Libertarians believe in laws that protect people from violent acts or fraud. How do they believe in enforcing them? Would it be possible for the market to provide such protection?
A libertarian society would certainly have police to protect citizens from gangs and criminals, they just wouldn't be tax-supported.
One way of providing this would be government provision, similar to today, but funded by donations, user fees, fee-based charges, or similar methods or combinations.
Another option is the market provision of some or even all police services. The marketplace is quite capable of providing police services, just as it already provides other vital services far better than the government can.
In fact, even today, with "free" tax-funded police protection provided by government, the great majority of police protection is provided by the private sector.
* Private security guards outnumber public law enforcement officers.
* Businesses, communities and individuals spend, on private security, more than the amount collected in taxes for government police services.
So we already have a mixed public-private police system, and the private sector part is the largest, and is growing.
How could a market provide all police services, which some libertarians advocate? Because no one can predict how a market might function -- because markets constantly react and adapt to new discoveries, innovations, and customer demands -- we can only speculate, based on examples already working today.
Private police protection might be by subscription. Private police could patrol neighborhoods, help their customers burglar-proof their house, etc. Those who wished such a service could pay for it themselves or as a package deal with other neighbors. Some San Francisco areas, for example, do this even today, to make up for the limited protection public police provide.
Police services might also be offered as part of an insurance package, since insurers have incentives to protect property from theft, arson, and damage.
Of course, some people might decide to go without such protection and rely on their trusty handguns. Others might call for help when threatened, and pay premium prices because they weren't regular subscribers.
Again, because the market is prolific and tends to move in mysterious ways, it can't be predicted -- but without doubt there would be constant improvement and innovation in these services, and other options would likely be available as well.
Read more of Dr. Mary Ruwart's responces to tough questions in her book Short Answers to the Tough Questions.