### 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)= x^{2}. 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)= x^{2}/(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)= x
^{2}], 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)= x
^{2}/(x+1)], the reward is much lower with a lower input, but it improves as the input value increases, finally

, it growgrows 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, shoul curate brillianilliant 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 rate as a communitmmunity 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 lso help to better conte 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 remain in the lowee 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-upheir post do not benefitenefit 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= $383.72Difference= $383.73.2= $0.72

ow, Wow, that's massive. With the same resources community judgment(linear reward)ucuces $0.72 which is almost 5 timtimes of isolated judgment($0.15).Let's calculate the curation reward from this post.

Pcurator= (1/2)

*(√P*(√P_{T})_{1}-√P_{0}) ΔtP

_{T}= Post Payout at the end of 7 days

P_{0}= Post Payout before voting

P_{1}= Post Payout after votingP

_{0}= 383.2

P_{1}= 383.72

P_{T}= 383.72Δt= 1 as I have voted after 5mins.

=> P

_{sapwood}= (1/2)*(√383.72)*(√383.72-√383.2)= $0.13In this example,

Isolated judgment produces a curation reward= $0.075

Community judgement produces a curation reward(linear reward)= $0.13So 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 resourcSP, 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.*

## Comments 62

Difference= $383.72- $383.2= $0.52

Dear @sapwood, there is an error in your calculation.

Thank you.

Corrected/edited.

👍👍

Yes

Dear professor @sapwood, my week 5 task post has not been review sir. I hope you review it sooner. Thanks.

This is the link to the task;

https://goldvoice.club/steem/@temitopef/homework-task-5-steem-blockchain-pob-voting-window-curation-or-lesson-by-sapwood

I will check it soon. Don't worry.

Thanks.

Respected Professor @sapwood, here is week 5 homework post. Please review it. I hope you will review it asap. Thanks

https://goldvoice.club/steem/@mawattoo8/crypto-academy-week-5-homework-post-for-sapwood

All are being checked serially. Don't worry. It will be curated soon.

Thanks

Good day professor @yohan2on. My week5 task haven't been verified. Please kindly check below.

https://goldvoice.club/steem/@reminiscence01/homework-task-week-5-for-professor-sapwood-or-steemit-blockchain-or

All are being checked in serially.

Don't worry.

Thanks

Dear sir @sapwood my homework for week 5 has is also waiting for your review ....

Hopefully you will check it ASAP. . Thanks .

Post link:

https://goldvoice.club/steem/@qamarsudagar/my-homework-of-week-5-in-cryptoacademy-for-prof-sapwood-or-or-pob-voting-window-curation

Will visit you soon.

Thanks

Here is the translation of this post

Link

please chack my homework for week 5 please then i can start new one

https://goldvoice.club/steem/@azizulhassan/steem-crypto-academy-week-5-homework-post-for-sapwood-by-azizulhassan

Please use the tag #sapwood-week5 and it has to be the one among the first 5 tags.

If you have done that then I will surely visit your post. I am curating now in the chronological sequence.

Thank you.

my home for last week is not chacked sir

https://goldvoice.club/steem/@akashhassan/steem-crypto-academy-week-5-homework-post-for-sapwood-by-akashhassan

It is being checked now serially. Don't worry. I will find your content soon.

Thank you.

thanks sir you are the best and the coolest teacher ever

हाय सर, आपने अभी तक मेरी पोस्ट नहीं देखी है।

https://goldvoice.club/steem/@tarunramalingam/cryptoacadamy-week-5-homework-for-sapwood

Checking now.

Thanks

sir can i translate this post into Urdu for Pakistani and Indian and Afghani people

You can if you want to.

Thanks

Hello respected prof here is a link to my last week homework task please visit my post..

https://goldvoice.club/steem/@janemorane/steemit-crypto-academy-week-5-task-steem-blockchain-pob-voting-window-curation-or-homework-task-for-prof-sapwood

Hello sir can i also start doing these homework ? I am new on this platform and my achievement 1 is not verified till now?

Yes, you can.

Thankyou so much for responding 🙂

THANK YOU SO MUCH FOR THIS! I can't tell you how many people/accounts I have asked for the formulas used to calculate the upvote values. It was as if no one knew. I haven't really delved into this yet, but I know I will tomorrow. This is amazing!!!!

Thank you.

Hello professor @sapwood

This is my submission

https://steempeak.com/hive-108451/@mandate/crypto-academy-week-6-homework-post-for-sapwood

Your article is informative @sapwood sir. You are legendary in your teachings. I am enjoying every bit of it. I hope to become a graduate of crypto currency in the varsity of steemit blog and under your tutelage and other professors and able coachings of the founders, Admin and host of other steem heads.

