Authority is a sort of personal trust that we have for someone, say, our doctor. If we say he is a good doctor then we express that he has authority with us. Hobbes realised that the state was based on such authority. Locke later called it tacit consent and David Hume said that it was based on opinion. But the Beatles had authority with many teenagers in the 1960s. Authority is like that. It is what we think is good about people or institutions, it mainly consists in what we value highly.
An anarchist is an individual who rejects the state’s authority within his own value system, but that hardly alters the fact that others are not with him there, so the anarchist can still see that the state is upheld by the authority it has with many others; maybe most others. So the state has power over him owing to the support for the state from other people, even though the lone anarchist has contempt for the state.
Locke made a serious error on the state, that Nozick, and also many libertarians, either made too or they might have followed Nozick, or other followers of Nozick or Locke, but it is one that Hobbes never made, and one that Hume rightly criticised as naïve, and that Burke and Bentham also rejected, maybe owing to Hume’s influence but that current common sense, greatly influenced in the UK/USA by Locke, tends to accept today. The serious mistake is that the state serves the public rather than governs them. It is the reason we call the state bureaucracy the “civil service”.
Authority is not over us but rather it flows from us. But the state does rule chiefly by authority rather than by force, as Nozick seemed to imagine. A massive part of Nozick’s error here is in his thinking that a defence agency in an anarcho-liberal society could be a candidate state. It is the naïve idea that the state even could be where it is today by mere brute force. Even in any gangster mob, we might, if we think a bit about it, get to realise that the best fighter in it rarely, if ever, leads it. The leader of the mob needs to have authority with the mob members he leads in order to lead it. Brute force is no good for that end but with authority from the mob then it might even be led by a cripple.