Entitled to meaning that the the citizen is entitled to a certain level of service under the law.
Now, you can argue that implementation is flawed and inconsistent. That's a far argument. But it's the flawed and inconsistent application of the standard to which someone is entitled. In the anarchism model, there is no standard, period. There is no debate as to whether or not someone is being treated to a lower standard as you point to with the Detroit mom and Zuckerberg.
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I disagree because you're making a purely utilitarian argument, to begin with. Both, your initial argument, as well as the conversation we had based on your argument, were only discussing what would "work" better.
Otherwise, the discussion would be a very different one. Both systems have inherent problems independent from their implementation but those aren't seen as a moral problem by the advocates of either system.
An exclusively market orientated form of society might not be able to offer protection for every single citizen.
Somebody who believes that every human interaction has to be based on voluntarism, either contracts or donations, will not recognize a problem there. He will respond that one individual's needs alone don't put moral obligations onto other individuals, that those certainly can't be enforced, that negative rights of those individuals who might either help or pay for help, trump the positive rights of another individual to help, that a solution based on coercion isn't a solution and so on.
In a statist society, we might claim we can provide protection to every member of the society. Of course, statism doesn't solve the problem of scarcity of goods and services and that's only possible because others are forced to fund service which one might not be able to acquire on his own. A statist will not recognize a moral problem there either. He might answer with implicit social contract theories, legitimization of political authority through a democratic process, arguing that government and society aren't distinguishable etc
But no form of society solves those respective moral problems from the ideological opponent's point of view.
They will always cancel each other out.
Your argument that it's only a problem of implementation goes back to what I said earlier: The only distinction is a hypothetical and moral one which currently isn't provided by any system. You might say "well on paper everybody does receive the same quality of services provided by LE, everything else is a matter of implementation. In Greoric's model of anarcho-capitalism, there isn't even anything which could possibly be implemented". But at the end of the day, that means: In both systems, it's theoretically
possible that everybody has sufficient access to LE services, neither system effectively
guarantees it in reality. So the question if having it written on a piece of paper makes a difference is a hypothetical question of morality. An argument which anarcho-capitalists will dismiss since they don't recognize a "right" to law enforcement services at all.
And regarding the efficiency or the actual outcome, writing something a piece of paper is meaningless.
Writing it down doesn't guarantee it and not writing it down doesn't make it impossible. Sorry for the long post.