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Index Wallets

Voluntary taxation, wealth equalization, and funding for public goods.

The stark inequality in wealth distribution and the underfunding of essential public goods — ranging from environmental conservation and education to public health and international peace and security — present pressing challenges. In this article, we’ll explore an economic mechanism called index wallets that fund public goods through selfish taxation. As a side effect of their unique funding method, index wallets also induce wealth regularizing dynamics.

Index wallets arise from two essential properties:

The ability to mint new, counterfeit-proof tokens

A payment mechanism called index payments (from which index wallets derive their name)

These properties can be implemented in software, and thereby permit adoption by anyone.

This article is intended to be a terse introduction to the mechanism set and arguments for the properties it would induce. If you’d like a more accessible introduction you can find:

A more

step-by-step explanation⁠

of index wallets (WIP)

video intuitively motivating the problem⁠

that index wallets solve

progress update video⁠

reviewing an index wallets simulation

A broadly accessible series of articles on index wallets (not yet published)

Index Payments

All of the key dynamics of index wallets arise from a simple constraint placed on the payment mechanism. Traditionally, when one has a wallet with different denominations of currencies in it, the payer must coordinate with the recipient to determine which currencies the recipient is willing to accept.

In index wallets, this coordination is solved by introducing a constraint. The constraint ensures that a person paying with an index wallet will always pay with all of the currencies in their wallet. The precise amount of each currency they send depends on how much of the total value that currency makes up in their wallet.

To understand this intuitively, let’s look at a visualization.

Let’s say this is someone’s wallet. Each bar represents a currency of some value:

⁠

Left of the line is a $1 payment, where the portion of each currency sent is proportional to its value.

⁠

Here’s a concrete example where you can play with the payment size.

If someone has a wallet with these entries, all denominated in USD:

⁠

[USD36][Ethereum100][Bitcoin64]

⁠

and they’re going to pay you

000

140

⁠

dollars

You’ll receive this as the composition of your payment:

⁠

18.00% USD 50.00% Ethereum 32.00% Bitcoin

⁠

Which is:

⁠

[USD$25.20][Ethereum$70.00][Bitcoin$44.80]

⁠

In total, you receive

$140.00

⁠

, just like you expect.

The key idea of an index payment is that the amount of each entry you receive is always proportional to the value of the entries in the payer’s wallet. You can test this by noticing that no matter how you change the quantity they pay you, the proportion of

USD, Ethereum, and Bitcoin

⁠

in the payment remains unchanged.

In symbols, we can define the total amount of a particular currency to be sent as:

⁠

Where:

q is the quantity in base currency requested as payment

⁠

p is the proportion of the payment’s value in that currency

⁠

t is the total amount of that currency to send

⁠

A common misconception is that index wallets allow you to either pay with an index payment, or pay with the currencies individually. This is not correct. Index wallets are constrained so that once a currency enters the wallet, it can only ever exit as part of an index payment. It’s permanently mixed.

This may raise questions of adoption. Why would anyone ever choose to constrain their currencies in this way? This will become clear by the end of this article.

Endorsements

If someone were to offer to pay you with an index payment you might reasonably be concerned about accepting the entailed currencies at face value. Let’s say you’re once again receiving payment from this wallet:

[USD36][Ethereum100][Bitcoin64]

⁠

What happens if you want to avoid receiving Bitcoin because you believe it will fall in price, or because you disapprove of Bitcoin’s use of energy?

To account for your distaste for accepting Bitcoin you might want to be compensated by charging an additional fee to act as conciliation for accepting the currency you don’t want. To allow you to do this, we’ll encode your preference in a value called your endorsement which you’ll set for each currency.

An endorsement works like this; if you want to charge

$140.00

⁠

to someone with this wallet:

⁠

[USD36][Ethereum100][Bitcoin64]

⁠

but you have set your endorsement of Bitcoin to

10%

⁠

Bitcoin endorsement (e)

000

0.1

⁠

they’ll have to pay you

$56.63

⁠

extra in conciliation to compensate you for the Bitcoin in their payment.

