[Steem] The Reward Pool and the Parable of the Token

@paulag wrote a response to someone a couple of days ago about the impact of unused steem power on the rewards pool which I thought fit in interestingly with the stuff that I was doing last week on analyzing the relative power of SP at the top of the most powerful accounts on the blockchain. In it she admits to being wrong in her response to the original commenter which inspired her work. It was very humbling and honorable.

Unfortunately, she was right the first time and her interrogator was utterly in the wrong. Not because of having worked out wrong numbers or the like, though I do have some slight quibbles with the numbers involved, but because understanding the underlying mechanism of how the rewards pool is divided and works at all is not only a rare thing but actively obscured in a lot of ways.

@sneakyninja has claimed that "this explanation is the single most important thing I have read on Steemit in a while," which I can only reply to by suggesting that if I'm the best thing you're reading on the platform, the platform has a lot bigger problems that whether or not people understand the basic mechanisms. I am a long way from the best content on Steemit.

But I do have a certain set of skills. I set of skills that make me a nightmare for people who seem to have some sort of authoritarian need to tell other people what they can do with their own property. Also I don't take myself too seriously.

So in the interests of living up to an implicit dare, I'll repost the comment in its entirety that I left for Paula. If someone else finds an extended parable that simplifies understanding and reasoning about how rewards work on the blockchain, so much the better.

If someone can do a better job of explaining it – I would think you immensely, because I'm certain I've missed more than a few of the nuances and had to gloss over many others in the course of trying to put together something comprehensible on short notice.

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In fact, I'm pretty sure that your analysis of how the reward will is allocated is wrong.

Remember, votes in and of themselves don't have value. I know that comes as a surprise considering how prominently they're displayed, but that value is a derived figure and can change as the rest of the rewards pool is shifted around by votes.

The system is really dodgy at explaining how this actually works, but I think I can illustrate it with a parable.

Let's imagine that I have a rewards pool and it is $100. I then create 100 voting tokens and sell them to people for a dollar each. Each of those people can handle their token once to whomever they want to vote for. Or they can sell their token to someone else for the same purpose. Or they can choose to do nothing and hold onto their token.

At the end of the night, we would like to give out the rewards pool. It has $100 in it. In theory, we are about to get 100 tokens back.

Except that's not what happens. Some of those tokens just get sat on. Some of them got lost. Some people are hoarding them. For whatever reason, we only get 50 back from the guys in the room.

That doesn't mean that the rewards pool is going down to $50. It just means that it gets cut into 50 shares and handed out. Each token becomes worth $2, effectively. For this round.

Tomorrow, we do the same thing. I refresh my reward pool $200, and I give out 100 tokens. The day goes on, people give their tokens out – but some people have tokens left over from the previous day. They have accumulated stake.

Tonight, we give out money from the reward pool again – and instead of getting 100 tokens back we get 125. That makes each token we got back worth $0.80. Someone could get exactly the same number of tokens that they got the night before and get a vastly different payout, because the number of votes has changed.

The value of a vote is not fixed. It varies entirely based on the number of votes which are in the votes cast to be reified into a value from the pool.

Now let's consider the case in which I don't put any limits on my currency and I offer to sell as many tokens for US$20 each as anyone will give me.

They have now staked significantly into my token blockchain.

I, of course, have cleverly retained 1 million tokens for my own pleasure, to sell, give away, or whatnot. I can do with them as I please, because I own them. Everyone else can do with them as they please, because they own them.

The voting pool, however, remains at $100 – both for simplicity for the illustration and because it's a set figure. It doesn't matter how much actual activity goes on in trading tokens, that's what we've decided the rewards pool will be. Does it make sense for other people to drop hundreds of thousands of dollars to buy my tokens so they can vote on the allocation of $100? Probably not. But you know someone will do it.

(This is why the value of steem/SBD is variable, but I'm speaking to the audience.)

The next night, we go to giveaway the whopping $100 reward pool – and we get 10,000 tokens back. Some people gave their tokens to other people and they are handing them in. Some people just gave their tokens from their own pockets to us (self-voting). Some people used tokens that other people had given them for performing a service during the day or making a product. Some people just use the tokens that were bought during that day during my ICO.

I, of course, still have my shit ton of tokens that I've been sitting on from the beginning, and not spending them. Though I've decided to give some tokens out during the day to people that I think will give them to other people and do things that I like.

The moment of allocation comes!

Each token is now worth $0.01. A fat one penny. That's a considerable drop in value per vote, especially since I just sold a whole pile of votes. Still, whoever has a token gets one penny, for however many they want to hand in.

It just so happens that out of the pool that was originally extant, about 200 tokens, all I can get from them is that original 200 tokens. That is the most influence they can have. The 10,000 tokens that I sold, some of which may have gone to the same people, represent roughly 50 times the voting power, in aggregate, as the folks who have been involved in the last two days.

But then there is the mass of tokens that I gave out of my own pocket. I'm still sitting on a huge trove, but I'm not using it to vote by and large. I've parceled out another 1000 tokens and gave them to people in the last cycle whom I thought would do good things with them.

