Convergent Linear Reward

It may not be possible to change the inherent characteristics of an individual with a set of algorithms or code, but you can definitely train them. The individual social characteristics may be a little complex, and may not even possible to train them on case to case basis with code/algorithm. But the social characteristics of the community are a lot easier to train, particularly in creating a social network, added with economic advantage.

That's what today's topic is-- Convergenet Linear Reward-- harnesses the social behaviors/judgment on curation & transforms them into a community judgment in Steem Blockchain.

It was the year 2016 when we witnessed the first-ever decentralized social platform Steemit on the top of Steem Blockchain, at that time the reward curve on Steem Blockchain was quadratic/superlinear, with its function f(x)= x². It really encouraged people to invest more in STEEM and then power it up as Steem Power(SP), as more SP you have, the more reward you can generate. But later it was found that it discouraged the common middle class and the Newcomers. Also, it led to-- "The rich get richer".

In the year 2017(June' 2017), the reward curve(quadratic equation) was replaced by a linear equation, f(x)=x. This really looked fair for all, in line with the spirit of decentralization & equal opportunities for all. But even if it looked fair to all, it led to a number of parallel posts, with no social intersection, people started self upvoting, so it was found that the social behavior tends to be selfish with a linear equation. Further, it also led to sheer abuse of reward pool by using bot upvote for poor content and pushing it to the top, which led to poor content discovery.

In the year 2019(Aug' 2019/ Hard Fork 21), to address the selfish behaviors, bot use, abuse of reward pool & to improve the content discovery, the reward curve(linear equation) was replaced by a convergent linear equation, f(x)= x²/(x+1). With this equation, self-upvote is discouraging in the context of monetary rewards, and you can gain more by upvoting other's posts. Further, the number of parallel posts got reduced with the introduction of convergent linear reward and it led to a better social intersection, hence better content discovery.

Those who find these math equations as tricky and complex, don't worry I will make it as simple as possible so that it becomes an easy cup of tea for all.

The difference between quadratic/Linear and Convergent Linear Equation(Reward Curve)

Input= [SP, VP], Output= [Reward, Upvote Value]

• In the case of Quadratic/Superlinear Equation [f(x)= x²], reward grows with [input]². For instance, if user A has SP twice as much as user B, then his upvote value is 4 times better than user B.

• In the case of Linear Equation [f(x)= x], the reward grows linear with input. For instance, if user A has SP twice as much as B, then his upvote value is 2 times better than user B.

• In the case of Convergent Linear Equation [f(x)= x²/(x+1)], the reward is much lower with a lower input, but it improves as the input value increases, and finally, it grows linearly with a higher input. For instance, if users A, B, C have small inputs(SP), their individual output(upvote value) will be smaller, but their collective output will be bigger than the sum of individual output.

In the 0 Layer,(at the Blockchain level), it does not recognize SP, rather it is Vests. They are like shares and the reward that is generated is known as Reward Shares. So when you upvote a post, it generates "rShares". The reward(STEEM) is then distributed based on the rShares generated in a post.

So we have two parameters--

• Reward Pool(STEEM tokens)
• rShares

The beauty of convergent linear reward is that every time a new user visits and curates the post, the STEEM reward per rShares increases. So more the people approve content, the more is the reward it generates and becomes a trending post, visible to all.

Further, as more and more rShares added to a post, it converges to linearity, which we will check by taking the real example(using SP and its upvote value)

Please don't get confused by rShares, Vests. I will simplify it by plotting a curve using "SP and upvote value". (At the Blockchain level, they are known as Vests(SP) and rShares(Upvote Value)).

Let's first plot the chart of superlinear, linear, and convergent linear equations.

Now let's get back to the real use of this equation in Steem Blockchain.

We have the input as (SP, VP) using which we upvote a post when we do so it generates rShares, and based on that rShares the reward pool is distributed.

Here, Input= SP, VP

Output= Upvote Value.

We will take a range of different input values (in increasing order) to check the output and then we will establish how and when it converges to linearity, what is the significance of this curve on the social behaviors & judgment(curation).

Here are the different SP values which produce different upvote value(Upvote value is calculated using the tool Steemworld.org)

Let's plot the chart of these values.

Observation:-

• For the lower values of input(SP), the output is much smaller. But with higher input values(SP), the output is much higher and started becoming linear beyond 2.5 Million SP.

• Higher input does not necessarily mean a single voter, it can be multiple voters also and if their combined input values(SP) is higher, then they can also draw a linear reward(upvote) as output. For example, if there are 50 individual voters whose combined SP size 2.5 million, they all can earn the linear rewards, should they curate brilliant content.

• If there are three curators-- A, B, C with SP values 10000 SP, 15,000 SP, and 20,000 SP respectively. If they all remain isolated in curation, then their reward will be less as individual curators. If all these three curators reach an agreement on quality content and curate as a community then they all earn a better curation reward.

Example,

Curator A- Upvote value with 10,000 SP(full weight)= $0.2044
Curator B- Upvote value with 15,000 SP(full weight)= $0.3131
Curator C- Upvote value with 20,000 SP(full weight)= $0.4249

Isolated judgment by A, B, C= (0.2044+0.3131+0.4249)= $0.9424

Now if all these three curators curate a single post, then their combined input will become (10000+15000+20000)= 45000 SP, the post payout with 45000 SP as input will generate an output = $1.0359

Community judgment by A,B,C= $1.0359 (with a combined input of 45000 SP).

