How can anyone one say they would instantly shoot the dog? I run bear with hounds and know dogs well. They will all run deer given the opportunity until broken off of them. What if that dog belonged to a family and their 5 year old daughter accidentally let him out of his kennel... what would you say then?
It would be one thing if you located the owner and they didn't care to do anything about it... but some dogs are magician's and get loose on their own. I had a pup in which I went through 5 diferent types of snaps before I found one that kept him on the chain. Can you believe he was getting off of a bull snap? A friend of mine caught a guy letting his dogs loose when he wasn't home.There can many reasons for a dog to be loose.

You need to exhaust all of your options andresources before resorting to shooting someones dog. They have collars... is there a name tag? Do they come to you when called? Do they appear to be skittish?