Their total payment comes out to:

⁠

[USD$35.39][Ethereum$98.31][Bitcoin$62.92]

⁠

or, in total, they’ll pay you what looks to them like

$196.63

⁠

, a conciliation premium of

$56.63

⁠

The composition of the payment they sent is unchanged, it still looks like this:

⁠

18.00% USD 50.00% Ethereum 32.00% Bitcoin

⁠

Since you only consider Bitcoin to be worth

10%

⁠

of they value they ascribe to it, you feel like you got this payment:

⁠

[USD$35.39][Ethereum$98.31][Bitcoin$6.29]

⁠

Which sums up to

$140.00

⁠

, exactly what you intended to charge.

Notice that as you increase your endorsement, the conciliation premium decreases.

⁠

Screen Recording 2023-04-13 at 2.27.05 PM.gif

⁠

This makes perfect sense. If you endorse it at 100% then there’s no premium to pay, you’re treating it as worth the same value they ascribe to it. If you endorse it at 0% then they’ll have to pay you a bunch more because you consider

32%

⁠

of the payment to be worth nothing.

In principle, an endorsement need not be bounded between 0 and 1. If someone really disliked an entry in your wallet they could set a negative endorsement. And if they really liked an entry in your wallet they might be willing to count it as more valuable than you do.

There is a natural motivation for the equation behind conciliation; imagine you consider Bitcoin to be valueless (endorsement = 0), they cannot just send you a payment that doesn’t contain Bitcoin because they’re paying with an index wallet, which only allows them to send index payments. Since the index payment they send to you contains 32% Bitcoin, to make up for that useless Bitcoin in their payment, they’ll have to send you another index payment worth 32% of the total payment. But since they’re now compensating you with another index payment, another 32% of that 32% will still be made of Bitcoin, which to you is valueless, so they’ll have to send another index payment to account for it, of which another 32% is valueless Bitcoin. And so on.

Here we visualize that process. On the left is the perspective of the payer, who sends repeated payments to compensate for the 32% of each payment that’s made up of a currency the recipient considers to be valueless (visualized with blue segments). On the right we see what the payment looks like to the recipient once all the valueless blue parts are removed; it comes out to a $1 payment.

⁠

This infinite sum has a closed form expression:

⁠

And thus the total conciliation in the case of a single disputed currency:

⁠

Where:

q is the quantity in base currency you requested as payment

⁠

p is the proportion of the incoming payment in the currency

⁠

e is the amount that you endorse the currency

⁠

Briefly, it’s worth addressing several common questions that arise with endorsements.

First, why wouldn’t you just decrease your endorsement in order to get someone to pay you more? As endorsement goes down, price goes up, right? If you could reduce your endorsement you certainly would. But remember that the person paying you only sees and cares about the price. So, reducing your endorsement is the same as raising your price for all the people that carry that currency. If you can raise your prices without losing customers, great! But if you have competitors with similar products then you risk customers buying from them instead.

And this raises the second point: doesn’t this mean that people who disagree about what currency is valuable will not want to transact with one another? This is likely to happen, and this is how we get self-assembling economic communities. Groups with strong disagreement will see large conciliation premiums, and so will avoid transacting one another. Ones with propinquity (they have shared beliefs and values) will have low conciliation and therefore will transact more and with less friction.

Does this mean that people who adopt this kind of wallet will be further entrenched in their ideological silos? No, quite the opposite. All players always have an incentive to increase their endorsement so they can have more competitive prices. The most penalized behavior is extremism because it’s associated with unusually low endorsements, whereas more tolerant stances have more moderate endorsements, and therefore are more competitive.

