Bite, fight and property rights
Those who feed and pamper the dogs while benefiting from wagging tails and warm cuddles are not held responsible for the nuisance dogs inflict on other citizens
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Another Idea - Capture all of them and sell them to Vietnam / China / Korea or some other country where they are had for food, and earn some valuable foreign exchange. If dog lovers want to stop this from happening, let them buy the dogs and keep them at their own place!
Makarand