Some of those people were assholes. They did nothing but vote for themselves. Some of those people were very active and aggressive about giving their tokens to people whom they like and, theoretically, who are doing things I like. Some of those people were doing things themselves that I like, and spent those tokens voting for themselves.

But that's another 1000 tokens in circulation, which makes the sum total of tokens 200+10,000+1000 or 11,200, and that makes the actual value of a singular token $0.00892857142.

However, just because I have dipped into my trove and thrown out five times the number of tokens into the population doesn't mean that I've screwed over those who had the fewest. I may have given my tokens to the people who had the fewest. The people I gave my tokens to may have given their tokens, in turn, to people who had the fewest.

Hell, the people who bought into my token economy may have given their tokens to the ones who had the fewest. We just don't know. That may be why they wanted to give us money in the first place.

Now for the conceptual leap…

Forget that we are talking about $100 in the pool. Instead we are talking about 100%. It doesn't actually matter how much money is in the pool for the purposes of determining how much impact unmoving SP which suddenly turned into moving SP would have. It's utterly arbitrary.

That pool will be static no matter what.

In a real sense, the more SP in motion in the system, the smaller the influence of any individual portion of SP will have on how the rewards pool is allocated. That's absolutely true. The more people playing in the pool, the less water there is to splash in any given direction.

However, from that truth does not follow that the more SP in motion, the harder the situation becomes for those who have less of it. Everything hinges on where that SP goes and what it does. And not only what it does, but to what end it does so.

If you delegate 10,000 SP to me and I use it to self vote my work, both of us may be extremely happy. You got that SP in the first place however you got it and you decided to become a patron. You provided me the ability to make money off of your SP, giving me the opportunity to create my work. I do so. We are both happy.

Now, there are a bunch of whiny people who look at that exchange and say, "well, you could have given it to me, or them, or any 10,000 people, and it would be better." That's where @freebornangle comes in. They don't like what you've chosen to do with your resources. They don't like what I've chosen to do with your resources. And they feel that they have a greater moral claim to decide what you do with your resources than either of us, the holder (the stakeholder, most specifically) or the recipient.

Nothing keeps them from getting as much SP via whatever means and using it to whatever ends they desire – they just don't want to have to do the work for the first part of that.

If I took that 10,000 SP delegation and instead gave out ten thousand 1 SP delegations to people who then used that one SP delegation to self vote – I would have affected the reward pool in exactly the same way as if I gave it all to myself. Each vote would be exactly as valuable in relation to the percentage of the reward pool that it entitled me to redirect.

It's just that @freebornangle figures they could get a bite of the pie if I'm giving it away with no regards for my own interests, only theirs.

The rewards pool cannot be drained. That is impossible. It is a set value which will be distributed on a regular basis. That's why we have 9.5% inflation on the steem blockchain (or whatever it is). Those tokens injected into the system on a regular basis at a steady pace are literally the inflationary rate. They are inflation. All voting rewards represent inflation.

All the tokens entitle you to is a share of the pie. One slice.

So you were wrong about being wrong.

I'm not sure if that's better or worse.

The only important question is where is that SP being motivated to. More activity on the blockchain deliberately and directly translates into smaller slices, as the number of tokens/SP increases and the size of the reward pool remains static.

This isn't hard to understand, it's just really poorly explained by the white paper, the blue paper, and every single time someone talks about the "value of votes." It's dynamic. It changes. If you want to see what it looks like in a much shorter term, more exposed environment – look at some of the voting bots. They are a mini laboratory for observing how token purchase and voting pools actually work. At a certain point, if all you care about is the value of your specific investment/vote, you have to work aggressively against other people entering the pool. It gets split more finely. If that split is less than your investment to get in, you lose money.

The steem blockchain is a very strange creature, in that you don't have to invest anything extrinsic to become vested in the architecture. You can lay claim to a portion of the inflationary rate and stick it in your pocket. The portion of that inflationary rate is limited only by, interestingly enough, the amount of that token that you already own. You can redirect as much as you like in proportion to the amount that you own.

Yes, that means that more delegation from sitting SP into active accounts might lead to a different distribution of rewards from the inflationary rate. It is not, however, immediately a given that small stakeholders would suffer the most. Small stakeholders already have claimed to a pretty small-ish slice of the pie. Percentagewise, it's hard to slice it finer.

To get back to your analysis, if @steem were to vote for itself 10 times a day, with full available power (which is actually a descending sequence of 100%, 98%, 96%, etc.), it could potentially redistribute up to 15% of the rewards pool in a different way. By your numbers, which I'm not sure I'm wholly on board with because they are more interested in specific vote values than vote influence percentages.

And this only applies to a single cycle. What you're doing is sort of looking at the Iterated Prisoner's Dilemma at the first frame and thinking that defines the entirety of the environment.

In truth, there would be subsequent votes, now influenced by the amount of SP that people had acquired from the previous round. This is going to change the dynamic of distribution across the pool a lot more radically than the initial token dump. It certainly may be considerably better for small stakeholders, depending on what the people who now have greater stake want to do and are interested in.

So, from a mechanical point of view, none of this really holds up as a valid analysis.