I'm surprised you write that Peterson has not given an indication as to what level of stratification is to be expected. Here is his 'The Principle of Unequal Distribution' from 12 Rules of Life - An Antidote to Chaos:
The Principle of Unequal Distribution
When a defeated lobster regains its courage and dares to fight again it is more likely to lose again than you would predict, statistically, from a tally of its previous fights. Its victorious opponent, on the other hand, is more likely to win. It’s winner-take-all in the lobster world, just as it is in human societies, where the top 1 percent have as much loot as the bottom 50 percent [11] — and where the richest eighty-five people have as much as the bottom three and a half billion.
That same brutal principle of unequal distribution applies outside the financial domain — indeed, anywhere that creative production is required. The majority of scientific papers are published by a very small group of scientists. A tiny proportion of musicians produces almost all the recorded commercial music. Just a handful of authors sell all the books. A million and a half separately titled books (!) sell each year in the US. However, only five hundred of these sell more than a hundred thousand copies. [12] Similarly, just four classical composers (Bach, Beethoven, Mozart, and Tchaikovsky) wrote almost all the music played by modern orchestras. Bach, for his part, composed so prolifically that it would take decades of work merely to hand-copy his scores, yet only a small fraction of this prodigious output is commonly performed. The same thing applies to the output of the other three members of this group of hyper dominant composers: only a small fraction of their work is still widely played. Thus, a small fraction of the music composed by a small fraction of all the classical composers who have ever composed makes up almost all the classical music that the world knows and loves.
This principle is sometimes known as Price’s law, after Derek J. de Solla Price, [13] the researcher who discovered its application in science in 1963. It can be modelled using an approximately L-shaped graph, with number of people on the vertical axis, and productivity or resources on the horizontal. The basic principle had been discovered much earlier. Vilfredo Pareto (1848–1923), an Italian polymath, noticed its applicability to wealth distribution in the early twentieth century, and it appears true for every society ever studied, regardless of governmental form. It also applies to the population of cities (a very small number have almost all the people), the mass of heavenly bodies (a very small number hoard all the matter), and the frequency of words in a language (90 percent of communication occurs using just 500 words), among many other things. Sometimes it is known as the Matthew Principle (Matthew 25:29), derived from what might be the harshest statement ever attributed to Christ: “to those who have everything, more will be given; from those who have nothing, everything will be taken.”
There is so much there to unpick, but I'll stick to discussing wealth. He argues that the same neurochemical mechanisms that create unequal territorial distributions in lobsters are the same mechanisms that create the unequal distribution of wealth in human societies. But he has not provided enough evidence to make that claim. One way he could support his claim would be to provide statistical evidence that the distribution of the areas of lobster territories is the same (to some high degree of confidence) as the distribution of human wealth. He hasn't done the work. It's intellectually lazy. That is why I find his claim to be unconvincing and unscientific. Taleb's alternative theory (see my previous posts) based on economic mechanisms of investment and accumulation of wealth has a better mathematical basis.
There is much to admire in Peterson's stance on academic freedom, and his attempts to maintain standards of rigour in the precise use of language. But I find him exasperating when he makes pseudo-scientific claims that aren't backed up by evidence. Perhaps I'm unfairly singling Peterson out here as he is such a prominent public intellectual. I'm critical of much that passes for logic and evidence in the social "sciences".