency will end up distributed and the currency
as a whole will fail to gain network effect. On the other hand, if only one voter defects then
that voter would win undeserved profits while having minimal effect on the overall value of
the currency.

note:  i'm not sure whether its entirely accurate to describe this game theory situation as a prisoners dilemma.  For one thing, the participants can communicate with one another.  It seems more accurate to describe it as tragedy of the commons, but regardless the point is easy to see.  To counter this problem, they devised a two tier system.

### The downvote method:  Big polices Big 
The first part of the system was primarily designed to counter abusive whale self-upvoting and self-upvoting from a whale-sized collusive group of self-upvoting non whales. . The idea was that whales would police other both other whales, and whale sized groups of collusive self-upvoters, with downvotes.  They believed that this would be feasible because there weren't likely to be many whales, and abuses of this nature would be immediately obvious.  For example, if abit or val one day decides to post the word "boobs" over and over and upvote it for the rewards, people would start to notice fairly quickly.  And even if they attempted to conceal the ploy (for example by cutting and pasting random content) it would still be pretty obvious.  At that point, the other whales could downvote the inappropriately upvoted material.  This is what the white paper had to say about this method:

>Regardless of how much money any one individual has, there are always many other
individuals with similar wealth. Even the wealthiest individual rarely has much more than
the next couple wealthiest combined. Furthermore, those who have a large investment in a community also have the most to lose by attempting to game the voting system for themselves. It would be like the CEO of a company deciding to stop paying salaries so he could pocket all of the profits. Everyone would leave to work for other companies and the company would become worthless, leaving the CEO bankrupt rather than wealthy.

>Fortunately, any work that is getting a large concentration of votes is also gaining the most
scrutiny (publicity). Through the addition of negative-voting it is possible for many smaller
stakeholders to nullify the voting power of collusive groups or defecting large stakeholders. Furthermore, large-stakeholders have more to lose if the currency falls in value due to abuse than they might gain by voting for themselves. In fact, honest large stakeholders are likely to be more effective by policing abuse and using negative voting than they would be by voting for smaller contributions.


### The quadratic method: Don't police small and medium
The downvote method used to police abusive whale self-upvoting did not seem like it would work for non whales.  For one thing, there were likely to be too many non-whales to keep track of.  For another, rather than a relatively small number of self-upvoted posts comments with top earnings, there would likely be a huge number of self-upvoted posts and comments with a very modest (but non-zero) payout.  For a whale, non-trivial abuse might look like 5  self-upvoted posts or comments a day with a $10 payout each.  For a non whale, it might look like commenting "cool story  bro" on 500 different posts, then self-upvoting all of them for 10 cents or something to get 50 bucks a day in ill gotten gains. 

In pure game theory, its no less effective to police the "cool story bro" guy with downvotes than it is to police whales and collusive groups of non-whales with downvotes.  However, in practice it would be more difficult.  More time would have to be spent hunting down many non-so-obvious small offenses as opposed to few obvious large offenses.  Also, it seems likely the small abusive self-voter seemed more likely to be a problem than the large one, because the small one had less stake in the success of the platform.  So you had an offense that was both more likely to happen and less likely to be noticed when it did happen.

The solution ,the n^2 reward curve, made it so that a single or small group of non-whale users could not influence the distribution of the reward pool meaningfully on their own.  If they couldn't do harm, there would be no need to police them.

>In order to realign incentives and discourage individuals from simply voting for themselves,
money must be distributed in a nonlinear manner. For example a quadratic function in
votes, i.e., someone with twice the votes of someone else should receive four times the
payout and someone with three times the votes should receive nine times the payout. In
other words, the reward is proportional to votes^2 rather than votes


### Quadratic voting makes sense.  Kind of.
Its important to keep in mind that quadratic weighting makes sense in many ways.  Consider what the white paper has to say "Assuming all users have equal stake, someone who only receives their own vote will receive much less than someone who receives votes from 100 different users. This encourages users to cooperate to vote for the same things to maximize the payout."  This makes perfect sense.  Because in this particular instance, when all the voters have the same stake, the person is being rewarded for honest-to-goodness cooperation and agreement on the quality of content (which is often difficult to achieve).  But the other effect, that of magnifying higher stake voting power -- thats not real consensus thats just one guy (granted, he's a yuge freakin guy) agreeing and cooperating with himself.

