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# The Rich Get... Poorer?

Wealth equalizing dynamics in mechanisms for funding public goods.
This article explores a mechanism that enables wealth equalizing dynamics while funding public goods. It achieves this by constraining the payment behavior of wallets that contain newly issued token classes. A simplified model of this mechanism in a two party interaction implies that less wealthy vendors may have a competitive advantage over wealthier vendors. This effect arises because the wealthier the vendor the more they’re affected by the inflation caused by accepting the newly issued token class. It seems to do this without blunting the incentive for productive output. In principle, this mechanism could be a promising additional approach to funding public goods.
Index Payments
Imagine this is someone’s wallet. Each bar represents a currency of some value:
On the left of the line is a $1 payment. It’s a fraction proportional to the value of each currency. Let’s imagine someone has a wallet with these tokens, all denominated in USD: [USD100][Ethereum400][Bitcoin300] If they’re going to pay you 000 100 You’ll receive this as the composition of your payment: 12.5% USD 50% Ethereum 37.5% Bitcoin Which is: [USD12.5][Ethereum50][Bitcoin37.5] In total, you receive$100.00
, just like you expect.

I’m tempted to talk about some properties of this payment mechanism I find promising but I’ll resist so we can get on to the main event. If you’re interested, ask me about why it seems that these can be used for 1) negative money that’s not debt 2) bribe resistant currencies 3) increased fungibility and liquidity of alt-tokens.
For now, we’ll continue straight on to considering the second mechanism:
Currency Endorsements
If someone was going to pay you with an index payment, you might reasonably be concerned about accepting the entailed currencies at face value. If you’re receiving payment from a wallet that looks like this: ​
[USD100][Ethereum400][Bitcoin300]
you might not want to accept all of the currencies. For example, you might eschew Bitcoin because you believe it will fall in price, or because you don’t like Bitcoin’s use of energy.
To account for your distaste for accepting Bitcoin we’ll permit you to receive a premium in addition to the standard payment which compensates you in the form of another index payment for the Bitcoin you didn’t want to receive. We’ll encode your preference for each currency in a value called your endorsement e. Depending on your endorsement and the total payment, the total premium the person will have to pay you is in addition to their payment is:
Here
is the original transfer quantity you agreed to (in base currency),
is how much you endorse currency
, and
is the proportion of the incoming payment that’s in the endorsed currency
.
In other words, if someone is going to pay you
$100.00 out of this wallet: [USD100][Ethereum400][Bitcoin300] But since you have set your endorsement of Bitcoin at only: Bitcoin endorsement (e) 0000 0.27 They’ll have to pay you$37.69
in premium to account for the Bitcoin in their payment.
Which is:
[USD$17.21][Ethereum$68.85][Bitcoin$51.64] Or, in total, to them it looks like:$137.69
You’re still receiving this as the composition of what you receive:
12.50% USD
50.00% Ethereum
37.50% Bitcoin
To you it still looks like:
$100.00 . Exactly what they agreed to pay you, but now treating the Bitcoin as worth only 27% of its value. Notice that as you increase your endorsement, the premium decreases. This makes perfect sense. If you endorse it 100% then there’s no premium to pay, you’re treating it as worth its face value. If you endorse it at 0% then they’ll have to pay you a bunch more. This equation has a natural motivation. Imagine you consider Bitcoin to be valueless ( ). If someone sends you an index payment which contains 50% Bitcoin ( ), then the person paying you will have to send you another index payment worth 50% of the total payment value to account for that useless Bitcoin. But since they paid with an index payment, another 50% of that 50% will still be made of Bitcoin, which to you is valueless, so they’ll have to send another smaller index payment to account for it. And so on. This infinite sum has a closed form expression: And thus we recover our equation for the total premium: Where: q is the quantity in base currency you requested as payment is the proportion of the incoming payment in currency i is the amount that you endorse currency i ← aside I moved a bit fast to get this to you. Normally I write the equation for premiums in terms of discounts (π) not endorsements (e), where π = 1 - e. To avoid talking about both endorsements and discounts which might be confusing I converted everything to endorsements, but in the process of converting I might have made some mistakes. So, here’s the original derivation, but in terms of discounts π which I’m much more confident in: /aside) The Goods As our final mechanism, we’ll allow a local community to mint some sort of new token to fund a public good. For now, we’ll completely ignore the conditions under which we permit this sort of behavior, and we’ll just allow people to do it as they wish. Let’s imagine for example that a community has printed a bunch of tokens in order to pay someone to fix potholes in the road. That worker has just received some of that newly minted money into their wallet, which is increasing the total monetary supply. We’ll call the person who was paid Marie. Marie would now like to go buy something using this newly printed money and the other currencies already in her wallet. Let’s call the person she wants to pay Charlie. It’s interesting to consider Charlie’s incentives. Notice that Charlie probably has a number of concerns. If he accepts this money: how much inflation does it cause for him? will he himself be able to spend the newly printed money? might his acceptance cause runaway acceptance by others thereby causing unforseen inflation? For our analysis, we’ll simplify all of these concerns by collapsing them down to a single dimension. We’re going to let Charlie be the economic dictator of the world. Whatever endorsement he sets, the rest of the world will also set. So, if he sets his endorsement to 53% for these new tokens, then the whole world will do the same. This makes our analysis much easier, but we should also be careful about how we generalize beyond these assumptions. Under this economic dictator assumption, Charlie should accept the payment as long as this condition is met: Where m is the percent of new monetary supply that token B will be (e.g. ~30% if there were 100 tokens in circ and you minted 43) e