In the lively words of Hans-Hermann Hoppe:
To the extent that intellectuals have deemed it necessary to argue in favor of the state at all, their most popular argument, encountered already at kindergarten age, runs like this: Some activities of the state are pointed out: the state builds roads, kindergartens, schools; it delivers the mail and puts the policeman on the street. Imagine, there would be no state. Then we would not have these goods. Thus, the state is necessary.
At the university level, a slightly more sophisticated version of the same argument is presented. It goes like this: True, markets are best at providing many or even most things; but there are other goods markets cannot provide or cannot provide in sufficient quantity or quality. These other, so-called public goods are goods which bestow benefits onto people beyond those actually having produced or paid for them. Foremost among such goods rank typically education and research. Education and research, for instance, it is argued, are extremely valuable goods. They would be under-produced, however, because of free riders, i.e., of cheats, who benefit via so-called neighborhood effects from education and research without paying for it. Thus, the state is necessary to provide otherwise un-produced or under-produced (public) goods such as education and research.
These statist arguments can be refuted by a combination of three fundamental insights: First, as for the kindergarten argument, it does not follow from the fact that the state provides roads and schools that only the state can provide such goods. People have little difficulty recognizing that this is a fallacy. From the fact that monkeys can ride bikes it does not follow that only monkeys can ride bikes. And second, immediately following, it must be recalled that the state is an institution that can legislate and tax; and hence, that state agents have little incentive to produce efficiently. State roads and schools will only be more costly and their quality lower. For there is always a tendency for state agents to use up as many resources as possible doing whatever they do but actually work as little as possible doing it.
Third, as for the more sophisticated statist argument, it involves the same fallacy encountered already at the kindergarten level. For even if one were to grant the rest of the argument, it is still a fallacy to conclude from the fact that states provide public goods that only states can do so.
More importantly, however, it must be pointed out that the entire argument demonstrates a total ignorance of the most fundamental fact of human life: namely scarcity. True, markets will not provide for all desirable things. There are always unsatisfied wants as long as we do not inhabit the Garden of Eden. But to bring such un-produced goods into existence scarce resources must be expended, which consequently can no longer be used to produce other, likewise desirable things. Whether public goods exist next to private ones does not matter in this regard, the fact of scarcity remains unchanged: more public goods can come only at the expense of less private goods. Yet what needs to be demonstrated is that one good is more important and valuable than another one. This is what is meant by economizing. Yet can the state help economize scarce resources? This is the question that must be answered. In fact, however, conclusive proof exists that the state does not and cannot economize: For in order to produce anything, the state must resort to taxation (or legislation) which demonstrates irrefutably that its subjects do not want what the state produces but prefer instead something else as more important. Rather than economize, the state can only re-distribute: it can produce more of what it wants and less of what the people want and, to recall, whatever the state then produces will be produced inefficiently.
Finally, the most sophisticated argument in favor of the state must be briefly examined. From Hobbes on down this argument has been repeated endlessly. It runs like this: In the state of nature before the establishment of a state permanent conflict reigns. Everyone claims a right to everything, and this will result in interminable war. There is no way out of this predicament by means of agreements; for who would enforce these agreements? Whenever the situation appeared advantageous, one or both parties would break the agreement. Hence, people recognize that there is but one solution to the desideratum of peace: the establishment, per agreement, of a state, i.e., a third, independent party as ultimate judge and enforcer.
Yet if this thesis is correct and agreements require an outside enforcer to make them binding, then a state-by-agreement can never come into existence. For in order to enforce the very agreement which is to result in the formation of a state (to make this agreement binding), another outside enforcer, a prior state, would already have to exist. And in order for this state to have come into existence, yet another still earlier state must be postulated, and so on, in infinite regress.
On the other hand, if we accept that states exist (and of course they do), then this very fact contradicts the Hobbesian story. The state itself has come into existence without any outside enforcer. Presumably, at the time of the alleged agreement, no prior state existed. Moreover, once a state-by-agreement is in existence, the resulting social order still remains a self-enforcing one. To be sure, if A and B now agree on something, their agreements are made binding by an external party. However, the state itself is not so bound by any outside enforcer. There exists no external third party insofar as conflicts between state-agents and state-subjects are concerned; and likewise no external third party exists for conflicts between different state-agents or -agencies. Insofar as agreements entered into by the state vis-à-vis its citizens or of one state agency vis-à-vis another are concerned, that is, such agreements can be only self-binding on the State. The state is bound by nothing except its own self-accepted and enforced rules, i.e., the constraints that it imposes on itself. Vis-à-vis itself, so to speak, the state is still in a natural state of anarchy characterized by self-rule and enforcement, because there is no higher state which could bind it.
Further: If we accept the Hobbesian idea that the enforcement of mutually agreed upon rules does require some independent third party, this would actually rule out the establishment of a state. In fact, it would constitute a conclusive argument against the institution of a state, i.e., of a monopolist of ultimate decision-making and arbitration. For then, there must also exist an independent third party to decide in every case of conflict between me (private citizen) and some state agent, and likewise an independent third party must exist for every case of intra-state conflicts (and there must be another independent third party for the case of conflicts between various third parties) yet this means, of course, that such a state (or any independent third party) would be no state as I have defined it at the outset but simply one of many freely competing third-party conflict arbitrators.
Let me conclude then: the intellectual case against the state seems to be easy and straightforward. But that does not mean that it is practically easy. Indeed, almost everyone is convinced that the state is a necessary institution, for the reasons that I have indicated. So it is very doubtful if the battle against statism can be won, as easy as it might seem on the purely theoretical, intellectual level. However, even if that should turn out to be impossible at least let's have some fun at the expense of our statist opponents. And for that I suggest that you always and persistently confront them with the following riddle: Assume a group of people, aware of the possibility of conflicts; and then someone proposes, as a solution to this eternal human problem, that he (someone) be made the ultimate arbiter in any such case of conflict, including those conflicts in which he is involved. I am confident that he will be considered either a joker or mentally unstable and yet this is precisely what all statists propose.