ERGODICITY AND THE TRAGEDY OF THE COMMONS
An example of tragedy of the commons. A city has access to a small forest.
If you are a citizen, self-interest would dictate that you cut a tree to get some wood to heat your house. But if everyone does, the wood disappears.
1/N
An example of tragedy of the commons. A city has access to a small forest.
If you are a citizen, self-interest would dictate that you cut a tree to get some wood to heat your house. But if everyone does, the wood disappears.
1/N
2/ The tweet below recently made me notice that this kind of problems can be formulated in terms of #ergodicity.
Let's see how and why it matters.
Let's see how and why it matters.
https://twitter.com/rorysutherland/status/1367555119479480323?s=20
3/ One of the definitions of ergodicity is "when the outcome of a person performing an action n times coincides to the outcome of n people performing the action once."
Here is how it applies to the tragedy of the commons:
Here is how it applies to the tragedy of the commons:
4/ The outcome of a person cutting a tree a year for many years: he has sustainable heating & the wood stays.
The outcome of many people cutting a tree: they have heating for a bit & the wood disappears.
They're different → tragedies of the commons are non-ergodic.
The outcome of many people cutting a tree: they have heating for a bit & the wood disappears.
They're different → tragedies of the commons are non-ergodic.
5/ Here is when it becomes interesting. I often talk about ergodicity in terms of phantom consequences.
For example, baking cakes is non-ergodic. Why?
For example, baking cakes is non-ergodic. Why?
6/ The outcome of ten beginners baking one cake is ten bad cakes.
But the outcome of a beginner baking a cake ten times is two bad cakes, three meh cakes, and five good ones (as he learns).
The outcomes differ → non-ergodic.
But what caused the difference?
But the outcome of a beginner baking a cake ten times is two bad cakes, three meh cakes, and five good ones (as he learns).
The outcomes differ → non-ergodic.
But what caused the difference?
7/ The difference is caused by learning. Learning is a phantom consequence that is inconsequential in the short-term but consequential in the long-one.
These phantom consequences are usually what causes non-ergodicity.
Another example 👇
These phantom consequences are usually what causes non-ergodicity.
Another example 👇
https://twitter.com/DellAnnaLuca/status/1339621378765537282?s=20
8/ Here is the big question: what is the phantom consequence in the tragedy of the commons?
My answer would be: fatigue, in its mechanical meaning of accumulated damage.
Let me explain.
My answer would be: fatigue, in its mechanical meaning of accumulated damage.
Let me explain.
9/ If you go to the gym and lift some weights, your muscles get stronger.
This is because lifting causes some muscle fibers to break and the body reacts by overcompensating, creating more fibers.
That's what Taleb calls an antifragile reaction.
This is because lifting causes some muscle fibers to break and the body reacts by overcompensating, creating more fibers.
That's what Taleb calls an antifragile reaction.
10/ However, if you go to the gym and lift the same weights ten times in five days, what happens is that your muscles might get weaker and even tear.
What happens is that the antifragile reaction needs some time to appear. If damage accumulates too fast, the antifragile breaks.
What happens is that the antifragile reaction needs some time to appear. If damage accumulates too fast, the antifragile breaks.
11/ The antifragile needs some form of growth, re-growth, or healing.
If damage accumulates faster than the rate of (re)groth, we have fragilization rather than antifragilization.
In the tragedy of the commons, that's what happens if trees are cut faster than they regrow.
If damage accumulates faster than the rate of (re)groth, we have fragilization rather than antifragilization.
In the tragedy of the commons, that's what happens if trees are cut faster than they regrow.
12/ More on antifragility and its temporal aspect in this thread:
https://twitter.com/DellAnnaLuca/status/1180860829094334465?s=20
12/ To sum it up:
When damage rate > healing rate, we have fatigue
Fatigue is a form of phantom consequence. Its effect is inconsequential over the short term but consequential over the long one
Fatigue is what determines tragedies of the commons
Fatigue brings non-ergodicity
When damage rate > healing rate, we have fatigue
Fatigue is a form of phantom consequence. Its effect is inconsequential over the short term but consequential over the long one
Fatigue is what determines tragedies of the commons
Fatigue brings non-ergodicity
13/ Reminder: this Saturday I’ll host a free talk on ergodicity.
Register here to see it live and ask questions gum.co/ergodicitytalk or to my newsletter to get a recording: Luca-Dellanna.com/newsletter
Register here to see it live and ask questions gum.co/ergodicitytalk or to my newsletter to get a recording: Luca-Dellanna.com/newsletter
• • •
Missing some Tweet in this thread? You can try to
force a refresh
