Well, police FORCES were non-existent until sometime in the 1800s. Prior to that time a sheriff or constable would enforce the law with a volunteer posse. Usually the expenses for that posse would be borne by the city/county but the members were seldom paid for their time.
For minor issues, individual citizens worked a solution out among themselves. Of course, dueling was still legal then too. Somehow, the possibility that one might have to pay for his foolish actions with his life made his decisions a bit more... thoughtful, shall we say?
“Somehow, the possibility that one might have to pay for his foolish actions with his life made his decisions a bit more... thoughtful, shall we say?”
Not guys like Billy the Kid, and there were lots of them.