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I think the model he uses is closer to parasitism, the host is the rest of the people. Once there are too many parasites competing for a limited resources, they start fighting each other. They are not necessary, they are not doing any complex tasks, their role is entirely predatory.
First off, Turchin isn't a Marxist. He accepts Marxist and Marxian ideas though especially when proven through empirical data. He obviously must he's a sociologist. He's ambivalent / neutral about Marxism.
His model is summed up as: When excess elites are not absorbed into the existing power structure and are locked out due to lack of space in that power structure, they become aggrieved by their low status and seek alternatives to that power structure in various ways. Since they are elites they have some means whether knowledge, skill or material, thus have the means to destabilize the power structure itself.
This quite literally describes the conditions that made Lenin and much of the intellectual vanguard themselves as they related to the power structure of Tsarist Russia. One of the things that many here do not really focus on is that Lenin and the Bolsheviks weren't just solving a problem for the proletariat, they were solving a problem for themselves too.
Here's a good blog putting together the historical info but focusing on the general nobility rather than the Bolsheviks only.
https://novum.substack.com/p/elite-overproduction-a-story-of-russia?s=w
Turchin's book is called Secular Cycles.
Turchin's substack is here: https://peterturchin.substack.com/archive?sort=top
He has a fairly interesting series called "A Chronicle of Revolution" that talks about the meta of revolutions themselves and relates it to current/historical happenings.
He uses Volterra predator prey models, he is literally modeling predation.
The model has no assumptions as to wether elites are necessary or not, the conflict is caused by resource competition.
Edit: the other user shared the original peer reviewed article in the post below. It's the last link.
equation 1 has a term for certain affecting wages
Eq 11 has a term were elite population increases as a function of imiseration
Eq 12 is about the sulprys available per elite.
The main difference with a lotta Volterra model is that predation reduces wages not overall prey population, and that Eq 9 asumes a constant rate of economic growth.
This poster is full of shit, I don't know why you are up outing him.
The predator prey models are not used in elite over reproduction work. They're used in his medieval geopolitical work.
Paper: https://escholarship.org/uc/item/82s3p5hj
Explainer: https://www.historica.org/blog/cliodynamics-and-mathematical-models-in-history-part-2
The elite overproduction paper does not use them: https://escholarship.org/uc/item/6qp8x28p
You are correct, the new model is more complex, and is not exactly a lotta Volterra model however, equation eleven in the last paper does show elite growth rate to be proportional to prey population, and later we get the following explanation,
Elite competition is still dependent on the available surplus, the new equations differ from the medieval ones in that it is now rising, and not decreasing.
It's not Marxist but it's still a materialist argument.
It doesn't make the assumptions you made in your original comment, that elites are necessary or that they can be integrated by making society more complex without increasing the relative resources available for them
Elite positions are as necessary as the stability of the social systems under which they're necessitated. If your argument is that elites are unnecessary then you'd need to explain a viable socio-political model where they do not exist.
We can argue about the elite efficiency, e.g. minimizing to necessary elites. However even the USSR, China, Makhnovshchina, and ELZN have elites. So it's not like they're going to go away without a new radical socio-technology that does not exist.
As far as the complexity argument, that's literally the path that many societies had effectively chosen to stave off elite overproduction issues from coming to a boil. Tsarist Russia for example arguably ran a century and a half by doing makework bullshit for elites (see the linked blog). I never argued that it effectively solved the root causes of elite overproduction simply that it was a solution.
The arguments here can easily be applied to "Pol Pot", which again is also not something I am advocating, but something I am enumerating.
They are necessary for the model because the model, models class societies, there is no therm in the model were w, or N increase as a function of E. So no, the model does not model the elites as offering any benefit to either wages or the overall population of humans, their role is entirely parasitic, as in they extract value, and cause instability.
Ideologically I agree that we need to transcend social organizations that stratify power.
Practically speaking framing it around a parasitic lens is ideologically pointless because socialist societies also tend to have this problem.
Im talking entirely from a modeling perspective. The model does not make any assumptions on the usefulness of elites, but there is a term that is effectively a predators fictional response in eq 11. And a coefficient that serves to model an inverse effect in eq 1. In the modeling paradigm, the elite class is either parasitic or not useful depending of those terms, it is never implied they serve a function. Likewise their conflict has material origins se the explanation I quoted, there are no terms to model structure other than the initial class division.