### N^2 is no longer necessary to prevent abusive self-upvoting
Institutions and procedures have been developed on steemit to use downvotes to police abusive self-voting
When the white paper was written, it would have been difficult to predict the formation of an organizations like steemcleaners, or predict the level to which non-whale self policing would emerge to prevent abuse.  I've included a couple links below to illustrate situations where spam/self upvoting was adderessed quickly by the community and efficiently killed in the womb.  

https://steemit.com/spam/@marcgodard/steemvoter-com-stats-dec-4th-201
https://steemit.com/steemit/@tannukas6/this-is-a-public-database#@tannukas6/re-tannukas6-this-is-a-public-database-20170131t232521312z

These are simply two that leap immediately to mind... there have been many comment spammers nuked.  Is it possible that someone might get away with it for a little while?  Sure.  Its also possible that a much higher amount of money would go to people self upvoting their own legitimate material.   But we don't have to prevent abuse or undesirable behavior entirely.  We merely have to keep it in check to such an extent that it does not significantly impact the platform.  An individual attempting to spam upvote himself would, in the best case scenario, realize a modest profit.  But even this type of moderate success seems unlikely given the level of scrutiny all posts recieve.

# Benefits of a linear Vshare system

### The penalty for fractional voting is removed
Imagine that there are two whales, evaluating 100 posts, all of which are brand new.  They both have 1 vote to cast.  The first whale is an elitist.  He votes only for one post  The second whale wants to spread the wealth around, he votes at 10% for posts 10 different posts.  

If the reward pool (say of 10000 steem) is distributed based on n^2, the first post would get 9090 and the other 10 would get 90 each.  If the reward pool were based on a linear distribution, the first post would get 5000 and the other 10 posts would get 500 each.  Does it really make sense of curtail the influence of the more active curator?

Because there would no longer be a penalty for fractional voting, many of the 1% votes on comments we see now would earn not only posting rewards, but non-trivial curation rewards.  One of the things @smooth pointed out to me in one of the earlier snowflake threads was that curation rewards are partially superlinear, because even if no one votes after them, the whales get 25% of their vote value back when voting on a new post past the 30 minute mark.  

Now consider for a moment.  Lets say @smooth 's full power vote on a new post is worth $20.  That would mean that every time he votes on a new post (after the 30 minute mark) at 100% power, he earns a minumum of $5 (25% of $20).   He might earn more if others vote after him, but he automatically earns that $5 no matter what.  

However, if he breaks up his vote, he loses out on those automatic curation rewards.  For example, if he casts 10 10% votes, those votes are worth 20 cents each.   That means that his guranteed curation reward goes from $5 to 50 cents.  If he casts 100 1% votes, he loses out on the guaranteed curation reward entirely (because his guaranteed reward would be under two cents and would get rounded down.)  With a linear system, if he splits his votes enough, he will still eventually lose out on a guaranteed reward, but only if the value of his vote on a brand new post dips below 8 cents (which it might be close in a linear system at 1%, since he will lose some vote value from the system no longer being superlinear.)

Which is all to say, we are currently incentivizing high SP users to vote at 100% for fewer people.

### Curation would become about finding good content, not about front running whales
In our super linear system, there are two things necessary to make any money at all through curation.  The first is that you must vote on a post that a whale also votes on.   The second is that you must beat the whale to voting on the post.  If the whale votes before you, his higher Rshares will suck up all the curation reward weight.  If the whale doesnt vote at all, the post won't pay enough to give anyone non-zero curation rewards.

This means bot voting (cause it has to be quick) only for authors with a reputation for attracting whales.  And its where many curators are at right now.

Even relatively good curators like @ats-david and @biophil are really in the business of predicting whale behavior, not finding good content.

### The butlarian Jihad
This will also make it far more profitable for front running bots (especially the big ones)  to stop front running and just post on content unvoted after 30 minutes.  As if stands, they leverage the superlinearity of the rewards to make up for the fact that they are sacrificing 90% of their 25% share to the reverse auction.   Without superlinear reawards, sacrificing that 90% will almost always be a bad deal.  

The bots that now  make everyone's life miserable will essentially (provided they follow the money, which it seems reasonable to believe that they might) be turned into ministrants of charity, upvoting posts that might otherwise be ignored.

I am going to post some specific numbers comparing our super linear system with a linear system, a less super-linear system, and a hybrid system where party of the curve is linear and part is super linear later on today.