No short answers then? And this is an honest question. Can't know whether there's any short answers without knowledge of the matter, you know.

No person or groups of people like any criticism especially if you're in their walled gardens. Anyway, here's a decent explanation of it and the schools of thoughts. https://en.wikipedia.org/wiki/Anarchism

The problem is that there is no signle anarchist ideology. It is like saying, "Can somebody give me a crash course on political philosophies that accept the state?" And somebody just tells you why they are a monarchist, and another person tells you why they support totalitarian state-socialism with nobody telling you about various "democratic" systems. 

Like I said before, go to the various anarchist subreddits. They'd be happy to entertain your questions and they are normal people. Going to a video game website's politics section and finding the handful of anarchists who are here is not going to give you a wide-breadth of anarchism and the various different answers to your question. 

Basically, let's ask the question "Why don't you support government?" Every anarchist will give you a different answer to that question. 

I would recommend asking your questions in the following: 

https://www.reddit.com/r/Anarchism/

https://www.reddit.com/r/Anarcho_Capitalism/

https://www.reddit.com/r/mutualism

https://www.reddit.com/r/MarketAnarchism

https://www.reddit.com/r/CapitalismVSocialism/  <---> (lots of different types of anarchists and statists debate here.) 

And that's all fine. If you ask "Why do you believe in a god", Catholics, Protestants, Muslims, everyone might answer differently, but that doesn't affect the validity of their arguments, does it? Everyone can answer according to what *they* believe.

But still, thanks. I might go to reddit eventually...

The next issue then is that there are many more religious people in the world than there are anarchists. It is easy to go to a site like this and find somebody from each of the groups you mentioned. 

The best you'll get for anarchists is a handful who might or might not share the same views. 

I just want to make it clear that you won't get a "crash-course" via this method. You'll get at best an understanding of that particular anarchist's views. 

If you want though, you can ask me some questions about my particular pleads for a stateless society. 

You're right.

Certainly. I mentioned two questions in the OP:

How do you abolish hierarchy and keep it from forming again, when it seems to be a natural propensity of not only humans, but most mammals, too?

How do you deal with conflict resolution and law enforcement without hierarchies and/or authority?

I am not a social anarchist, so I am less concerned about "hierarchy." It is very hard for me to identify a clear and consistent definition of hierarchy in use by them. For example, some social anarchists seemingly support democratically determining who has authority over certain public goods. To me it seems hierarchial to do something like this, as it would mean a certain group of people have a claim to goods more than any others - which they supposedly say is wrong when it is private property. But since it is democratic, somehow it isn't hierarchial to them. That is all I will say about hierarchy it becomes a very convoluted discussion. 

I am more interested in people being able to choose the organizations they are part of and not part of. The authority comes from an individual's consent to be part of said institution, with the assumption that they understand the organizational structure of the institution before agreeing. They can also leave any time they want and join an independent institution if they care to do so. 

States are involuntary institutions, and that is why I oppose them. How can we abolish the state? Well we won't get there with a population that cares for the state. Like with the enlightement era which turned people against monarchies and absolute rule, there has to be a change in people's minds. People will have to want the state abolished first. As for methods, there are agorism, countereconomics, and civil disobedience. I only support violent action if it is in self-defense. So if state agents are attacking somebody I don't think people are wrong to fight back, but otherwise I don't support premeditated violence or terrorism. It will be a centuries long process, but eventually if we oppose the state enough we can transition to a polycentric society from a monocentric one, in which all people choose their institutions voluntarily. 

Most conflicts can be solved through arbitration and dispute resolution. For example, suppose a neighbor kills another's lawn through pollution. The polluter recognizes that he polluted, but doesn't think the price the pollutee is asking for reparations is fair. This leaves the polluted neighbor a few options.

1. Force his neighbor to give him all the money for his polluted land. This is risky. If they get into a violent altercation, he might lose his life. There is no state to send to jail, and he'd leave the burden of reparations to his family. Is it worth it over grass? 

2. Agree to the other neighbor's evaluation. 

3. Have an agreement with his neighbor that they should ask a third party to decide, one whom they both trust. 

#1 is not very likely because it is costly. #2 resolves the problem. Let's think about situation #3. Let's say both neighbors know a guy whom we will call Judge. They both trust Judge a lot and think he can make a fair ruling. So they both agree that Judge will determine how much polluter has to pay polutee for his damages. They go and ask Judge, and Judge gives them a particular amount. 

This then gives polluter a few options. 