Thank you.

https://goldvoice.club/steem/@maykit55/steemit-crypto-academy-steem-blockchain-convergent-linear-reward-week-6

#

https://goldvoice.club/steem/@maykit55/steemit-crypto-academy-steem-blockchain-pob-voting-window-curation-week-5-for-maykit55

Ho professor@sapwood, this is my entry for week-6 homework task. Kindly help review.

Thankshttps://goldvoice.club/steem/@xkool24/steemit-crypto-academy-steem-blockchain-convergent-linear-reward-week-6-or-or-lecture-by-professor-sapwood-or-or-homework-done

Thank you Professor @sapwood for the class

This is the link to my homework Task

https://steempeak.com/hive-108451/@dprogress/steemit-crypto-academy-task-6-by-professor-sapwood-or-convergent-linear-reward-homework

Dear professor @sapwood, your lecture was a great one as always. Thanks for opening our sights to knowing more about the Steem blockchain.

This is the link to my Task 6 solution;

https://goldvoice.club/steem/@fredquantum/steemit-crypto-academy-week-6-steem-blockchain-convergent-linear-reward-or-lecture-by-sapwood

Thank you, sir.

Hello professor, thank you very much for this great lecture, here I share with you my homework. Greetings!

https://goldvoice.club/steem/@selva1/steemit-crypto-academy-steem-blockchain-convergent-linear-reward-week-6

Hi @sapwood Here is my submission

https://goldvoice.club/steem/@chimzycash/steemit-crypto-academy-week-6-homework-post-for-sapwood

Esta es mi Tarea Profesor @sapwood

Tarea # 6

Saludos

Hello dear sir @sapwood , Here is my submission of home work task for week 6. Please check it out as soon as possible so that I could get reward of my efforts.

https://goldvoice.club/steem/@steemlover63/steemit-cryptoacademy-homework-week-6-for-sapwood-or-or-convergent-linear-reward

Thanks.

#

Did you use the correct tag- #sapwood-week5 #sapwood-week6

And the tags must be among the first five tags.

I would request you to edit your tags and include the relevant tags in the first five tags. I will definitely find you.

Thank you

Thank you teacher @sapwood, the correction has already been made, waiting for you to review my homework thank you.

https://goldvoice.club/steem/@maykit55/steemit-crypto-academy-steem-blockchain-convergent-linear-reward-week-6

Hi, @sapwood This is my homework post submission

https://goldvoice.club/steem/@designieplay/crypto-academy-week-6-steem-blockchain-by-sapwood

Please professor @sapwood can you take a screenshot to show me from where I can calculate the upvote value in steemworld.org

Stimulate SPSPsize of your choice, e.g. 10,000 SP or 50,000 SP or any amount you wish toOK.upvote valueof your input.here is my homework fr week 6 thanks for teaching

https://goldvoice.club/steem/@azizulhassan/steem-crypto-academy-week-6-homework-post-for-sapwood-by-azizulhassan

Gracias quería saber esto

Hello @sapwood my entry

https://goldvoice.club/steem/@simonnwigwe/steemit-crypto-academy-week-6-task-steem-blockchain-convergent-linear-reward-or-lecture-by-sapwood

Hola, estimado profesor, aquí le dejo mi tarea 6 para ser revisada, gracias por su clase.

Hello, dear teacher, here is my assignment 6 for review, thank you for your class.

https://goldvoice.club/steem/@danay/steemit-crypto-academy-steem-blockchain-convergent-linear-reward-week-6-danay

Saludos profesor @sapwood, aquí le dejo mi investigación de la TAREA 6

It's really a nice lecture by professor @sapwood. Here is my homework post for #week-6

https://goldvoice.club/steem/@prudent2/steemit-crypto-academy-steem-blockchain-convergent-linear-reward-week-6-or-or-lecture-by-professor-sapwood-or-or-homework-done

my homework

https://goldvoice.club/steem/@akashhassan/steem-crypto-academy-week-6-homework-post-for-sapwood-by-akashhassan

Hi! Professor, thanks for the class.

Here is the submission of my homework task below

https://steempeak.com/hive-108451/@grace-p/crypto-academy-week-6-homework-post-for-sapwood

Greetings Prof. @sapwood this is the submission of my post

https://goldvoice.club/steem/@davchi/steemit-crypto-academy-steem-blockchain-convergent-linear-reward-week-6-or-homework-done-by-davchi

Respected Professor, here is my submission for week 6. I have tried my best but errors are expected. Please let me know to rectify these errors. Please review it as soon as you possibly can. Thanks

https://goldvoice.club/steem/@mawattoo8/crypto-academy-week-6-homework-post-for-sapwood

https://goldvoice.club/steem/@akmalshakir/cryptoacademy-homework-task-6-for-sir-sapwood. Sir @sapwood check my post if you are free.

Hi @sapwood This is my homework task for week 6

https://goldvoice.club/steem/@amjadsharif/crypto-academy-week-6-homework-post-for-sapwood

Fantastic information and i'm a lot clearer about how the rewards works. Will get cracking on the subsequent projects and assignments.