Finally, what if the person you pay also puts their own

10%

⁠

endorsement on Bitcoin, just like you? Is it really fair for you to pay a premium on a currency you got from someone else? The important thing to notice is that the premium has already been covered by the person who paid you. Consider for example the worst case scenario where the most recent payment you receive makes up the entirety of the value of your wallet (your p_i is equal to their p_i). When receiving this payment, if your endorsement was

10%

⁠

32%

⁠

of their payment, then they must have paid

40.45%

⁠

in conciliation. If the person you’re paying has that same endorsement of

10%

⁠

the conciliation you can pay is also

40.45%

⁠

, which was already covered by the first payer. A minimum viable implementation of an index wallet probably tracks this for you so you can easily see which conciliation fees you’re about to pay yourself vs which were already covered by those that paid you.

← more generally

⁠

Since we’re considering the case where their payment is the only thing in your wallet (which is the worst case scenario), your e, p, and Currencies will be the same as theirs.

⁠

Since you can’t spend more than the amount that they paid you

⁠

We can conclude that your conciliation on next payment is less than or equal to their conciliation when paying you

In sum, endorsements use competitive dynamics to enable self-assembling economic communities while granting a systematic advantage to pluralistic behavior.

Impact Certificates

As our final mechanism, we’ll allow a community member to mint an impact certificate to fund themselves for their contribution to a public good.

Let’s imagine for example that a community has printed a bunch of impact tokens in order to pay someone to develop an open source project. That software developer has just received some of that newly minted money into their index wallet. Let’s call this engineer Marie.

Marie would now like to go buy something from Charlie using this newly printed money and the other currencies already in her wallet. It’s interesting to consider Charlie’s incentives.

Notice that Charlie probably has a number of concerns. If he accepts this money it’s as though he’s legitimizing the newly printed tokens, he might wonder:

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 endorsement dictator of the world. Whatever endorsement he sets, the rest of the world will also set. So, if he sets his endorsement to 31.4159% for these newly minted tokens, then the whole world will do the same. This makes our analysis much easier for now, and it’s a worst case scenario as it is the situation in which Charlie has the most power and therefore the least incentive to accept Marie’s newly printed money.

Under this endorsement dictator assumption, Charlie should accept the payment as long as the profit he stands to earn from the payment is more than the inflation he’ll incur by endorsing the new currency. Here’s the equation that captures this idea:

⁠

Where:

e is the amount of endorsement by Charlie

m is the percent of the post mint monetary supply made up of new currency (e.g. ~30% if there were 100 tokens in circulation and you minted 43)

w is the amount of wealth that Charlie has measured in dollars or some base currency

r is the profit that Charlie will make on the sale

The left-hand side of the inequality is the inflation Charlie experiences. The right-hand side is the profit he expects.

← Expand to see a derivation for this equation

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 wealth to buy the same amount that his previous wealth could:

⁠

Where w is his wealth and m is the proportion of new monetary supply that the newly minted money will make up.

If you’re economically inclined and this looks unfamiliar, know that m is just:

⁠

Where S_1 is the starting supply of money, and S_2 is the ending supply.

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 of that currency. Which leaves us with this monstrosity:

⁠

Which we can simplify to:

⁠

What’s fascinating about this equation is that Charlie’s best move depends on the amount of wealth he has. It should be obvious why this shows up: the inflation effect on Charlie (the left hand side of the equation) is going to be greater as long as he has greater savings. A richer Charlie will endorse Marie’s newly minted money less so as to protect himself from losses due to inflation.

But as we know, the lower Charlie’s endorsement of Marie’s currency, the more expensive for Marie. This means that if there were someone less affluent than Charlie who was selling the same product, that person would be able to sell to Marie at a lower price, even with the same expectation of profit.

Charlie’s endorsement

⁠

With this endorsement Charlie expects to experience inflation of

$0

⁠

Let’s imagine that Charlie runs an airline and Marie is purchasing tickets to a far away country.

And Marie would have to pay Charlie

$2,353

⁠

$353

⁠

in conciliation

I’ve assumed some parameters for you.

