Supporters usually argue that anarchism is naive and goes too far towards simplicity, while libertarianism is often too allowing of vested interests, and that what they call minarchy continues traditions of classical liberal philosophy in their original form.
Radical minarchists usually agree that government should be restricted to its "minimal" or "night-watchman" state functions of government (courts, police, prisons, defence forces). Some other minarchists include in the role of government the management of essential common infrastructure (roads, money); some, by what is sometimes reproached to them as a slippery slope, include quite a lot in such essential infrastructure (schools, hospitals, social security). Actually, these minarchists often accept (in a conservative rather than principled way) as valid some of current government's domain, and consider it more urgent to stop the expansion of government than to reduce its domain to any particular size. Minarchists are generally opposed to government programs which transfer wealth or which subsidize certain sectors of the economy.
Minarchists usually justify their vision of the state by referring to basic principles rather than arguing in terms of pragmatic results. For example, in his book Anarchy, State and Utopia Robert Nozick defines the role of a minimal state as follows:
A directly competing theory is eco-anarchism, which some consider also a form of minarchism. In this view, anarchism is basically right about all relationships between humans, but there are rules required for dealings with non-humans and the ecosystems that provide nature's services to them. The "night watchman" can thus be restated as a "forest ranger" or "game warden" but the basic theory remains the same.