In an index wallet, how does someone know how to set their valuation?

There are three things that matter when choosing how much to endorse:
1. how much new business will I get
2. how much inflation will I incur
3. how much will I be able to spend it for

This weekend I found a nice visual way to think about it

The only problem is externality pricing.

Building https://negationgame.com

It's easiest for me to think about this using a much simplified setup.

Let's imagine you exist in a community with only 2 tokens, and only 2 potential customers.

Here's an example of one way that could look, each arrow is a customer's valuation of those tokens.

E.g. here the left customer values A @ 0.9 and B @ 0.2

The natural question to ask is: what's the best valuation for you to set based on this?

(p.s. endorsement = their_valuation / your_valuation)

my favorite way to think about this is as little mountains under each customer, the further away your valuation, the less valuable their currency feels to them to buy from you

This immediately tells you where to put your valuation, you should put it on the saddle right between the two mountains:

(note: this is true if these mountains represent "total willingness to spend", which makes sense because a customer that feels rich with you but doesn't want your products is quite useless to you)

However, this is clearly not a complete answer, since you don't just care about how much business you can get, but also about how much that business is worth when you go to buy something with the new money.

This means we also need an arrow to represent our supplier, the person who sells us stuff.

What you should then notice is that this is just the same problem as before, but now you are the customer, and the supplier is in the role you were in.

We could also put the supplier's supplier on here, and so on, but let's imagine for simplicity this is the best your supplier can do, how should your valuation adjust?

So far, this is pretty simple and intuitive. You can kinda think about the tokens in your index wallet as recording your preferences, values and beliefs.

This has two dynamics:
1. goods are cheaper when you buy from vendors with shared beliefs
2. as a vendor you have a persistent reason to value wider belief sets

But, this analysis isn't quite enough, because there are two more dynamics to consider:
1. competition
2. inflation

We can consider them independently, and it should give you the ability to think about them both intuitively and how they might interact.

Let's start with competition.

Let's imagine that there's a new competitor that arrives on the scene.

We'll imagine that they buy from the same supplier as you, and they don't have any strong preferences themselves, they're just trying to make a buck.

They position themselves halfway between the left customer and the supplier, what should you do?

Assuming that your products aren't differentiated, the leftmost customer is going to exclusively buy from your competitor, it's cheaper.

This means you might as well get a bit closer to your supplier and customer so as maximize the amount they buy from you, and minimize the price you pay to your supplier.

So that's competition.

In the context of competition, vendors differentiate themselves so as to specialize in serving certain communities.

This creates a new axis of competition: values alignment.

If you highly value climate issues, you can increase its valuation and companies that also value it highly feel cheaper.

But of course, as your valuation vector sloshes about, other people are going to feel that as you buying less from them (because it's more expensive for you).

In fact, let's imagine just that. Let's say your competitor goes out of business and you put your valuation back.

Your supplier notices you're now buying less

Depending on how much of each token you own, increasing your valuation can cause you to 

For example, let's imagine a highly simplified economy where you own 1/3 of all token A, and 2 / 3 of all token B in circulation.

Before increasing your valuation, when token A was worth .1 and token B was worth .5, you owned 75% of all the wealth.

To make this simple to think about, let's imagine that when you increase your valuation of token A, this time your supplier does the same (but just with token A).

Since all your suppliers increased their valuations, the value of token A has increased, at least for you, since it really means that you can buy more stuff with it.

However, at the same time, your proportion of the total wealth has gone down because many other people also own a bunch of token A. You feel inflation.

However, somehow you've also become wealthier. Before you had 1.1 units of wealth, and now you have 1.3. Your slice of pie is narrower, but it's also much taller.

Whether this is a good thing for you depends on whether the total wealth has increased. This is where we get voluntary taxation

this is starting to make sense haha. gotta go to yoga bie

While I'm not yet certain the exact equation to solve this, it's a pretty intuitive movement.

You should move your valuation so that you maximize the gains from new customers that can be used to buy the most goods from suppliers. Just move a bit down and a bit left.