Glad you aren't our neighbor. Shooting any dog on sight is definately on the paranoid side, most dogs do not become instant killers when loose. We don't allow our dogs to roam, but we have one that will run if he gets an opening and we aren't home, despite our best efforts. He's not hunting, he's looking for us. We worry about him endlessly till some kind soul finds his phone number on his collar and calls, sometimes miles away. There's a difference between people who make no attempt to control their dogs, even those known to be dangerous, and pets that can sometimes get out purely by accident. Ours is no risk to stock or pets or children and even a moderately astute eye would see that. Please don't shoot without discrimination.
I've seen the cutest little chihuahua cross viciously kill 100 chickens just because she was a dog. Dogs are dogs, they are our best friends but they still have pack instincts and they do what nature calls them to do.
Besides, it isn't like we live in a city neighborhood, we wouldn't be able to shoot a gun there nor would we have any kind of livestock.