You will have competing law providers in the same area of land. There is a high demand for security and law and order and many entrepreneurs will be willing to provide it. The reason they don't now, is because the government has a monopoly and forbids it. It does this because it's good to have a monopoly on the provision of force in a geographical area. Allows you to extort your victims. It would be too expensive, in a competitive setting, for one company to build up the necessary force to dominate everyone else. The profit margins would be too slim and the company would go bankrupt before it even got close.
I still don't see much logic behind what you say. Ultimately it doesn't change anything from where you start and instead of one "law provider" you get by the choice of majority another with brand new laws and some part of the population disagreeing with them...
What does this all have to do with anarchy?
