Like any self-respecting anarchist, I am going to reply first to the question, and not to any other anarchist’s propositions or descriptions.
Anarchy, like atheism, is a “NOT-x” formulation and it is fair to first, therefore, pay some attention to what anarchy is NOT, since it is defined in terms OF what it is not. “Archy” is a system, any system, in which the modality for establishing and maintaining social order is dependent on a hierarchy of authority. People over other people. Bosses and those who must obey them or be punished. Archy is inherently involuntary (we’re not talking about playing a board game here, you do NOT get to opt out); it is enforced, hence coercion is structurallly and deliberately organized to impose obedience. Where obedience cannot be obtained through some civic sense of propriety and loyalty to the system and its hierarchy of command, it is obtained through fear, and when that doesn’t work through literally imposing force to produce the desired behaviors.
The presence of social order, understood and expected-to-be-understood codes of conduct, traditions, and so forth are not necessarily archic. Law enforcement makes it archic.
Anarchy is essentially a belief that social order based on a different premise is possible. That peace, productivity, good relations between people, and other facets of a functioning society could exist without the presence of a social structure dependent on people with official authority over others.
I could write six or seven dozen declarative statements below this that would outline MY SPECIFIC notion of anarchy but not all anarchists would necessarily agree with them. Down to this point I’d expect anarchists in general to agree with what I’ve written, but there may be disagreements with the following assertions which are my own:
• anarchy means no money system, no currency, no economic system in the sense of a market economy whatsoever: not communism, not capitalism, not barter, NOTHING. goods would be distributed (or picked up) and services provided but not in conjunction with any kind of exchange procedure in which the goods or services are paid for. It is possible that things like reputation would be meaningful in obtaining (or finding it difficult to obtain) cooperation of other people in joint endeavors.
• a hierarchical structure would probably exist, would probably NEED to exist: just not one of people over other people. Rules can exist in a hierarchy: more permanent ones above less permanent ones above yet more transient or temporary ones. Collectivities of people can also form a hierarchy: the individual, the neighborhood, the community, the village, the town, the county, the state, the nation, the planet. Or some equivalent of that. Initiative as well as freedom would presumably be concentrated at the lowest possible level that things people desire to get done can BE done effectively.
• all observations about “human nature” proferred as reasons anarchy “cannot work” are observations about human nature as observed in a context. Archist contexts reward certain behaviors. If you play Parkers Brothers’ Monopoly, you only win if you attempt to acquire all the properties possible, charge extortionist rents, and render the other players broke & bankrupt. You can play with other behaviors but if you do you end up broke and bankrupt yourself. It’s how the GAME works, it has nothing to do with human nature.
• Reciprocally, no claims are made for any “human nature” that is intrinsically “unselfish” or “good” or that people can and will “change their natures”, but rather that anarchy is a different game that creates a context that rewards certain behaviors. “Big Chief” economies (primitive redistributivist economies) are environments in which one gains power and prestige by acting like Santa Claus, giving away wealth to others. It’s not a personality trait, it’s the desire for power and prestige that motivates them, although, so motivated, they may wish indeed to see those to whom they give things do well as a consequence of their largesse. Anarchy is in part a belief that voluntary cooperation is just another game, with rewards and prestige and reputation being serious considerations in the absence of coercion and economic currency. Or, rather, such things become economic currency.
• Anarchic systems need not depend on first overthrowing or dismantling archic structures; unless there is a law against such networks, anarchic networks can coexist with such structures as representative federal republican democracies, and could “take over” simply by gradually demonstrating themselves to be more efficient and effective at organizing human activities. Violence is intrinsically archic and ——at the risk of making a “no true Scotsman” assertion ——I say that no one who seeks to change a system (at least a system as dependent on pervasive voluntary cooperation as representative federal republican democracies are) with violence is an anarchist. Organized violence is coercive, military groups are the most hierarchical and archic of human organizations, and voluntary cooperation is one thing that cannot be forced upon people; if there ever was something you absolutely can’t get to by forcible means, this is it.