In a completely free society, there would be no public provision of law enforcement. Justice would simply be another service provided by the free market. Some might object by saying, "Justice sometimes requires violence and a market for violence is not moral and cannot be tolerated". Unfortunately for any such skeptic, there is already a market for violence and the state has given the public police a monopoly in that market. Additionally, the private provision of justice has always been around and is still around today. Therefore, I find it prudent to compare public police and private police in various relevant areas.
Public: The state gives special rights to police employees that do not apply to other people.
Private: It is recognized that police employees have the exact same rights as everyone else.
Public: The police enforce the arbitrary laws that the legislature enacts. Many of the laws that the police enforce prohibit activities that are voluntary and non-harmful to the property of others.
Private: The police only prosecute crimes that truly violate the property rights of others.
Public: When someone violates the property rights of another, the police punish the criminal through imprisonment and fines. Usually no restitution to the victim is required.
Private: When someone violates the property rights of another, the police require the criminal to make restitution to the victim, thus making the victim whole.
Public: The state gives the public police a monopoly over law enforcement in a particular geographical area. In most cases, the state bans or severely restricts the activities of other providers of law enforcement.
Private: Any law enforcement provider is free to compete in the free market.
Public: Police budgets come from taxpayer money and are subject to the political process. Police agencies, therefore, have the incentive to lobby for the criminalization of more and more activities in order to justify a larger budget. Additionally, police agencies have the incentive to punish, fine, and seize the property of average citizens, instead of criminals, which are difficult and expensive to track down.
Private: Police budgets are directly related to profits which, in turn, are generated by satisfied customers. In trying to satisfy customers, police agencies have the incentive to quickly restore lost value to any customers who have been victimized.
Public: There are no real costs because the taxpayers are forced to pay for everything. The result is that there are no limits on the operations that can be performed, whether the public agrees with the operations or not. Any action deemed "criminal" by the state can be prosecuted.
Private: As a private business, all operations must be part of a calculated strategy to maximize profits and minimize losses. The result is that all operations will be geared towards serving customers by enforcing restitution from criminals to their victims. Victimless "crimes" are most likely not prosecuted.
Public: Any collateral damage that is caused by the police is either ignored or paid for through coercive taxes on the population. The police agency is not accountable.
Private: Any collateral damage that is caused by the police is understood to be the financial responsibility of the police and cannot be passed on to anyone else. Any police agency that causes more damage than can be paid for will go out of business.
Public: As the state-enforced monopoly provider of law enforcement, any allegations of abuse perpetrated by police employees are investigated by other employees of the state. Conflicts of interest are unavoidable.
Private: Allegations of abuse perpetrated by police employees can be investigated by any police agency that the victim chooses. Conflicts of interest can easily be avoided.
Public: As employees of the monopoly provider of law enforcement and possessors of special rights, police employees are ideal targets for corruption by special interests. If key employees are corrupt, there is no competition that can restore justice.
Private: In order for special interests to be effective in corrupting police employees, key employees of every police agency in a geographical area have to be corrupted. Such a scenario is unlikely, and even if such a thing did occur, that would create instant demand for a new non-corrupt police agency that an entrepreneur would quickly act to satisfy.
Public: Because the police do not require the support of any customers to function, there is no consideration given to the possibility that certain tactics might be offensive to the public. This results in the widespread use of offensive tactics.
Private: Police agencies require a customer base to stay in business. Therefore, the tactics that are utilized are most likely vetted in order to ensure that the police agency retains a positive image in the minds of current customers and potential customers.
There are significant moral and practical advantages that a system of private police has over a system of public police. Therefore, I recommend the abolition of public police in order to enable a transition to a system of private police.
For information on the actual use of private police in the United States, and in other parts of the world, see this article from the Mises Wiki.