Anarchy in the sense of no government just ain't gonna happen -- not unless everyone becomes a hermit. How else can it work?
Once again, my usual disclaimers: (1) Calling
Anarcho-Capitalism pure anarchy is like calling a
chickpea a chicken. (2) Anarcho-Capitalism is a personal philosophy that I believe in, not a political system I am proposing for society at large. (3) Politically, I am a (small-l)
libertarian /
Minarchist, and I understand that even the most moderate changes would take many years to accomplish.
I look at government as an inherently evil entity that exists by violating the
Non-Aggression Principle (NAP), most notably by collecting taxes and not giving individuals a choice. (Voting does not produce individual results.) And in some cases tens of millions of people have been murdered by their governments - though the powers that be only resort to those measures if seriously threatened. No large society can ever be 100% aggression free, but it must still be resisted at every opportunity.
A group of people will always want a system of making decisions. Even if they don't elect/designate a leader/decider.
The individual is sovereign, and all delegation of individual sovereignty must be justified.
In a small group of people, like a family, the leader's authority is direct. If a father is the head of the family, then he convinced his spouse(s) to marry him based on whatever terms they agreed to (hopefully a partnership of equals), and it was their decision to bring any children into this world. The spouse(s) can get a divorce (in accordance to their marriage contracts), and children can sue for emancipation / adoption, or someone else can sue on their behalf, or they become automatically emancipated upon reaching a certain age. Without a government to regulate family law, families would be very explicit in what their rules are, and many would voluntarily choose to delegate some authority to organizations that they trust -- a church, a secular family counseling NGO, a free-market arbitration organization, etc -- to help resolve disputes.
The vast majority of individuals and families will want to live without being raped, kidnapped, stolen from, or murdered; and thus it would be in their interest not to do those things to others (principle of reciprocity), and to protect themselves from the small fraction of society which does not accept the NAP as the one and only universal commandment necessary for existence of human civilization, a "social contract" if you will. Since a person who robbed / raped / murdered someone else might come after you next, it is within the self-interest of all good people to cooperate in the efforts of establishing justice. The justice system can be centralized (i.e. a Minarchy with a tiny constitutionally-bound government) or decentralized (based entirely on voluntary organizations like competing free-market arbitration companies and charitable organizations). The former is close to what the founders of this country envisioned, but government power found a way to escape its bounds and grow. The latter is a theoretical concept, and would first be practiced in self-selected enclaves of society and spreading if successful.
I know I make it sound too easy, but the main cause of criminality throughout human history has come from non-recognition of individual human rights based on the principle of
self-ownership. (See
flash video here.) This was mostly based on early man's tribal economy and the need for violent competition with the neighboring tribes. After man has found the means to use the earth (not to mention the rest of the universe) to allow for survival of all humans (even working as a prostitute for 10 minutes will buy you bread for a week), violent competition became inefficient, and improvements in communication and information technology continue to make cooperation easier (ex. self-driving cars playing a virtual game of rock-paper-scissors to decide who yields to who).
Another cause of criminality has always been the idea of legislating morality in the tribe's mutual interest (i.e. victimless crimes): ban recreational activities that can cut into work time, decrease the birthrate, reduce the willingness and ability to fight for the tribe, etc. With advances in individual ability for survival by exchanging value for value (i.e. capitalism), this too is an inefficient and unnecessary ideology. Society works better when each individual can decide how to live one's life, as long as he harms no one but himself and his rightful dependents.
One day you say that a thing is decided because the majority voted for it. The next because the loudest voted for it. The next because the guy who owns the football has threatened to take it home unless we play by his rules. How long are people going to live like that?
The former two examples ("majority" or "loudest") have nothing to do with Anarcho-Capitalism. The property rights of "the guy who owns the football" must certainly be respected, but ultimately it's the guy who owns the playground that makes the rules. Don't like the rules? Exit the playground.
As humanity continues to advance, the number of other playgrounds a person will be able to access (say in 10 minutes of travel time) will continue to increase, and if you're willing to pay a membership fee you will find plenty of businessmen interested in building new and better playgrounds with rules more appealing to whatever customers they care to attract. And if someone donates money for this cause, more accessible charity playgrounds can be built as well.
If I've understood... In anarcho-capatalism, things like the police force are funded voluntarily. Which means that advertising is going to play a factor. Which means ownership of resources is going to play a factor.
They would probably be called "security attendants" (like in a shopping mall or a train station) or "peace officers" (like in a residential community). I'm not sure if I understand what you mean by advertising, but ownership of resources will definitely be a major factor. If you run a successful bank, you definitely have enough money to afford awesome security, and at a much lower cost than the taxes you'd pay to the state. If you're a charity housing project - good luck. But ultimately it will be in the best interest of various competing security agencies to cooperate (perhaps with the aid of independent industry organizations), and a bank security agent who catches a bank robber today prevents him from mugging some poor old lady in her front yard tomorrow, and vice versa - by protecting poor old ladies a bank-funded security firm will reduce the odds of it being robbed, and get good publicity in the process.
So on what basis is anarcho-capitalism better than what we have? Is it supposed to be a purer form of capitalism? If so, then surely that gives even more power to those with capital -- ie: it aims to be even more of a plutocracy.
Yes, as I've said, the rich will become richer. In some ways they will become more powerful - if Bill Gates can ever afford to buy the Grand Canyon, fill it with cocaine, and dive into it from a helicopter, the government won't be there to stop him. (He'd also have to pay to make sure any cocaine blown by the wind doesn't get on other people's property, but more on that later.)
In some ways, though, they would become less powerful. There's no way Bill Gates can do what the government gets away with - forcing people to pay taxes, fight wars, follow silly laws, etc. If he tried to do that, his popularity rating would fall past Hitler pretty darn fast, and not only would most people stop buying software from him, they would also boycott any businesses that use his software. Free market soldiers cost lots of money, and pretty soon Billy G's little army would be wiped out, he would have to answer for his crimes, and billionaires (or trillionaires) everywhere would find it in their interest to donate lots of money to mutual defense charities to improve their public image after the damage Evil Bill has done.
I like the idea of anarchy in the sense of no ruling class. Democracy, in theory, is such anarchy -- anyone can run for office. There is no particular class which is favoured.
Democracy, in practice, is very easy to manipulate to maintain status quo - those who are in power influence public opinion, and public opinion keeps them in power. All they need to do is convince the most gullible 51%, and power is theirs. This is particularly easy through fear: tell the public the bogeyman is out to get them and they will vote for anything. Another trick the government elite can use is create fake opposition: have your voters argue whether Communist A or Communist B is better or worse, in the end they're merely voting for their favorite artificial flavor on the same corn cracker.