$1.0359 > $0.9424

Hence all three curators will earn better curation rewards if they reach an agreement as a community in their judgment on curation.

Put simply, convergent linear reward curve encourages a curator to reach an agreement with the community in Proof-of-Brain. Further, isolated judgment rewards less, hence the individual curators are motivated to visit other's post and find quality content, in the quest of quality content they also help to better content discovery, because the individual curators can reach an agreement with the community only on quality content/popular content which adds value to Steem Blockchain and its ecosystem.

• The self-upvoted content, poor quality content, will always remain in the lower zone(or Sub-linear zone) of the chart, as the output will be much lower if the input is lower. So those who self-upvote their post do not benefit from such a reward curve. Similarly, poor content hardly find the attention of the community, they also remain in the sub-linear zone

• The moderate-quality content will be seated somewhere between linear and sub-linear zone. They may find some support from the community but may not find sufficient traction to reach linearity.

• The high-quality/brilliant content definitely trends the page and remains in the linear zone. In this zone, the isolated judgment transforms into community judgment. The individual curators reach an agreement with the community. The reward curve further encourages the people to curate such content as they all earn linear reward which is always greater than sub-linear reward.

Let's have an analytical approach to find how encouraging it is to curate a post on the trending page.

With the current resources [SP, VP] that I have if I cast a vote with the full weight, then it will generate an upvote value of $0.15, from this value I can earn a curation reward of $0.075.

Let's go to the Steemit trending page, and pick one of the trending posts with a high payout(linear reward).

I have taken the screenshot both before and after voting this post.

Before voting, the post payout was= $383.2
After voting, the post payout is= $383.72

Difference= $383.72- $383.2= $0.72

Wow, that's massive. With the same resources community judgment(linear reward) produces $0.72 which is almost 5 times of isolated judgment($0.15).

Let's calculate the curation reward from this post.

Pcurator= (1/2) * (√P_T) * (√P₁-√P₀) Δt

P_T= Post Payout at the end of 7 days
P₀= Post Payout before voting
P₁= Post Payout after voting

P₀= 383.2
P₁= 383.72
P_T= 383.72

Δt= 1 as I have voted after 5mins.

=> P_sapwood= (1/2) * (√383.72) * (√383.72-√383.2)= $0.13

In this example,

Isolated judgment produces a curation reward= $0.075
Community judgement produces a curation reward(linear reward)= $0.13

So even if I voted much later(when the whales have already voted, thereby not gaining from early voter's advantage) I still gain significant curation reward from such a post(as compared to isolated judgment).

That's the beauty of Convergent Linear Reward.

To draw a conclusion:-

• Do engage to discover better content.
• Engineer time and position of your upvote to gain early voter's advantage. (Before a whale's vote)
• Even if you are not an early voter in trending posts, you can still gain better curation rewards (as the reward curve has reached linearity), so you can vote such posts.
• Don't self upvote- The reward curve discourages you to do so. It does not create social intersections either, so the community also does not encourage it.
• Do engage regularly to remain synchronized with dynamics of trending posts, contests/challenges to discover popular posts, and engineer your curation effort.

Homework Task

(1) What are the economic & social ramifications of self-upvote in Steem Blockchain? Do you gain better curation rewards by upvoting others as compared to self-upvote? (Include real examples)

(2) What is the difference between isolated judgment and community judgment in curation? How do you adapt to community judgment on quality content in Steem Blockchain? Does that bring economic incentive for you? If yes, explain with real examples, (include screenshots and compare them with your isolated judgment)?

(3) Go to Steemworld.org, check your Upvote value( at the current SP, VP). Take a screenshot. Then go to the Steemit trending page, find a post with a payout of more than $10 but less than $50(Age less than 6 Days 12 hrs). Upvote it. Take screenshots before and after upvote. Similarly, go to another post on the Trending page, find a post with a payout of more than $100( Age less than 6 Days 12 Hrs). Upvote it. Take screenshots before and after upvote. Tell the differences between the two. Which one has produced a greater Upvote value & Curation reward for you with the same resources(SP, VP)? Explain?

Guidelines

• Your article should be at least 300 words.
• It is always better to gain user experience before submitting your article.
• Refrain from spam/plagiarism. This task requires screenshot(s) of your own experience with Steemworld.org/Steemit. Use images from copyright-free sources and showcase the source, if any.
• This homework task will run until 21st-Mar'2021.
• Add tag #sapwood-week6 #cryptoacademy in your post and should be among the first five tags. You can also use other relevant tags like #blockchain #steem #curation or any other relevant tag.
• Those who include the real examples with screenshots will score better.
• If you have not participated in Steem Blockchain Week 5, then you should visit this POST to have a better understanding of Curation Rewards.

Thank you.

(Please feel free to join the comment section if you have any doubt on Homework-Task)

Cc:-
@steemitblog
@steemcurator01
@steemcurator02

Unless otherwise stated, all the images, infographics, charts, tables, etc(if any) are my original works.