1. Pay polutee the amount Judge said is fair. 

2. Don't pay polutee and fight polutee some more (remember costs of money and time are building up.) 

3. Ask polutee if they can gather some more opinions. If not, then he is left with option 1. and 2. If so, rinse and repeat.

If the amount Judge says to pay polutee doesn't seem like enough, then polutee also has these options. 

The more time and the more people they get involved, the less motivation they have to not settle the disagreement. Eventually they settle the disagreement and are happy.

So I have a few questions to ask now? 

1. Was there a forced hierarchy here? Was anybody above anybody else?

We can say maybe Judge was an authority, but his decision wasn't really binding and they both agreed to him. So probably not. 

2. Will the dispute get resolved eventually? 

Yes

3. Is violence ever really a consideration when the risks are so much higher in a stateless society than in a state-based one? 

Possibly in some other scenario with more at stake, but not in this one. 

Overall, I can see most situations happening like this. People will form agreements not because some higher authority told them, but because it is less costly to resolve disputes in a timely manner than to not do so. 

I am sure you can think up vastly more complicated cases, and I can tell you vastly more complicated solutions just as we see in the current systems. Think of dispute resolution similar to how nations resolve disputes on the international scale. Is it always the case that every country is at war? No. Yeah it happens some times, but we can't really prevent that. Is there not order despite there being no ultimate authority of law? Yes there is. We can then say there is a sort of anarchy among nation-states. Why not among individuals then?  

Ad hierarchy:

Since we're not in disagreement over this, I'll drop it, then.

Ad voluntary participation in organisations:

That's all fine in theory. We basically have this now, only with the state and its branches as the only involuntary one... But do you see that as something that would produce more good than evil? Even today, when organizations are at least regulated by the state, there are huge levels of coercion, indoctrination and downright abuse associated with these "voluntary" organizations. If they weren't, don't you see those things rising immensely?

Ad abolishing the state:

Again, no disagreement here. It is possible to take down the state. Theoretically. I doubt it will ever happen, all with quality of life rising and all, and I don't want it to happen, but... still perfectly possible.

Ad conflict resolution:

There is one huge problem in your whole proposition: it expects everybody to be reasonable and fair, which is not (and simply cannot) be the case. If I've done something wrong, I *don't* want the issue to be resolved, it's against my best interests. In your first set of options, I can simply choose option 4: None of the above.

Actually, it also connects to the voluntary organizations point. Who can be this "judge"? Who can be relied upon to be impartial in a place where nobody can be prosecuted for anything or forced to do anything? And what if there's no one able to judge competently in a really complicated issue?

In fact, how do you even know who is supposed to be judged in the first place? In your scenario, both sides of the conflict are clear. What if they're not?

And finally, how do you deal with people who will not be deterred by any means from doing harm? How do you deal with psychopaths, insane people, extremists?

In short, your whole system stands on everyone being willing to cooperate. The second somebody isn't, it crumbles down.

Ad international justice:

I'm actually really glad you likened your system to the system of international justice, because I think the comparison is fitting. Does the way the world works on the international level strike you as just? The United States can literally do anything they want, because they have the strongest military and the (second) largest economy. They don't participate in many agreements where most of the international community particpate, they can't be convinced to limit pollution, to submit to the International Criminal Court, to prosecute war criminals, to stop invading sovereign countries or spying on people. They are the biggest kid in the playground and everybody has to deal with that. Where do the countries hurt by the U.S. foreign policy go to receive recompense? Does this strike you as just?

I'm just really perplexed by your bringing up international relations as something that goes perfectly and in a just manner... I don't think many people would claim this.

(And by the way, I'm not (very) anti-American and I'm not holding them responsible for anything - I'm merely stating facts.)

voluntary participation in organizations:

 Yes I think it will be more good than evil. Regulatory capture and limited liablility are probably the principal reasons why such organizations get away with the "huge levels of coercion, indoctrination, and downright abuse" that you talk about. In an anarchic society, they are not protected from being personally liable nor do they have state priveleges to outgun their non-compulsive competition. The rest of the population can hold them accountable for any damages they've done through cooperating against them. 

abolishing the state

 Cool, just want to re-emphasis that it would be a slow-process and more akin to society shedding the state than abolishing it. 

conflict resolution

 I don't know how people interact where you live, but where I live 99% of people want to get along with each-other and are indeed reasonable and fair. When that is the case, the other 1% can't really do too much. They are limited by the 99% cooperative people.  By choosing "none of the above" how are you going to get your money? And if you are the other person, choosing "none of the above" how are you going to prevent your neighbor from using force to seek reparations or seeking others whom represent him to do so? If you choose to do nothing, his only course of action is to use force, and since you showed you aren't willing to cooperate other people will be on his side, putting you at a big disadvantage in the situation.  

