Right, so from what I can gather Hell is somewhere between a Feudal system and a Technocracy then? Its a decentralized hierarchy (there really aren't any truly dictatorial ruling systems anyway seeing as they really just amount to Oligarchies with a single figurehead) where roles are assigned based on the natural affinities and personalities of each demon. Demons of the same 'type' would only resemble each other because their physical, psychological and magical traits are what got them into their profession in the first place. Lucifer is the 'leader' by virtue of his sheer power and his laissez-faire ruling style.
The aristocrats possess power simply due to influence whether due to being popular, being powerful, or through intellect or cunning. The aristocrats of the Ars Goetia are presumably ones who assisted King Solomon as opposed to being bound to him as the book says they were. This is presumably why they introduce themselves to each other by stating their number within that book, seeming more like comrades than fellow prisoners along with why the summoning rituals don't seem to actual bind them if they do not want to.
Aristocrats are not necessarily even demons seeing as Andromalius is a title passed on by Fate Contractors and Aspects. I would assume that the rank was gained through the provision of high-powered Fate weapons which are likely effective against Angels due to the intensity of their distortions increasing their power when they impact defenses such as Entropic Shields used by Angels. Loyalty is probably ensured in that case by the fact that most instances of Andromalius weren't even remotely sentient and just let their servants do as they please. In the case of Andras, I would, taking @Elf's nature into account along with the fact that Andras takes the form of a police officer and has his loyal servants assist him without much issue, come to the conclusion that his power is in the form of charisma and popularity, possibly with power helping the process. Effectively I suspect he is more of a leader figure that his followers support as opposed to Lucifer and Andromalius who have power from a combination of their capabilities and unwillingness to exercise either.
Souls are constantly injected into the economy either through being claimed or being distributed by the Grim Reaper, it is likely that the claimed ones tend to be the ones used as trophies, symbols of power and rank or ones of significant use. Comparatively, the unclaimed would mostly be used either as currency or placed in a suitable role within the workforce. To avoid causing excessive inflation and to allow some degree of economic control, souls may be shifted between work roles and currency roles. A further means of reducing inflation is trade, since souls are also a resource, they may be sold to other realms thereby effectively removing currency from the economy and gaining various products and services in return. I would imagine that one of the key roles of the aristocracy amounts to finding ways of creating work so that there actually are jobs for work souls.
Is that correct?