Privatise the police?

The Lothian and Borders police are thinking of charging companies for providing additional patrols:

The Chief Constable wants councillors to give him the power to strike cash deals with private companies in return for mounting extra patrols.

I always thought that the police force was a "public" service and was meant to provide law enforcement for all of us. That is the justification for its tax-funded status. The Chief Constable is acknowledging that policing may not be a public good after all. If that is so, and I suspect that it may be, then the police force should be privatised. Who knows, there may be a market for a police company and court system that actually catches and punishes burglars.