is the amount of endorsement by Charlie (in the range 0 and 1) s is the amount of savings that Charlie has (in dollars or some base currency) r is the profit that Charlie will make on the sale ← Expand to see where this equation comes from Charlie should say yes as long as his profit is greater than his loss due to inflation: ​ Where r is profit. But what is the loss due to inflation? Well, we know that in the case that he’s 100% endorsing it, he’ll need this much in savings to buy the same amount that his previous savings could: Where s is his savings and m is the percent of new monetary supply that the newly minted money will be. Which means he’ll need this much compensation: What about the case where he sets an endorsement that’s not 100%? For that, we’ll need to swap out our m for this much longer equation: Where e is the amount of endorsement. Which leaves us with this monstrosity: Which we can simplify to: What’s fascinating about what this equation implies is that Charlie’s best move seems to depend on the amount of savings he has. It should be obvious why this shows up: the inflation effect on Charlie is going to be greater as long as he has greater savings. A richer Charlie will have to set a lower endorsement of Marie’s newly minted money to compensate himself for his losses. But as we know, it’s not free for Charlie to set that lower endorsement. The lower his endorsement, the more expensive Marie’s payment will be. This means that if Charlie were poorer he would be willing to sell to Marie at a lower price, even with the same expectation of profit. To explore this dynamic, let’s add a new person, Charity, who is not as rich as Charlie. We can find the upper limit of endorsement that Charity and Charlie should set using this equation: (assuming s > 0; 0 < m < 1; r > 0, which are all reasonable assumptions) Now let’s look at the prices that Marie will subjectively pay depending on whether she’s paying Charlie or Charity. The difference between their situations is: Charlie’s savings are$100,000
Whereas Charity’s savings are
$19,000 Everything else about their situations are the same: The price they’ve set for the sale is$1,000
The profit they both expect from the sale is
$250 20% of Marie’s wallet is made up of the newly minted tokens Marie's Payment 0 (I’ve made some parameter assumptions for you here, which you can adjust if you want but you don’t need to in order to understand) profit r 0000 250 percent of wallet p 000 0.2 quantity of payment q 0000 1000 savings Charlie s 000000 100000 savings Charity s 000000 19000 Cap the endorsement at 100%? This graph is showing you that no matter how many new tokens are printed (m), it’s always cheaper for Marie to pay Charity than it is to pay Charlie. This is entirely due to the difference between their respective wealth. Remember, from the perspective of both Charity and Charlie, Marie is paying what looks to them both like$1,000
, the additional cost from Marie’s perspective is entirely due to the fact that both Charity and Charlie are charging Marie extra to account for their loss due to inflation. Those losses are simply larger for Charlie because he’s wealthier.
Charity and Charlie both know that Marie is choosing between buying from one of them. This means that if Charlie could, he would increase his endorsement of the tokens Marie is holding so that his price is more competitive. One way he might become more competitive is by increasing the amount that he benefits from the public good which Marie was paid to maintain. If he does this, he can count that personal benefit toward his profit on the transaction.
Where b now is the benefit from the public good that the vendor can attribute in this transaction. This seems to create a dynamic whereby vendors want to maximize their valuation and utilization of public goods because it allows them to be more competitive. It’s as though they have better access to customers in exchange for paying taxes. It also seems to incent more localism. If Charity lives on the same street that Marie helped maintain, then Charity can more easily increase her endorsement of Marie’s new money because it has directly benefited her. By contrast, if Charlie lives far away he’s not so willing to pay for the public goods that are local to Marie, and therefore Marie will have to pay higher prices to purchase from him.
What might be exciting about this is that it implies that there could be an incentive environment where poorer vendors have a price advantage over wealthier vendors, especially when funding local public goods. Furthermore, this effect is achieved purely mechanistically, without requiring any external intervention via a revenue service, progressive taxation, nor universal basic income. It seems to continue to be friendly to productive incentives: Charity still has marginal incentive to produce a better product than Charlie, but now she’s been given additional capability to start up and compete.
Conclusion
Under assumptions, this mechanism set seems to offer certain promising characteristics.
A method for funding of public goods through new token issuance
A competitive advantage for less wealthy vendors
A competitive advantage for local over global vendors
However, this analysis really is incomplete because of the simplifying assumptions we made. When choosing whether to accept a payment, Charlie was wondering:
how much inflation does it cause for him?
will he be able to spend the newly printed money himself?
might his acceptance cause runaway acceptance thereby causing him unforseen inflation?
We collapsed all of these assumptions by allowing Charlie (and later, Charity) to be economic dictators. In their respective universes, whatever level of endorsement they chose the rest of the world followed suit. However, this is a highly unrealistic assumption. If we forge into more realistic assumptions, what dynamics play out instead? Optimistically, it would seem that giving each player less control over the global money supply would only improve their willingness to accept a currency that was emitted to fund a public good, as long as they had reasonable confidence that others in their community also benefited from, and therefore endorsed, that public good. However, it would feel better to have a concrete model of that.
Finally, it would seem that the details of the governance that controls the emission of new tokens is critical to ensuring the plurality of the system while maintaining healthy macroeconomics for a community.
I’d love to collaborate in exploring this, and for help finding out where I’m wrong. To ease you into a critical mode you should know that I made at least one mistake, lmk if you catch it :)