Hello Steemit CryptoAcademy community. Hopefully all of you will be good in your health.

This is my submission of the homework of week 6 for dear sir @sapwood . Today's our topic name is Convergent Linear Reward.

History of the BlockChain :

First of all we will disscuss about the criteria of the Steemit Blockchain to pay reward to its users. So in the beginning of this great platform the distribution of the reward among the users is takes place in the influence of a formula which is known as Superlinear/Quadratic Functionwhich was f(x)=x^2.At this time the people on Steemit was really encouraged to invest STEEM and buy the SP as they now that the reward gained is directky proportional to the amount of SP you may have. The platform organizers noticed that this function is encouraging the old users but the new users are discouraged and there is no justice in this type of division.

So due to this fact they changed the reward curve from the quadratic/superlinear function to the linear function which was f(x)= x . This division of the rewards among the users is really looking too fair as compared to the previous one but there was also a type of selfishness in this function. The people on Steemit started Self-Upvoting so in this way the social behaviour of the Steemians become selfish as they know that they can get the same as output just equals to that of the input(SP). So, this kind of act was also failed to provide a just circumference to Steemit.

After that the organizers developed the third and the last one reward curve function which is known as the Convergent Linear Reward which was f(x)=x^2/(x+1). With the issuance of this function the self upvoting which is a bad act was discouraged and one can get more reward by upvoting the others. This is the way in which the users can get more reward by upvoting others besides that of self upvoting themselves.

That is some history about the reward curve of Steemit. Now I will discuss some questions asked by our professor in the regard of this 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?

Self-Upvoting:

The term selfupvoting means to upvote your own post by your own by utilizing your own SP as an input. More the SP you may have , more will be the reward you may get. There are many social and economical disadvantages and dis benefits of self-upvoting. Self upvoting is just like same as selfishness and ignorance .Self voters are the people which wants to increase their worth leaving behind to think about the worth and importance of the others.They are just like the men who thinks only about their benefits and ignore the others.

Self-upvoting also have many disadvantages in the econonical point of view. The self upvoted contents always remain at the bottom of the graph between the output and input. You will be cleared about that in this picture.

source from professor's post
When the organization developed the covergent linear reward f(x)=x^2/(x+1) system till then to now the self upvoters are in disadvantage. This function discourages the people who self-upvote their own posts to use their SP as a source of the fame, importance and the trend of their post. In the past, when there was the superlinear and the linear function of the reward curve, people get benefits by self-upvotings . But now there is no such chance of abuse of your own inputs in the seek of better outputs.

Yes, we can gain better curation reward by visting the other posts, upvoting them , encouraging them and utilize our SP there to earn better curation reward instead of self upvoting.

(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.

Isolated Judgment:

Isolated judgment term is used when we discuss about the reward of a user if he upvotes a post as single voter. In this type of judgment there is no any interfere of the community reward systems and oen will upvote the post by its own and he will get reward according to the input (SP) he possess. If he has more SP then he will get more reward and vice virsa.

Community Judgment:

Community Judgment is term used when a user curate or upvote a post along with some of the other curators. Community judgment also plays a vital role in increasing the curation reward for the curators as well as the reward for the content creator.

Yes,community judgment economic incentive for the curator.

Let us discuss this with an example.

Let, the upvote value of three curators is as follow:

Curator 1 : Upvote value with 15,000 SP (100% upvote) = $0.3131
Curator 2: Upvote value with 20,000 SP (100% upvote) = $0.4249
Curator 3: Upvote value with 30,000 SP (100% upvote) = $0.6595

Isolated Judgment= 0.3131+0.4249+0.6595 = 1.3975

Now if all these three curators curates a same post then their total input(15000+20000+30000)becomes 55000 SP. The post will get $1.42 .

Hence it is cleared that these curators can earn better reward as curation reward through an agreement of community judgement.

(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?

This is the screenshot my account statics You can see that I have 45 effective SP and there is no any value of my full weight upvote. But no worries, I can earn better reward through the community judgment. This time my upvote value is $0.00 .

1st Upvote (to a post having reward less than $50):

Before my upvote:

After my upvote:

The pending reward of the post was $44.38 before my upvote and this reward becomes $44.39 after my upvote.
In these screenshots you can see that my upvote value to this post is $0.01. ut when I saw the upvote value of my account (45 SP) is $0.00 . This thing clears that one having low SP can also earn better reward through the community judgment.

2nd Upvote(to a post having reward more than $50)

Before my upvote:

After my upvote:

The pending reward of this post was $349.25 before my upvote and it becomes $349.28 after my upvote.
You can see in these screenshots that my upvote value for this post is $0.03 which is 0.03 times that of the orignal upvote value which is $0.00 with my input (45 SP). So, it is cleared that one can earn more through community judgment that that of the isolated judgment.

Curation reward for 1st upvote

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

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

PT=44.39$
P0=44.38$
P1=44.39$

By putting in formula :

Pme= (1/2) * (√$44.39) * ($44.39-√$44.38) (1) = 0.002$

So, the curation reward from this post is 0.002$

Curation reward for 2nd post:

Pme= (1/2) * (√349.28$) * (√349.28$-√349.25$) (1) = 0.007$.

So, I will got $0.007 from this post.

Conclusion:

It is cleared from this example that even my upvote value is very low but still I can get curation reward through the effect of community judgment. Moreover I can get much reward from a post with a higher curation reward as compared to that which has lower curation reward. The reason is that the reward curve becomes linear when the input provided to the post is much enough to bend the reward curve to the linear function.

So, that's all about this home work task.

Special thanks to sir @sapwood for his amazing lecture and for teaching us in a kind and lovely manner.

Respected Mentions:

@steemcurator01
@steemcurator02
@steemcurator03
@steemitblog

Regards : Your loving Steemian , @steemlover63

Steem On !