Who pays for the blogging and curation rewards? (Part 2)

In part 1, I derived the math for the share of the cost of rewards that is paid (as debasement) by STEEM POWER (SP) holders.

I’m going to attempt to make that math more comprehensible to the average person. And I will explain the share of the cost paid by liquid STEEM holders. ^{(which you might realize, includes all the STEEM held on exchange markets such as Poloniex)}

Whitepaper Clarified

Some readers wanted clarification of how the linked section the white paper related to the first two paragraphs of Part 1. The white paper says that total (curation+content) rewards minted (i.e. created out-of-nothing) yearly are 3.875% + 3.875% = 7.75% of the money supply. That is 77.5% of the 10% of the money supply that is minted yearly for curation+content rewards, mining rewards, and (the currently disabled) SD liquidity rewards. Note the white paper needs to be updated because the split between curation and content rewards is no longer 50/50, but that change is irrelevant to what is discussed in this blog post. Edit: @arhag has supplied some updated numbers of 5.5% to SP, 0.75% to STEEM, and 3.25% to SD.

By the end of an entire year, 100%¹ of the money supply has been minted (i.e. a doubling), with 90% being distributed to existing SP holders, 0.75% to STEEM, 5.5% to new SP holders ^{(not 5% which was an error in Part 1)}, and 3.25% to STEEM DOLLARS (SD). The latter two items include the 7.75% curation+content rewards which are according to @arhag no longer split 50/50 between SP and SD.

SP Debasement Clarified: simplified model

In Part 1, we first considered the math for the debasement of SP in a simplified approximation to get an intuitive feel for the concept, before moving on to the more precise and obtuse model.

The simplified model is to ignore the 5.5% of the money supply minted as SP for rewards, and just consider the 90% of the money supply minted yearly as SP, which is distributed proportionally to existing SP holders— somewhat² analogous to a forward stock split.

As an example of the simplified model, if we assume there are 90 units of SP for every 10 units non-SP in the money supply ^{(where non-SP means all STEEM and SD)}, then if we normalize the money supply to 100 and thus assume there are 90 SP, the yearly money supply increase of 100 adds 90 SP to the money supply. So at the end of an entire year, the supply of SP increases to 180 while the money supply increases to 200. Since 180 ÷ 200 = 90%, the ratio of SP:non-SP remained at 90:10. So this shows that in the simplified model, there is no debasement of SP when the ratio of SP:non-SP is90:10.

SP Debasement Clarified: precise model

To account for the 5.5% of the money supply minted as SP for rewards, we can’t model an entire year monolithically because every hour when the hour’s portion of the aforementioned yearly 90% are distributed to existing SP holders, also a hour’s portion of the aforementioned yearly 5.5% is created for rewards to new SP holders. Then on the next hour, those new SP holders are included in the list of existing SP holders who receive the next hour’s portion of the 90% distributed to existing SP holders. So conceptually I hope readers can visualize in their mind that every hour the existing SP holders are being debased by the new SP holders relative to the sharing of the aforementioned 90% that will be minted for SP holders in an entire year. That is a bit complex to explain and understand, so you might need to read this paragraph more than once.

To derive the math for this model, we write down an equation normalized to 100 money supply, with one term for each (of the 8760) hour of the year as follows. The equation represents the amount of SP received by those who were holding SP at the beginning of a year period and which held for the entire year. Note the hour’s portion the reward is subtracted from the hour’s portion of the forward split and accumulated for each hour of the year as follows.

where r is the ratio of SP:non-SP expressed as fraction, but I think I had an error in Part 1 and r can be always set to 1 because this ratio is accounted for else where in the overall computation.

Simplified to:

And employing the equation for the nth triangular number:

^{(note: the prior versions of these equations before I made edits suggested by @arhag are still on the blockchain, if readers want to research the facts of the discussion in the comments between @sigmajin and myself)}

So the example from the simplified model adds 90 - 2.75 SP to the money supply. So (90 + 90 - 2.75) ÷ 200 = 88.625%. So compared to the starting ratio of 90%, the preexisting SP holders are debased by 1.375% of 90%, i.e. 1.375 ÷ 90 = 1.5% loss of proportion of the money supply. Here is the corrected chart from Part 1:

SP:non-SP	Yearly Debasement Rate
100:0	6.4% loss
95:5	4.1% loss
90:10	1.5% loss
87:13	0.1% (~forward stock split²)
80:20	4.5% gain
70:30	12.3% gain
60:40	22.7% gain
50:50	37.3% gain
40:60	59.1% gain
30:70	95.4% gain
20:80	168% gain
10:90	386% gain
5:95	823% gain
1:99	4313% gain

^{In the comment section of Part 1, @sigmajin thought my math was in error because I didn’t mention the way the blockchain “invisibly” accounts for SP as VESTS. This is entirely irrelevant to my correct math, because when the vesting fund is increased by the 90% money supply, this 90% is distributed to the existing SP holders and thus any adjustment to the number of STEEM per VEST is a “wash” (i.e. forward stock split) for the existing SP holders. The new SP minted for the rewards paid out of a 5.5% portion (i.e. 55% ) of the other 10% of the money supply created, is also accounted for in my math as explained earlier in this section.}

STEEM Debasement

The debasement of existing STEEM is always 50% loss because 100% money supply is created yearly and none of it distributed to preexisting STEEM holders.

The ratio of SP:non-SP only impacts the number of STEEM units which are debased 50% loss and the change to the said ratio, but not the rate of STEEM debasement. And as shown in the prior section, impacts the rate of debasement of SP holders.

Alternative Designs

It is interesting to consider the effect of alternative designs for a Steem-like blockchain which would use a different ratio than 95.5 units of SP minted for every 3.25 units of SD and 0.75 units of STEEM (note afaics @arhag is missing 0.5 units), i.e. 90 units distributed to preexisting SP holders for every 10 other units minted.

As that ratio drops, the amount of debasement of STEEM declines for the same amount of rewards as a percentage of the money supply and the rate of increase of the money supply reduces. And the debasement of SP increases for any SP:non-SP ratio. For example in the simplified model if 10 units are distributed to preexisting SP holders for every 10 other units minted, STEEM yearly debasement reduces to only a 16.7% loss and SP yearly debasement increases to only 7.9% loss for the 95:5 ratio of SP:non-SP. And the money supply only increases 20% yearly.

Who Actually Pays

The debasement of SP holders is not a complete picture of who pays, because the game theory for rewards indicates that perhaps hypothetically deviant whales could in theory offset any debasement and increase their share of the money supply. Although I haven’t developed a precise model, it appears that the more SP stake a holder controls, then proportionally some non-linear less debasement. Meaning I posit that the system appears to hypothetically economically favor concentration of the wealth to those who already concentrate the wealth in the deviant scenario. But this theory is yet unconfirmed.

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¹ The level is currently significantly higher than 100% and is continuously dropping until it will eventually (afaik sometime next year) stabilize at this 100% yearly level.

² When the ratio of SP:non-SP is 87:13, then it is precisely (well 0.1% is close enough) analogous to a forward stock split because each SP holders’ share of the money supply doesn’t change.