What about Anarchy?
The Objectivist position of government is best summarized by the phrase "minimal government". It's the view that the government should just protect rights, and should have minimal impact in our lives. It's sometimes referred to as "minarchism".
Anarchism, on the other hand, is the view that no government is necessary or desirable. I want to bring up some of the more common reasons given for the anarchist position since you'll almost certainly deal with them in the Objectivist world.
The first reason given to support anarchism is the efficiency of free markets. By allowing competition between companies, they have to compete with one another through better value for your dollar. Why not allow governments to do the same thing? Why not allow competition, and then the world will get better and better?
This is what Rand called the fallacy of the stolen concept. That means that the concept is used while denying or ignoring it's necessary foundation. In this case, a free-market doesn't automatically, magically provide good results. It's because the use of force is outlawed between the companies, and the customers are allowed to not deal with any of them, that they have to offer the customer values for trade, and they have to offer the most. If governments themselves compete, that assumption of freedom, and the inability to use force, is not valid. The governments are dealing with force. Some anarchists still try to claim that "market forces" will make it all work out, but it all rests on this false foundation.
A different approach to arguing for anarchism is that minarchism is necessary immoral. The first version of this is a weird interpretation of Rand's writings. She discussed government as having a monopoly of force in a geographic region. And of course, monopolies are bad. More to the point, this would seem to mean that self-defense is illegal, you can't have private security firms, etc. Minarchists don't suggest any of these things, so this argument is one that confuses a definition with a concept.
Another reason a minimal state is considered bad is because it taxes people. The fact that minarchists believe it is possible to fund a government voluntarily is ignored because it sounds too difficult. It's never clear how 50 anarchist governments are able to be funded but 1 is impossible. So this is applying a different standard for the two.
Another reason governments are considered immoral is because no government has even been created as a minimal state, or stayed that way. The United States was considered an excellent start (minus slavery, unequal rights for women, and a lot of other problems), but the parts it did get right at the beginning slowly gave ground to government abuse. So anarchists assume that since government has never been constrained in the past, it's an impossible job. Again, the standard for anarchy is different. Since anarchies have always historically ended in government, it should make their alternative sound equally impossible. This is conveniently ignored.
But no discussion of anarchism would be complete without asking the fundamental question. Why do we need government in the first place? I've explored the human need for the harmony of interests, the protection of individual rights and consequently the ability to use retaliatory force, and with that the epistemological issues of determining across a society whether an act was an initiation of a retaliation. How does anarchism solve this problem?
The market anarchists suggest that their competing firms will have "market incentives" to come to peaceful conclusions. They suggest that they'll hire third-party arbiters to decide whether a use of force of proper or not. The problem there, which again is epistemological, is that if the two firms have different standards of what is proper or not, they won't be able to come to a resolution. Inviting a third party in to reconcile two different standards of evaluation won't help. In practice, then, a conflict either requires one firm to not use force as they believe appropriate, or they go to war with the other firm. In other words, either the job of the protection agency is dropped in a conflict, or one agency destroys another. If we have a need for retaliatory force, the first means is not an option. And if the second means is used, you have consolidation into a single government.
But so far that's just discussed the legislative side of government, meaning it's only covered the different standards. What happens if two competing agencies actually agree on the standards? This again makes us refer to the epistemological needs related to government. If one agency decides that someone has initiated force, and decides to retaliate, what does the other agency do? It would have to convince itself that this new act of force is not an initiation itself, or it might decide to retaliate.
In other words, the whole epistemological issue is opened up again. The agencies will have to agree on every instance of retaliatory force or one will believe the other is initiating force. Again, if there's a conflict, war is the only solution.
Just to go through all the possibilities, what happens if the agencies decide that they both have to agree before either uses retaliatory force? In that case, by solving the epistemological issues, they actually form a single government. They've combined their two agencies into a single agency where cooperation is necessary.
The discussions and debates on anarchism have lasted for decades and are probably not near an end. My personal belief is that the anarchists crave a system where they are free from taxation or government intervention, and fantasize about a system where you can always just walk away from the existing government. They've arrived at their conclusions based on their desires, and not based on logic and reasoning. They then try to support their fantasy with reasoning, but it usually involves applying a different standard between minimal government and anarchism, or relying on stolen concepts or utopian premises.