Actually, the authors don't have to imagine any such society - they can read about them in history. London, for example, before 1829, had no professional police force. It did have a sort of neighborhood watch system such as the article calls for.
And how did that work out with respect to crime? I'll leave the answer to the curious researcher, but I bet you can guess.
There were very few cops in the US prior to the Civil War. Most places had a sheriff...but he had the right to REQUIRE any and all able bodied men to help him chase down criminals. That was the militia: men capable of using arms to protect their community, who could be called upon at any time to stop robberies, etc.
“The notion of a posse comitatus has its roots in ancient English Law, growing out of a citizen’s traditional duty to raise a “hue and cry” whenever a serious crime occurred in a village, thus rousing the fellow villagers to assist the sheriff in pursuing the culprit. By the seventeenth century, trained militia bands were expected to perform the duty of assisting the sheriff in such tasks, but all males age fifteen and older still had the duty to serve on the posse comitatus.
In the United States, the posse comitatus was an important institution on the western frontier, where it became known as the posse. At various times vigilante committees, often acting without legal standing, organized posses to capture wrongdoers. Such posses sharply warned first-time cattle rustlers, for instance, and usually hanged or shot second-time offenders. In 1876 a four-hundred-man posse killed one member of the infamous Jesse James gang and captured two others.”
http://legal-dictionary.thefreedictionary.com/Posse+comitatus