[1] http://spot.colorado.edu/~huemer/Contents.pdf
[2] http://www.cato-unbound.org/2013/03/04/michael-huemer/proble...
So we'll have "protection agencies" who have military arms and logistics arms to manage the necessary affairs of the agency. Those agencies will somehow provide equipment to their military, or else they'll be inferior to the other agencies, meaning they will not be giving protection free of charge, instead they will run capitalist markets within their domain and somehow extract a profit (either by taxing transactions, or charging individuals). How exactly is that different from the current nation-state paradigm?
Huemer's anarchy is very different from the current state; it is not 'the same with one or two changes'.
Seriously? There is a huge advantage to being the biggest, baddest agency. If you're substantially larger than the competition you just go to them and say "hi there, give me all your stuff or we kill all of you and your clients".
> It is unlikely that the agencies will fight with one another, as they have strong disincentives
You're completely leaving out the incredibly strong incentive of "Give me your stuff or I kill you". It's infinite profit!
There are two ways history has proven to prevent "Hobbesian War" as he calls it: One incredibly powerful military hegemony, or a delicate balance of multiple exactly equally powerful military hegemonies. Anytime neither of those exist in an area, you get war because it's a lot easier to take someone else's stuff than it is to make your own. To think otherwise is hilariously naiive.
It will be very difficult for you to come up with off-the-cuff arguments which will best a book written by an experienced philosopher over more than a year, and you are unlikely to win over anyone who agrees with Huemer in this forum for exactly that reason. If you wish to discredit him, I suggest you find an academic who has written a thoughtful critique of "The Problem of Political Authority", or that you write a book or paper on its flaws. Anything short of that is most likely to be self-satisfying but ineffective rhetoric.
If my characterization is incorrect, please describe a viewpoint-neutral algorithm capable of determining whether the anarcho-socialist group has a claim to the goods they do not possess. If no such algorithm exists, the socialist protection agency is indistinguishable from a group of theives.
It should also be noted that Huemer explicitly states that socialist groups would likely exist in the anarchy he describes. They would, however, not be able to coerce non-members.
Do you have any idea just how much property in a capitalist economy is possessed by someone other than the owner? What happens if I'm renting a house from you and you try to evict me? Now it's your protection agency--not mine--trying to take something that other people possess.
In fact, capitalist economies also have shades of legal ownership, i.e. lienholding--so I might even be the legal owner of a Camaro, but if I don't pay the car payment the repo man is legally entitled to take something I not only possess, but actually have some legal title to! And this only works because there's an unambiguous and authoritative legal framework in which these kinds of actions are permissible within bounds of regulation. OK, so if your anarcho-capitalist protection agency tries to repossess my Camaro and my anarcho-capitalist protection agency doesn't think your protection agency followed enough due process, where do we go from there?
The entire point of having a monopoly on the legitimate use of physical force is that these kinds of disputes are inevitably going to come up, competing sides are going to be unable to come to a settled agreement, and in the absence of a state, these disagreements will escalate to violence. This isn't a theory, it's the observed history of humanity.