We’ll assume Charlie has

$1,000,000

⁠

in wealth, and he’s charging

$2,000

⁠

15%

⁠

of Marie’s wallet is made up of the newly minted tokens. The newly minted tokens make up

2%

⁠

of the post mint monetary supply.

This should help to clarify why someone like Charlie would adopt index wallets in the first place. If Marie has been paid with tokens from an impact certificate, she’d like to spend them. If she can find someone who will accept them she’ll prefer to purchase there. In this way you can see that Charlie refusing to adopt an index wallet is the same as if he adopted an index wallet but then set his endorsements to 0 for everything but his preferred currency. We’ve already shown that in that context competitors with higher endorsements of a customer’s tokens will be able to offer more economical prices.

This effect becomes particularly interesting when we consider what happens when we vary the wealth of a vendor.

Inverse Wealth Effects

To explore this dynamic more fully, let’s add a new airline run by someone who is not as rich as Charlie, we’ll call her Charity. We can find the largest endorsement that Charity and Charlie should set using this equation:

⁠

(assuming w > 0; 0 < m < 1; r > 0, which are all reasonable assumptions)

Now let’s look at the prices that Marie will subjectively pay for her tickets depending on whether she’s paying Charlie or Charity.

The difference between their situations is:

Charlie’s wealth is

$1,000,000

⁠

Whereas Charity’s wealth is

$100,000

⁠

Everything else about their situations are the same:

The price they’ve set for the sale is

$2,000

⁠

The profit they both expect from the sale is

$250

⁠

15%

⁠

of Marie’s wallet is made up of the newly minted tokens in both transactions

The new tokens make up

2%

⁠

of the post mint monetary supply

In order to pay Charlie

$2,000

⁠

, Marie will have to send

$2,348

⁠

. This is because the largest endorsement that Charlie can set without losing money to inflation is

1.23%

⁠

Meanwhile, to pay Charity

$2,000

⁠

, Marie will have to send

$2,303

⁠

. This is because the largest endorsement that Charity can set without losing money to inflation is

12.25%

⁠

You see in this example that since Charity owns fewer resources she experiences less inflation and therefore can accept the payment with a higher endorsement.

In fact, if Charlie were to try to match Charity’s endorsement of

12.25%

⁠

he would end up losing about

$2,500

⁠

due to inflation on the sale,

which is much more than the $250 profit he expects to earn.

⁠

← I’ve made some parameter assumptions for you here, which you can play with if you want but you don’t need to in order to understand the above.

profit r

0000

250

⁠

percent of wallet p

0000

0.15

⁠

quantity of payment q

0000

2000

⁠

percent of post mint money supply made up of new tokens m

0000

0.02

⁠

wealth Charlie w_charlie

0000000

1000000

⁠

wealth Charity w_charity

000000

100000

⁠

Permit endorsements greater than 100%?

⁠

Charity's Competitiveness as Wealth Inequality Grows

Charity's Competitiveness as Wealth Inequality Grows

⁠

Here we see that under this worst case scenario of endorsement dictatorship, there’s a natural tendency for wealth to accrue to the less wealthy, quite the opposite of what we expect from our current economic systems.

Voluntary Taxation

Charity and Charlie know that Marie can choose to buy from either one of them. This means that if Charlie could he would increase his endorsement of the tokens Marie is holding so that the price for his tickets is more competitive with those of Charity. Of course, all the normal rules of economics apply here, so if Charlie could find ways to lower his cost or improve demand for his tickets, those be viable strategies for becoming more competitive. However, if Charlie’s customers are paying with index wallets, there is one additional way that Charlie can try to become competitive with Charity.

Let’s say that Charlie is a user of a free software produced by Marie, whereas Charity is not. If Charlie benefits daily from the software that Marie helped develop, he might begin to justify to himself that the money printed to develop the project was not a pure cost to him. After all, he’s deriving at least some value from the software. If he can determine how much he benefits from Marie’s work, then he can increase his endorsement, which makes his ticket prices more competitive with Charity.

