Libertarianism is a movement that is filled with schisms and wars between competing factions. The natural rights advocates hate the utilitarians, and vice versa. The Randian Objectivists hate the Rothbardian Anarcho-Capitalists, and vice versa. But few fights are as fierce, or as famous, as the duel of the minarchists vs. the anarchists. The minarchists believe that there should be one central unified state, but it should do the bare minimum of activities necessary to govern. The anarchists believe in anarcho-capitalism and competing governments instead of one centralized state.
Which form of government should you believe in? Minarchy or anarchy? There are good arguments for and against both:
The minarchists accuse the anarchists of being hopelessly naive and unrealistic and impractical. As a practical matter, competition between governments and police forces, if each competing state was armed and authorized to use force, would lead inevitably to wars between governments. This is proved because when one considers the Earth as a whole, there is competition between the different national governments, and nation-states tend to resolve their conflicts by means of war, and not by the citizens giving more tax dollars and support to one government instead of the others. At the height of the Cold War Rothbard stated that the Russian USSR would not attack and conquer the USA if we eliminated our armed forces and switched immediately to total anarcho-capitalism and pacifism. This is probably not true, and the end of a unified American armed forces would leave the USA vulnerable to attack, a prospect which seems far fetched only because the American people have become so used to the defense and peace of the U.S. military that we take it for granted.
The anarchists say that the minarchists are one small step away from becoming statists. As soon as you accept the premises of minarchy, you begin to roll down a slippery slope which can only end in statism, by being corrupted with power. A minarchist government would inevitably seek to grab more power for itself and collapse into statism. The Ronald Reagan government of the 1980's, the so-called Decade of Greed, was an unprecedented implementation of minarchy-style libertarianism. It produced prosperity for a little while, but in a matter of time the statist establishment corrupted the government, and the USA soon returned to Big Government and statism. The anarchists say that the minarchists are sell-outs who betray the true libertarian principles.
I used to consider myself a minarchist, and to believe that competing police departments were a hopelessly impractical idea because of the likelihood of wars between competing governments. I believed that what made the state dangerous was its right to use force, not a lack of competition, so competing governments would not remove the problem of the statist state. I no longer feel that way. I now see the minarchy vs. anarchy debate as a distraction, a mere tool to split the libertarian movement using a "divide and conquer" strategy.
Let's examine minarchy vs. anarchy. Assume that the government does not have the power to tax, and must be funded entirely through voluntary payments. Now let us hypothesize an anarchy with competing governments. If there was a conflict between two governments, or if the citizens defended by one police force had a big fight with another group of people who paid a competing police department, then the threat of war would be inevitable. But most people would see this, and they would not stand for it. As a practical matter, conflicts between states would definitely arise, so the choice the people would face would be constant wars, or else one unitary central government. If enough people came to see this then everyone would choose the one state that did the state's job the best, and everyone would voluntarily choose to give their business to that one state. The dynamics of the market would almost certainly lead a diverse marketplace of competing police to condense into one centralized government, as a result of market forces. Anarchy would evolve into minarchy.
So I am a minarchist, you think? Don't jump to conclusions. The logic works in reverse, as well. If there was one central unified government, but it was clumsy and inefficient and bureaucratic, but it did not have the power to tax by force and was required to subsist on voluntary payments, then it would also be inevitable that market forces would motivate some entrepreneurial people to begin new, different states to compete with the central government. Then the people would have choices and would give their business to the best, more efficient state, and this competition would destroy any inefficiencies arising from a failure of the state to face market competition. So minarchy would dissolve into anarchy.
I don't think that either minarchy or anarchy are "correct," they are merely two theories to posit for what a libertarian future would look like. Why then is the fight so savage between the anarchists and minarchists? First, because the little sect bosses within the libertarian movement, the Rothbardian leaders on the one side or the Randians with their Objectivist groups or the leaders of the movements of followers of Milton Friedman or Hayek or Mises, etc., enjoy having their little slice of political power within the libertarian movement, and having an enemy to fight against in the name of ideological purity unites their followers around the leaders. Second, the statist status quo establishment likes to keep libertarianism as an extremist fringe movement, which is accomplished when the libertarian movement has vicious duels over such a ridiculous debate. In conclusion, there is no need to answer the question of "minarchy or anarchy"? First let us create a libertarian world with libertarian voters. Then the market will produce an answer to this question, an answer which we cannot impose upon the market for state-provided services as a result of our deductive political logic prior to the experience of a libertarian existence.