I have a number of friends who are anarchists and others, like myself who do not believe it can work. We view is as "utopian." First, libertarianism is different from anarchy and objectivism. Mainstream libertarian theory assumes some minimal state will be necessary to protect individuals against rights violations by others. There are libertarianist exceptions but they are in a minority. I repeat, Ayn Rand's theory may not share that assumption, but it is not "libertarianism" it is, by its own words "Objectivism. See the National Libertarian Party
Platform sec 1.6. If this isn't what libertarianism in the U.S. is about, at least from the activist perspective, I don't know what is.
The primary issue is crime control. Without formal police, courts and corrections institutions, crime, esp. rape, murder, assault, child abuse, sex offenses, etc. will run wild.
Anarchists have a number of
answers. First, they say the current system is the source, causation of crime. There are no biological or evolutionary bases for crime. I agree that much of the human environment is criminogenic. However that is not the whole story. There is much evidence that aggression, distrust and dislike of people who are "different" in certain respects, and other negative tendencies are
factors inherent in human nature and are products of our evolution.
Sexuality which is easily mixed with aggression will not disappear. Sociobiological factors are factors in causation. For an overview
see. Check any recent graduate or undergraduate textbook on criminology. There is much evidence supporting sociobiology. Second they say "the people" will set up conflict resolution and other mechanisms that will deal with crime until it disappears. "The people" in a large, racially, ethnically and religiously divided society will not agree and this lack of consistency and ethnocentrism/tribalism will result in Balkanized justice with outsiders facing injustice. The most likely result is that the strong will enslave the weak. IMHO, it just won't work.
However read this anarchist
explanation and see if you are convinced.