There is no leading anarchist theorist that I can refer to. I know many of the anarchist writers, a few of whom wrote in the post-Civil War period. Anarchy theory has always assumed that small groups of people, size of the groups is seldom specified, will self-organize and that a government structure, whether kingship or democracy will not be needed.
The most salient attribute of an anarchist society is the absence of a police or military.
Most public functions in an anarchist society are locally self-organized like fire brigades, water supplies, roads and sewers. Some anarchist models have private enterprise organizations and others are more kibbutz-like.
No anarchist has seen anything like what we have today. An entire city with all the traditional city services and functions but no functional government. San Francisco, a leader in most other areas, is now the first truly anarchist city on a scale of 800,000 people.
The city government doesn’t work. Taxes are collected and salaries to 33,000 city employees are paid as are the pensions of retired employees. But virtually no one works. Streets are rarely repaired, a few fire stations, very few, respond to fire calls but there are three times as many fire personnel as are needed. Most importantly the police, which operate at one-third of the standard street patrol staffing level, seldom carry out police functions because the police know that the courts and District Attorney will not prosecute most arrests. A small proportion of crimes are reported, and they only result in filing a paper on an internet form.
Pretty amazing. Crime is up, especially minor crimes. Anarchy works fairly well. Few people complain. Crime is a nuisance that results in complaining but most people live with it.
In a large established prosperous city where most life is established and functioning, anarchy works.
(Footnote to the photo: I created and promoted the first 'painted ladies' postcard for my Third World Tours.)