Lior: Are you talking about a mugger, or about a cashier who you claim shortchanged you. When you are arrested for mugging the cashier, you may have some trouble. Police tend to side with the storekeepers.
If there is a good reason not to call the police (e.g. you are an illegal alien, there are warrants out for yhou, etc.), I can see the point. But getting into a fight that you may not win isn’t in your interests. If there is no evidence that can prove you case, the one caught breaching the peace gets arrested.