Hi! This is a follow-up of this post! If you liked this, I strongly encourage you to resteem this for visibility (to make a change) or upvote (to show appreciation)!

I was working on retyping the original post out but in a more organised fashion, but 1,000 words in I decided to stop as it's kinda pointless, so instead I'm going to create some theoretical case studies for my proposed algorithms and make amendments as necessary!

Note: all algorithms are like stage 1 prototypes, I appreciate, in fact encourage anyone to better these! I'm working with my limited 18 year old knowledge so these algorithms don't utilise the true complexity and intricacies of mathematics, so please do if you have the skills to improve these!!

A new rewards pool to build the foundation of a new curation system (full explanation here

• Creation and curation rewards to be split 50/50
• Creation and curation both rewards SBD and SP, instead of just author rewards being half/half
• Each upvote/curation operate on a shares system (explained below)
• Curation rewards reputation too (scale to be decided)

Shares system examples (pretty much what we have now)

• Someone with 1000 SP upvotes 50% while his vote power is at 50% = 250 shares
• Someone with 2000 SP upvotes 1% while on 100% power = 20 shares
• Someone with 500 SP upvotes 100% while on 100% power = 500 shares
• Each person receives a portion of the daily rewards proportional to the amount of shares they have, all accumalated rewards are distributed after 7 days of posting
• Shares for curation rewards will be explained later in this post

Testing of my reputation algorithm in isolation (high rep upvote low rep = more curation rewards)

M = 0.0001R(R+10) + 1, where M is the multiplier and R is the difference in rep.

Note: anything under reputation 25 is considered to be reversed, e.g rep 20 = rep 30, rep 0 = rep 50, rep -17 = rep 67 (@berniesanders). This encourages users to be careful what they do on Steemit as being flagged while being on low rep could snowball their account downhill more as others are less likely to upvote them.

Rep 50 upvotes rep 25 = 8.75% more rewards
Rep 75 upvotes rep 25 = 30% more rewards
Rep 75 upvotes rep 50 = 8.75% more rewards
Rep 50 upvotes erp 75 = 0% more rewards

This encourages voting for minnows but the rewards aren't so great it discourages minnows from upvoting others! The main multiplier is the early voters algorithm explained later!

This algorithm will be revised tomorrow. Instead of the difference in rep squared, I'll use the difference of each reputation cubed, with a different constant. This is needed as a rep 50 upvoting a rep 25 is extremely different from a rep 75 upvotng a rep 50 due to the non-linear increase in reputation level. Further tests will be done!

Testing of my (revised) early voters algorithm in isolation + in-depth explanation

Something I remembered half way through, I forgot to add a flagging system! This will be included in my next post!
(Changes: simply added a 0 in Part 3 of the algorithm to make it less punishing to upvote whales)

The algorithm aims to:

• Incentivise voting for quality content
• Incentivises voting early to bring more attention to quality content (put it on hot/trending)
• Reduce people abusing curation rewards by voting for whales with tons of followers who always get a ton of upvotes
• Not punish voting for whales so hard that people don't vote for whales anymore
• Each post's payout is equivalent to the value people perceive it to be worth

Part 1: Basically, the more upvotes on a post the more curation rewards everyone gets
Part 2: Basically, the earlier you upvoted, the more curation rewards you get. This encourages voting early to bump posts into the trending or hot section. Also discourages people from voting on content with heaps of upvotes already, as if you're towards the end of the upvote chain, you'll receive very little curation rewards. This promotes people upvoting posts only when they think the posts deserves more value, thus author payouts are approximately equal to the public's perceived worth of each article!
Part 3: Reduce rewards for whales with high rep and high visibility already
Part 4: Reduce rewards for whales with high upvotes already, hopefully this won't hurt minnows who has one massively upvoted post, perhaps change to average upvotes but that punishes people for creating consistently high quality content. This part will need revising.

Case study of Part 1 and 2 (positive multipliers)

• 1st upvote on post with 1000 upvotes = 2775.62% increase
• 500th upvote on post with 1000 upvotes = 2456.43% increase
• 999th upvote on post with 1000 upvotes = 323.78% increase
• 1st upvote on post with 100 upvotes = 979.45% increase
• 50th upvote on post with 100 upvotes = 814.34% increase
• 100th upvote on post with 100 upvotes = 72.24% increase
• 4th upvote on post with 36 upvotes = 397.94% increase

As you can see, these reward increases are logarithmic, i.e opposite of exponential. This means the greater the amount of upvotes, the less the gradient of the curve! Below is a pic of a logarithmic curve (graph and units are arbitrary).

Case study of Part 3 and 4 (negative multipliers)

• Penalty for rep 75 ( *0.1916 multiplier) with 3000 max upvoted post ( *0.6452 multiplier): 87.63% penalty
• Penalty for rep 50 ( *0.4444 multiplier) with 1000 max upvoted post ( *0.7596 multiplier): 66.24% penalty
• Penalty for rep 25 ( *0.8649 multiplier) with 0 max upvoted post ( *0.9901 multiplier): 14.37% penalty
• Therefore, upvoting a minnow will yield approximately 592% more rewards than upvoting a whale

Some potential issues I found

• Gives whales SIGNIFICANTLY more power in terms of curation and the power to bump a minnow into trending and get massive curation rewards, but then again that's the whole point of this so maybe this isn't an issue
• Might create a system where bots upvote whales. Voting first on a post that gets 1000 upvotes from a whale with 75rep and 3000 max upvoted post still yields 255% increase in rewards!

How shares system comes in with curation

Same system as how author rewards work!
If your vote is worth let's say $0.50, after a 50% rewards multiplier, you won't receive $0.75, you'll receive a share of the total curation rewards! So your $0.50 was a 10% vote at 50% vote power at 5000SP, you get 250 curation shares and those are multiplied by 50% = 375 curation shares. You'll receive a certain amount of SBD and SP proportional to your shares after 7 days of the post being posted. You receive your reward at the same time as author payout and will share in that day's curation rewards pool!

DISCUSSION IS WELCOME, IN FACT PLEASE DISCUSS!!

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