The most commonly used definition is Max Weber's,[6][7][8][9][10] which describes the state as a compulsory political organization with a centralized government that maintains a monopoly of the legitimate use of force within a certain territory.
The most commonly used definition is Max Weber's,[6][7][8][9][10] which describes the state as a compulsory political organization with a centralized government that maintains a monopoly of the legitimate use of force within a certain territory.
In short, the authority of these private organizations are opt-out, while the authority of the state is not.
It's circular logic to say that a state has a monopoly on only legitimate violence since it's the same state which defines which violence is legitimate and which is not. Can you think of any organizations that successfully exercise a monopoly on illegitimate violence? Successful states do not allow such activities to continue for long.
A state is, as others have already said, simply a political institution which exercises a monopoly on violence and determines how to apply it within its political domain.
This feature is so critical to how the modern system treats territorial integrity that we sometimes refer to states which can't control violent groups within their own borders as "failed states."
See, the reason why the war in Afghanistan is controversial is precisely because it is not clear that a country has a casus belli against another country if there is a (remote) connection of offenders to that country. In fact, the pilots lived and planned most of the plot in Germany.
A better example of a failed state would be the results of the war on drugs in Mexico.