Why Are Curation Rewards on Blurt Almost Always Half the Vote?

Having discussed the reward-curve in a previous post, time to look at the curation-curve.

The reason the Blurt curation rewards do not show the same behaviour as on Steem or Hive is for precisely the same mathematical reason as the reward-curve is behaving differently - that "content constant" is way too high for this economy.

Now, this can be fixed in two ways: we can fix that constant so that curation behaves as intended; or we can fix the whole formula so that we retain these 50% curation rewards. The discussion about this choice will be the subject of my next post. Here, I really just wish to look at what is going on at the moment. Also, the combined post grew so large that I decided to split it into two.

The Curation Curve

At Steem's HF21, the linear reward curve was replaced by the convergent-linear formula and the curation square-root curve was replaced with a convergent-square-root function. I do not wish to delve into the reasons for coupling these two formulas as it would take me on a long trip into the minds of their creators. But we do need to note what the effects of this curation-curve are on voters.

The new curation-curve retains many of the features of the previous curve. In essence, your curation-weight is a measure of how large your vote is compared with all existing votes on a post at the time of voting. Your curation-weight never changes during the life of that post. Your curation-rewards, however, will change and depend on the total votes on payout, thus both before and after your vote. So, what is this curation-weight?

The Blurt block explorer now shows more voting data for each post, with columns added for Rshares and Curation Weights - with thanks to @ericet. The curation-curve is that function, W(r), that converts rshares into curation-weights - very similar in concept to how the reward-curve turns rshares into claims.

The formula used is

where s=2e12, and then

W(voter) = W(after-voting) - W(before-voting)

So when you vote, your curation-weight is the difference between the W-values for the whole post calculated before and after your vote. It is thus a measure of how important your vote is, given the existing votes.

Hence, you may start to appreciate how average curation rewards, as a percentage, decrease as more and more people vote on the same post. Imagine the unusual situation in that everybody votes exactly 10 BLURT each on a post. You can see that the second voter has added an extra 100% to the post, doubling its value from 10 to 20 BLURT. But the 21st voter is adding 10 BLURT to a post already worth 200 BLURT, thereby adding only 5% to its total value. Hence, the curation-weight for that 21st voter will be much lower than that of the 2nd voter. (There are some complications with very high whale votes but will discuss that in the next post.) This is just a very simple example of how the curation-weight can increase for larger votes but also decrease for later voters.

So Why Are Curation-Rewards Proportional on Blurt?

Now, given that Blurt made some monetary changes upon launch, that content-constant (s=2e12) is way too high for our current economy compared to the rshares generated by even our largest voters. If you look at the Blurt blockexplorer, a quick calculation will show that each rshares value is about 2 million times the curation-weight. This gives us a clue!

Let me just write out the mathematics first,

What this shows is that as the value of s is very much larger than the rshares, r, that the whole formula ends up being approximately proportional to rshares and with a constant factor of... 2 million. That tiny rshares in the denominator is dwarfed by the content-constant and hence can be ignored as a first approximation as it has a negligible effect.

There are very small fluctuations, but on the whole, that square-root function is behaving like a proportional function.

That's why most everyone's curation-rewards are almost exactly half of their vote values. This is also where the constant of proportionality of 2 million comes from.

Mystery solved, we shall discuss the different ways of fixing this in the next post. Indeed, there is time to reflect on whether Blurters are enjoying this "accidental" change in curation rewards. It strikes me that it makes it more human, although I think there are some second-order issues to be ironed out before going fully proportional.

As always, any questions, please just ask.

PS. Some users have queried as to whether the 5-minute "reverse-auction" is working. I have found posts in which it is manifestly working and the curation-weights have been duly decreased by the time-formula.