I once tried to make sense of it in a fudgy way as something like – "the power law is the bell curve applied to networks". Ie just as there is a likeliest outcome (average height), there is a likeliest schelling point (wealthiest person), and the wealthiest person gets wealthier
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One way to think about it: When a bell curve distribution encounters a winner-take-all situation, the person/people at the tail end of the curve get power law returns. More here:https://jamesclear.com/the-1-percent-rule …
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Per Bak, Self-Organized Criticality was the old classic on this. They never did find a general result like central limit theorem iirc, only local constitutive laws and mechanisms like preferential attachment. Graphs, sand piles etc all have local explanations. No grand theory.
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Do you have any recommended reading material for this? I'm interested in the question - what makes certain domains amenable to power laws vs not.
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Runaway positive causal loops create power dists, until the system stiffens and locks up. When the system can't continue in the stuck form, due to environmental threats, the system discretely shifts to decouple from the power dists
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I like this idea of the power law being just a different form of equilibria.
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Feedback loops essentially. So advantage compounds. An early headstart provides advantage, which compounds into more advantage. Whether it’s a tree in the jungle, a city, a company.
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compounding &/ feedback loops
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To (maybe?) answer the second q, I'd predict power laws where advantage tends to be cumulative. So, well-cited academics' names appear in print more frequently, leading to more citations; people who have more money can be more risk-neutral, leading to higher expected returns etc.
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oh i am reading about this kind of thing in
@nntaleb’s Black Swan right now. He calls bell curve land Mediocristan and the other place Extremistan, though he characterizes the latter as more unpredictable and Mandelbrotian than power law-ish?Thanks. Twitter will use this to make your timeline better. UndoUndo
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