Steemit Corner#7 : How does convergent linear reward affect post payout in Steemit?

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Background :

Human behavior is the product of individual or collective action. It is a major determinant of people's health, as this behavior leads to many expected and unexpected results, including many people participating in supporting and encouraging changes in their behavior and the behavior of others. Of course, many seek to change their behavior and may seek support others to do so, so it is important to identify effective methods and strategies that stimulate change and maintain positive behaviors adopted.

In this context, the rewards curve in the steemit ecosystem witnessed drastic changes in the way it is calculated in an effort to train users' behavior within this social network with an economic character added.

Since the launch of Steemit in 2016 as a decentralized social platform based on blockchain technology, the reward curve was then based on a quadratic equation according to the function f(x)= x², which helped bring more users to invest in steem to convert it to SP in order to increase the value of the reward They have, and this has had a negative impact on non-investment users and newcomers, a system similar to savage capitalism, meaning the more you have, the more you earn.

So in order to achieve fairness among all categories of users, this approach was changed in 2017 to a linear equation meaning f(x)=x, which seemed at first to be in line with the principle of decentralization and equal opportunities, but it clashed with social behavior that tends to be more selfish, as many publications appeared. It has bad and useless content, which relies mainly on self-voting or by bots, which enabled it to reach the top, which is what contributed to the difficulty of discovering good content.

So, in order to bypass this selfish behavior that led to the misdistribution of the reward group, since the hard fork 21 in August 2019, it has been relied on a convergent reward curve according to the equation f(x)=x²/(x+1). It is an equation that destroys the desire for self-voting and encourages voting for other publications of value and avoiding parallel publications, which led to better social convergence and content discovery.

For those who find these equations difficult to understand, I will try to make them as simple and understandable as possible in the rest of the article, so I invite you to continue reading to benefit.

What is the difference between quadratic, linear and convergent reward equation?

• X-values represents the value of Steem Power and the Voting Power
• Y-values represents Reward and Upvote Value.

From the accompanying table, we notice a difference in the value of the reward from curve to another, as its value doubles in the case of the quadratic equation f(x)=x2, which means, for example, if user A has an SP value three times that of user B, he will get a reward nine times more.

In the case of the linear equation f(x)=x, user A's share of the reward will be only three times greater than user B's.

But, the matter is different in the case of the convergent linear reward, although the value of the input increases the value of the output as well, we observe that the result Y is very little for the smaller input X, to rise with the increase in the value of the input and then decrease again for the more expensive inputs to tend to be the same value for the input and the output.

What does convergent linear reward add?

As we all know, the sum of the reward for a post which is collected by voting for it by the users creates a so-called reward pool filled by the rShares, which is later distributed according to exact rules which can be identified by visiting my old publication.

This brings us back to identifying the contribution of the convergent linear reward which makes it possible to increase the reward pool each time a new user reads and curates the publication and therefore increases its trend and visibility on the platform, and at the reward level, it converges to linearity.

We can check that, by plotting the curve of each equitation:

How the function f(x)=x²/(x+1) is applied in Steem Blockchain?

When upvoting on a post which has a value which represents the outputs (Y) , it generates rShares which mainly depends on the value of SP and VP which represents both the input (X), and based on these rShares, the reward pool is distributed.

We will take an ordered range of input values to determine the output, and we will see when it converges to linearity, what is the meaning of this curve on social behaviors and judgment (curation).

Here are the different SP values that produce different upvote values (we will calculate the upvote value using the Steemworld.org tool based on a Vote power which is equal to 100%)

By plotting this values, we obtain this chart :

Remark :

• We notice that the upvote values are reduced for lower entries (SP), on the other hand they are higher with important (SP) to begin to become linear from a few million SP.

Isolated curation Vs Community Curation

• Let's take the case of 5 curators who respectively have the SP values 10.000 SP, 25.000 SP, 50.000 SP and 100,000 SP. If they upvote a post individually, their reward will be less, but if they upvote quality content and curate as a community, they all earn a high curation reward.

To prove this, we will calculate the two output upvote values:

Curator 1 - Upvote value with 10,000 SP (with 100% PV) = $0.07
Curator 2 - Upvote value with 25,000 SP (with 100% PV) = $0.17
Curator 3 - Upvote value with 50,000 SP (with 100% PV) = $0.37
Curator 4 - Upvote value with 100,000 SP (with 100% PV) = $0.81

Curation isolated by 1, 2, 3, 4= (0.07+0.17+0.37+0.81)= $1.42

Now, if all these four curators upvote the same post, combining their inputs which becomes (10,000 + 25,000 + 50,000 + 100,000) = 185,000 SP, paying for the post with 185,000 SP as input will generate an output = $1.67

So 01.67$ > 1.42$

Therefore, the four curators will earn better curation rewards if they come to an agreement as a community in their curation judgment.

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I wish that this seventh post in this series helped many users to understand about how convergent linear reward affect post payout in Steemit blockchain in the hope that the series will continue in a future episodes.

Best Regards,
@kouba01

Cc- @steemcurator01