Civilizing Process and reduction of violence in open societies

Perhaps there is a process that reduces violence by a recursive process until it becomes very very low and almost totally eradicated.
First process delegates violence to the state until a monopoly is achieved.As societies increasingly turn to democracy and open society it would be also an increasing trend that the monopoly of violence is withdrawn from individuals and minority groups.
Second process reduces the amount of violence a state can exact on its people as the people are in control of this monopoly of violence. And they would not like to to be on the receiving end of their own punishments.
As the first process is followed by the second and the second increases the first in turn a loop emerges that recreates itself  like the Ouroboros snake that eats its own tale.