We can represent this as Charlie counting the benefit of Marie’s software as part of his earnings.

⁠

The value Charlie believes he benefited from Marie's public good is represented by the quantity b. As Charlie finds new ways to benefit from Marie’s free software, he can increase his endorsement of Marie’s tokens, this in turn lowers prices for Marie, making her more willing to purchase from him.

Notice that this gives Marie the incentive to make her software free to use — at least to those who have index wallets. After all, more people will likely use the software if it’s free, and then as they benefit from the software they’ll increase their endorsement of the tokens that Marie is seeking to pay them with. In other words, not only do index wallets provide a funding mechanism for public goods, but they also incent the creation of public goods over private goods, at least in the cases where more benefit will occur if the product or service is offered for free.

In addition to providing Charlie a reason to retroactively fund this free software proportional to his benefit from it, this dynamic also gives Charlie an incentive to make further use of Marie’s software. If we imagine that Marie’s free software is one of two competing softwares Charlie could use in an upcoming project, then independent of the other merits of the products if Marie frequently purchases from Charlie then Charlie might find it worthwhile to invest in building on top of Marie’s software, since it allows him to further endorse Marie’s tokens, and therefore offer lower prices to Marie, enticing her to buy from him over the competitor.

Since Charlie stands to lose the quantity on the left hand side of the equation to inflation, he’ll need to consider the benefit from Marie’s software to be worth at least

$2,250

⁠

in order for it to merit completing the transaction. A common misconception is that perhaps Charlie could avoid this inflation by moving his money out of his wallet. But that won’t work, the inflation affects him no matter where his money is. In fact, he could have not yet received the money and yet still consider it part of his wealth. For example, if Charlie knows he’ll receive a payment tomorrow for $1m, even though he hasn’t received that money yet he would be wise to incorporate it into his inflation calculation, adjusting only to account for the benefit he determines he’s enjoyed from Marie’s free software, and the profit he expects from Marie’s payment.

And this is the key idea: since we can think about inflation as a type of taxation, Charlie will only ever endorse a certain type and amount of taxation if it allows him to attract new customers, or if he benefits directly from the public goods created by those taxes. This kind of highly consensual taxation can be pithily summarized as “no taxation without compensation.”

Final Considerations

We’ve now reviewed the key ideas of index wallets and the consequences of interleaving these three mechanisms:

Index payments

Endorsements

Impact certificates

Even under our worst-case assumptions — that of a person with so much economic power they can dictate the price of a currency — we’ve shown this mechanism still provides promising properties:

Funding for public goods

Wealth equalizing dynamics

Voluntary taxation

The most important next step in exploring this mechanism will be to depose the economic dictator. The worst-case assumption that there is a single person who can control everyone else’s endorsements is unrealistic (and logically inconsistent once it grows to more than one person). This means the next step in evaluating the viability of index wallets must address this shortcoming.

In addition, there are many open questions which seem valuable to explore beyond those covered in this brief article. Here are but a few:

How might this be implemented so as to preserve maximum privacy?

What relationship might index wallets have with negative externalities?

What are pragmatic ways for members of a community to set their endorsements?

What sorts of institutions might be required to allow the smooth functioning of a community using index wallets?

What properties does the average case scenario have in comparison with the worst-case scenario?

How might new business models be able to be built on the back of impact certificates and how does that change intellectual property?

In what ways might people seek to circumvent the mechanism set so as to free-ride, for example via nepotism, and how can that be addressed?

How do the incentives of producers change, especially as they become wealthier?

What are the implications for an artificial intelligence operating in this sort of economic environment?

How do saving and debt behaviors change?

How do work, entrepreneurship, and education incentives change?

If you’d like to get in touch, you can find me on Twitter at

@connormcmk⁠

and on Farcaster

@nor⁠

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