[greysphere]

Here's a simple model: people have a desirable quality that exists in some people and doesn't in others. This quality is randomly distributed among all people. To express the quality, a person must have access to some amount (K) of resources. How do we maximize the expression of this quality? We maximize the number of people with K or more resources. Assuming some power-lawish distribution of resources what coefficient of that curve accomplishes this? The answer is the flattest one, assuming the total amount of resources exceeds K*population.

This model is communicated at large in various forms, "meritocracy", "you can do anything if you put your mind to it", "inalienable rights of life, liberty and the pursuit of happiness", "every life is sacred" and so on. It's such a common model, it seems unsurprising that many people balk at a need for explanation. It's like asking 'explain from first principles why 2+2=4'.

[bbwwnn]

If the amount of resources is below Kpopulation - e.g. K/2population, wouldn’t that model suggest allocation K to half the population and 0 to the other half? If it is significantly above - e.g. 2Kpopulation, what’s the issue with giving everyone K and e.g. one person all the remaining resources?

[greysphere]

I agree the model quality expression model suggests both those resource distribution models would be maximal. My supposition though is resource distribution is going to be power-law-ish, which it doesn't have to be restricted like that, but seems a natural expectation.

And yes when the available resources are below the saturation point, more analysis will be necessary to determine what's optimal. A more advanced model would account for a variety of qualities, each with different importance and different Ks, suggest distributions for those and relate them to total available resources. My intuition, based on 'lots of distributions end up being gaussian' is that equality is maximal except when significantly resource constrained (ie some state like war or famine), or k for some particularly important quality is extremely high (which interestingly is another common narrative: Noah's Ark, the Manhattan Project, Armageddon, The Martian.)

[Al-Khwarizmi]

That there is not one K, but many, and we don't even know their exact values.

[bbwwnn]

Could you or someone elaborate on that? It’s not obvious to me how uncertainty around K implies that equality is a good thing… it feels like there is some (perhaps obviously correct) assumption here on the distribution of K that’s missing here. Now if we say that utility provided to society by a person is concave with respect to their resources, then equality becomes obvious, but that seems different than this toy model (and also not obviously correct).