In Pay People (a heading under ) we told the story of , who was concerned about the fraction of the incoming payment that was intrusted in a claim which thought was likely to fall in value. ‘s solution was to “discount the claim.” Since thought that 100% of the value of the claim would go to $0 while still unspent, used a stance to request more money to cover the expected loss. Had instead thought that 50% of the claim would be unspent by the time it resolved to $0, ‘s stance could have been 50% instead of 100%. This would have made it cheaper for both and anyone that paid .
How Payment Size Changes
In general, if an employer agreed to pay to And if ‘s stance prices the claim “Cigarettes are benign.” at And if dollars of the payment is intrusted in “Cigarettes are benign.” Then the amount the employer pays to is:
Here’s an example of what the total payment due would look like as the stance increases while of the value of the payment is made of priced claims ( of the weight of the payment is in a claim the recipient doesn’t want).
Why does it work this way?
However, it turns out it matters more why it works this way than just that it works this way.
Why does it work like this? The idea behind priced disagreement is really simple. Let’s explore it with a story about cheese.
Each variety of cheese in this story is roughly equivalent to a token representing an intrustment in a particular claim, and the mice represent the possibility that a particular claim might resolve.
There’s a village of townspeople who really love cheese. They love it so much that they pay one another in cheese.
Gorgonzola, brie, cheddar, gouda, mozzarella, munster, swiss, and loads of other kinds you’ve never even heard of.
But they’re not the only ones that like cheese. The mice that live in the village like the cheese, too.
To protect the cheese from the mice, the village people keep the precious pieces in great cheesecloth tarps that they sling over their shoulders and carry everywhere they go.
But the mice are sneaky, and every once in a while they’ll hanker for a particular variety. In order to get away with their heist, they’ll coordinate so as to spring on the village people all at once, ferret the cheese out of the cheese cloth tarps, squirrel it away in their hidey holes, and then wolf it down. The mice would like you to know, however, that they are civilized animals, not monsters. They take from each cheese round proportional to its size so as to not overeat from any one person. They’re equitable, mice.
Needless to say, the village people aren’t fond of this behavior. Not only do they lose their cheese to these sneaky mice, but it messes up their economy.
See, before the mice, you could just give someone some munster and even if they didn’t like the munster (which, let’s face it, who does?), they could hang onto it until they found someone who did. But now, if someone pays you with munster, and munster happens to be on the mouse menu that night, then all the sudden much of your munster money has disappeared down the mouse’s maw.
So, the villagers meet in the village square to come up with a plan.
The village leader speaks, “At this point, we must concede that we won’t win this war with the mice by catching them or killing them. They’re too sneaky and too numerous. Instead, I’d like to propose we approach it from a different angle.
“How can we make sure that if the mice pick gouda tonight we’ll all loose a little bit, but none of us will lose everything?” asks the village leader. “We spend way too much time bartering for the exact right mix of cheese so we don’t get moused. Does anyone have an idea?”
“I have an idea!” says the village cryptocurrency enthusiast. “What if we all agree to use blue cheese as the one single fungusible cheese that we trade, and then if we want brie we can just figure out how much blue cheese has to be exchanged for some brie.” Blue cheese, as you might have guessed, is the village cryptocurrency enthusiast’s favorite cheese.
“Boo!” boos the cheddar head, “We should use cheddar, more durable.”
“Nein!” shouts the Swiss villager, “We should use Swiss. More holes.”
“No!” nos an inflatable monkey with a compressor hose in its mouth to keep from deflating, “We should cut special shapes into every piece of cheese so that it will be impossible for us to compare their worth.”
The village leader gently catches their attention.
“Thank you for the idea village crytpocurrency enthusiast. Unfortunately, I don’t think it can work, what would happen if the fungusible cheese that we choose is one day chosen by the mice?”
The village cryptocurrency enthusiast looks deflated, but not nearly as deflated as the inflatable monkey with a compressor hose in its mouth.
“I have an idea,” says a little girl. And the village leader bends down to listen to her.
The next day the village gathers to practice the little girl’s idea. The village leader explains.
“Ok, Alice, let’s say you want to pay Bob 2 kilos of cheese. The little girl says that the first thing you need to do is to weigh all of the cheese in your cheesecloth.
“How much does it weigh all together?”
“10 kilos,” says Alice.
“Great. Now, since you’re going to pay Bob 2 kilos of cheese, we’ll give Bob 2 / 10 of each piece of cheese that you have. This way, Bob gets the total 2 kilos of cheese, and an equal amount of each cheese in your cheesecloth. Bob gets more cheese of a certain variety if you have more cheese of a that variety. Bob doesn’t have to negotiate over each variety of cheese, instead, Bob can just look at the whole spread and immediately see what he’s getting.”
Alice cuts out an equal piece of each cheese to give to Bob.
“Ok Bob,” says Alice, “here’s your 2 kilos of cheese. The payment is composed of 2 / 10th of each cheese varieties in my cheesecloth.”
“But hold on,” says Bob, “you know I really don’t want the munster – let’s be honest, who does? – and I have a hunch that tonight they’re mousing the brie again. The munster and brie make up a whole kilo of cheese I don’t want.”
