Price's Law Sanity Check
Price's Law is a hypothesis that in an organization, or across an industry, roughly half the productive output is being generated by a number of people equal to the square root of those participating in the activity. For a classic example: in a business of 100 people, half of the output can be traced to 10 participants.
For a physical analogy - of all the momentums of all the particles in a balloon, the only ones that contribute measurably to the balloon's shape and strength are the ones whose momentums are perpendicular to the balloon's surface, and only the momentums of the particles located at the balloon's surface have any value. Thus the square-cube relationship.
The following analogy might not be accurate, but for the sake of the question please assume that it is generally correct : just as there are many unique locations along a balloon's surface, there are many distinct roles in an organization or in an industry. They may be "young adult author, fantasy 18-20". These people, and only these people, receive useful feedback from reality about their performance, related to their role "I am #3, or #10 medium weight men's boxer". Having one lump role for a society "I am a #56,428 human being" is too generalized to be actionable. Having smaller roles encourages investing in what works, and does not necessarily eliminate social mobility (you can try to move up a weight or division).
My purpose in asking this question is, for the sake of a sci-fi story, I'm interested in comparing the output of a highly centralized society (which is going to be suffering greatly under Price's Law) from a highly decentralized one. Say, families attempting feed themselves, and where everyone has a role : "artist", "performer", "cook", "labor".
My thought is that the decentralized society, if I look along any axis it's investing in, will not take many people to be outperforming the centralized society with "programmer pools" of thousands. I would think you can sum labor, instead of square root, by drawing boundaries whose output takes care of the needs of the group (ex: "farming families (3-7 people) with a cow and acres"; "a roboticist in the family servicing the equipment"); as specifically opposed to a few hundred robiticists in an industry (needs met by salaries).
Does this understanding of Price's Law, and this structure sound, generally, right?
For the sake of a fictional story, you should be thoroughly aware that the author is playing as a god. The laws are what you want them to be, and what you say happens is what happens.
I am not aware of any experiments to determine the validity of Price's hypothesis. If you want it to be true in your story, make it true. Many stories explore the consequences of "what if this notion were true?"
Whether your story will be entertaining or not lies in a different axis.
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