Arguably, it's one of the risks of democracy that motivates anarchists. (Now, there's a case to be made that anarchy also risks devolving into mob rule by a different path than non-anarchic democracy does, but they still aren’t the same thing.)
I think the idea is that if you don't like where the majority is going, within a particular community or group, you move to a different group, or found one yourself, so you will be part of a group which is doing what you want.
It is however anarchy (the term), which is much older, and used to convey precisely lack of order and mob rule.
No, it's ochlocracy; there's a reason the same people who named anarchy made a separate word for it.
Anarchy is lack of rule - not the same as anarchism (the ideology and ideal for self-government), as several oppressors can and are still at play in a state of anarchy, or everybody might be fighting each other and there can be constant power shifts...
Ancient Greeks used the term with this meaning, not to describe some anarchist utopia.
So ochlocracy is like the people turning into a mob carrying pitchforks. They are the law...
Anarchy - in the ancient Greek sense - is like there's no state and no all-encompassing rule of law to turn to. It's the "law of the jungle".
True anarchy can only exist in very low density situations where population is very low and very sparsely settled. Let’s say fewer than 5 people per square mile actual (not average) on good land. One or fewer would be better. Rural Siberia -Yakutiya, Rural Mongolia. Colonial era trappers and such when they were not in town.
DENNIS: I told you. We're an anarcho-syndicalist commune. We take it in turns to act as a sort of executive officer for the week,...
ARTHUR: Yes.
DENNIS: ...but all the decisions of that officer have to be ratified at a special bi-weekly meeting...
ARTHUR: Yes, I see.
DENNIS: ...by a simple majority in the case of purely internal affairs,...
ARTHUR: Be quiet!
DENNIS: ...but by a two-thirds majority in the case of more major--
ARTHUR: Be quiet! I order you to be quiet!
It’d be an idealized primitive culture -technology will produce power relationships. So will density (water rights, hunting rights, fishing rights, etc)
The difference is academic, of course, so long as the current level of power relationships in society is well above what even the liberal democracy advocate would consider "optimal".
I have never heard any articulation of how the minimum can actually be zero that is anything other than a straw man.
I think that anarchism is an idea that necessarily leads to minarchism. Once you get to minarchism, the debate is then back to ‘what is legitimate power?’ which is the perennial question.
I'm going to start out with the disclaimer that I am not personally opposed to all power relationships in the very broad sense used by some anarchists. I believe that there are universal natural rights, including both self-ownership and property, and that people have a right to enter into ongoing power relationships with others so long as they do so voluntarily of their own free will. So instead of "power relationships" the rest of this comment will use the term "force" or "aggression"—by which I mean power relationships involving violations of the individual's natural rights without their freely-given consent, except as a proportional defensive response to actual or imminent aggression by the other party. This is more-or-less the standard libertarian, anarcho-capitalist, or voluntaryist definition of aggression.
With all that said, the answer depends on whether you're talking about the minimum amount which is actually present or the minimum amount which can be considered "legitimate". It would be nice for both to be zero, of course, but I think we both agree that some amount of aggression is inevitable in practice—we aren't likely to eliminate all violent crime, for example, no matter how hard we try. The minimum amount of "legitimate" power, however, is trivial to simply define as zero. We are under no obligation to consider any act of aggression legitimate.
The distinction between anarchism and minarchism lies in how much aggression is deemed legitimate, not how much is present. The anarchist recognizes that aggression exists but does not consider any aggression to be legitimate, even when the goal is to reduce the overall level of aggression. The minarchist is willing to sanction a certain amount of aggression in order to achieve what they consider to be a greater good.
In my opinion the minarchist approach is neither principled nor pragmatic. It makes you an accessory to the aggression, normalizes it, and sets the stage for others to argue that ever increasing acts of aggression can be justified "for the greater good". Humans readily justify atrocities on the basis that a society organized "the right way" would somehow be free of violence or other ills. It doesn't work out well in practice. Better to aim for no aggression and consistently oppose such acts wherever you may find them rather than making exceptions.
Anarchy means no established order / ruler -- there can be tons of ad-hoc ones.
The whole idea of laws being ruled unconstitutional is that there are some things that even the majority can't do.