Anybody can be the judge. Like I said, it is a mutual agreement between the persons in conflict. They must both agree to him/her. What do you mean by "clear?" Is it not the judge's or the group of judge's responsibility to determine that? 

The same way we deal with them today. If they try to harm you, you harm them back. Otherwise you ostracize them from society. With the internet and reputation databases, this wouldn't be hard to do at all. We already see things like this with Yelp, Uber, and Angie's List. Anybody who has commited such a crime, and doesn't want to pay reparations for it would easily be recognized as such by people who encounter him/her in the future (via background checks.) 

It doesn't require everyone to cooperate, just most people. Most people cooperate today, and no it isn't because they are told to, but because there are social, moral, and individual pressures to do so. 

international justice

   Two things: It is just. Every country retains its autonomy, but progress is still made. The world is becoming a more peaceful and safer place. Sure the U.S gets away with a lot, but it also has done good. Also take note that the U.S won't be able to continue in the long-term doing what it does, even if it gets away with it for now. If the U.S only does the bad things it does in the long-term it will alienate itself from the rest of the world, and the rest of the world will choose to reciprocate with the U.S. Even with its size and stature, the U.S still cares what European states, China, Japan, etc think and is limited by them. Most of the examples you gave are effects of collectivization. The U.S doesn't do these things (climate change regulation, reduced war, etc) because there is either internal stife preventing it from doing so, or it isn't a rational entity with real costs. Individuals don't have these constraints. Individuals have full autonomy over themelves (no internal struggle) and they feel the costs of their actions. 

Now imagine that instead of approximately 200 actors (countries), there are thousands, millions, or billions. The ability for any one entity to have the level of influence over others that the U.S has becomes practically nothing, they are so vastly outnumbered by everybody else. 

There will always be outlaws who don't play by the rules, but that is true of any system. 

Right, they're not protected. No one is. So today, they need undue protection from the state to be able to "outgun" competition, i. e. the state failing. In an anarchist system, all they need to outgun competition is *to be physically able to*. As long as they're self-sufficient and powerful, they can handle "everyone cooperating against them". And who cares about accountability?

I would like to live where you live, then, because here, 99% of people want to get along with each other and are indeed reasonable and fair... right up until the point when the situation involves money, sex, religion, class, sports and God knows what minor squabble they care about. Then they become hostile, vindictive and (passive-)aggressive and they use anything to get ahead, as long as they think they can get away with it.

EXACTLY! Exactly what I'm talking about. There's nothing preventing anyone from doing anything. There's nothing stopping me from going to his house tonight and taking what I fell he owes me and there's nothing stopping him from coming tomorrow and taking it back with interest.

And what do you mean, "I showed I'm not willing to cooperate"? It's a word against word. Remember, I don't have to say "there will be no judge", I can say I'd only consider [list of my friends] as a judge and that's it. What's going to happen next? Maybe the community decides a judge? Looks a bit like the state to me, mate. And it only relies on how many friends i have - if I have a lot of friends and he doesn't, the selected judge will be on my side. Where's the justice?

By "not being clear", I mean "Somebody stole my bag of grain last night and I don't know who." What's the judge to do? If I don't have to cooperate with the judge, he's impotent. If I do have to cooperate (to prevent the community from assuming my guilt and turning against me), then congratulations, we literally have a police state... where anybody can be the police and they don't even have to forge evidence.

Wait, so violence as retribution is allowed? Because if not, I don't think an insane serial killer has to be that concerned about being ostracized. And holy c**p, have you not heard about that site where you can rate people that gathered immense resistance? You're actually down with that? Do you not realize how abused this can be?

Calling the international community just is just baffling to me and I just cannot accept this, I'm sorry.

And I don't know why you refer to individuals as if they were the only thing that exist in anarchy. There will be organizations with their own internal strife and not being rational entities with real costs.

Yes, imagine. Today, Armenia and Azerbaijan are at war. Do you know why? Do you know who's in the right? How do you "judge" them? Do you think less of any of them? You don't, do you? Because keeping track of even 200 actors is downright impossible. You keep track of the important ones and even at that, you can attain only a VERY limited knowledge about them. Consider BILLIONS.

Sure, only in anarchism, their views and interests are just as valid as anyone else's.