“Well how would you like to handle that?”
“Why doesn’t Alice just remove the brie and the munster from her payment, and instead add more of the cheddar? The good stuff.”
“Cause Bob,” says the village leader, exasperated, “then we’d be back to negotiating over each and every cheese variety. It would take forever. Plus, it would mean there would be certain cheeses that no one would ever accept like, let’s face it, munster. It would be better if Alice just evaluated how much it would cost her to pay you, and then she can decide whether it’s worth it.
“The little girl thought of this and has an alternative idea. How about for every kilo of brie and munster we pay you, we’ll pay you an extra kilo from the cheesecloth because you don’t like brie and munster.”
Alice looks at her cheesecloth where the brie and munster totals 5 kilos. “So, since I’m paying 2 / 10 of each cheese to Bob, and since I have 5 kilos of brie and munster, I would normally give Bob 1 kilo of brie and munster.”
“Sounds right so far.” says the village leader, who notices that the little girl who came up with this idea seems to be scratching furiously at the rind of a plump havarti.
Alice continues, “And since I’m giving Bob that 1 kilo of brie and munster, which he doesn’t want, I have to give Bob one extra kilo of cheese.” Alice cuts one fifth of one fifth of each cheese.
“Bob doesn’t want the brie and munster, but we want Bob to have it so it’s easy to make these payments. Here you go Bob, here’s 1 more kilo of cheese.
“In total, I’ve now given you 2 kilos of cheese.”
“Wait!” Bob says, “this isn’t fair! Sure, you gave me an extra kilo of cheese so that when my kilo of brie and munster inevitably gets moused tonight I’ll have an extra kilo of cheddar to keep me feeling sweaty and sick, but now one half of that new cheese is more brie and munster! That means that half of the extra you paid me is what I don’t want!”
“Right,” says the village leader, “Now Alice, let’s give him an additional extra half kilo of cheese from the cheesecloth. This way Bob you get a total of 3.5 kilos of cheese.”
Alice slowly cuts each of the additional slices of cheese and passes them to Bob. “Here you go, now we’re even.”
“But wait!” says Bob, “Now one half of the extra half kilo you gave me is brie and munster, so you should give me another one half of one half of a kilo of cheese.” It suddenly dawns on the village leader that this could go on for a while. In fact, as she thinks about it more, there’s zeno chance they’ll finish this payment before the end of the day.
Many hours later, Bob is still furiously demanding that Alice pays him half of a half of a half of a half of a half of, well, you get the idea. The village leader’s patience is thinner than the shavings from Alice’s cheese.
“Alright Bob, are you happy? This is getting ridiculous. We abandoned the lemon zester at round twelve and now the sun is setting.”
“Ok fine. We can stop now. Good enough, thanks Alice. That was fun. Wow, that took longer than I expected. Now, I’m ready for Charlie to pay me.”
At this moment the little girl saves Bob from cheese related violence. The village leader has picked up a hunk of cheese and is winding up to swing at Bob’s head.
However, the scribbles in the plump havarti cause pause in the fists that grip the fast falling rind.
“Of course,” says the village leader, inspecting the cheese now as a wheel of wisdom rather than the weapon it once was. “The little girl has figured out how to do this in one single payment!”
The little girl had inscribed these symbols on the havarti:
With this new approach, when Charlie pays Bob it takes only a single payment instead of infinite rounds. Thanks to this, the mechanism works and the village lives happily ever after.
The most important takeaway from this story is not the above equation, but rather the rationale for why Bob wasn’t allowed to just pick the cheeses he wanted from Alice’s cheesecloth. At the time, the village leader gave this explanation:
Cause Bob, then we’d be back to negotiating over each and every cheese variety. It would take forever. Plus, it would mean there would be certain cheeses that no one would ever accept like, let’s face it, munster. It would be better if Alice just evaluated how much it would cost to pay you, and then she can decide whether it’s worth it.
Instead, we can choose the proportional payment approach which makes the cost of disagreement transparent and it localizes the future pain of disagreement to that payer before they’ve paid.
Let’s imagine that we let Bob have his way and he just got to decide which of Alice’s cheeses he wanted to accept.
Under that regime, cheeses like munster, which are disliked, and cheeses like brie, which are mistrusted, become completely unusable. No one will accept them because no one else will accept them. The effect will happen somewhat silently. Alice would tell Bob, “Sure, I can pay you in just cheddar.” but Alice has no way of knowing if someone else in the future will accept the remaining brie and munster in her cheesecloth. This means that Alice could one day realize she had accidentally traded away all of the valuable cheeses in her cheesecloth and she can no longer transact with anyone except for those few that still accept munster and brie. But because fewer people accept munster and brie, she’ll also herself discount munster and brie, and then other people will too, in a vicious feedback loop that ends in the cheeses being locked up valueless in cheesecloths.
Under that terrible mechanism, the value of the less popular cheese varieties crumble until there is only a single trusted variety. This is how we end up with singular fungible (or as the cryptocurrency cheese villager calls it, fungusible) currencies in our current economy. However, under the village leader’s recommended payment method, even people with very different cheese preferences can transact because they can know they can always spend a cheese variety, it may be less valuable, but rarely valueless.