itself is summed up thusly:
In a neighborhood, if a window is broken, and not fixed, those who are inclined towards petty crime (graffiti, littering, vandalism, etc.) are more likely to commit those offenses. This brings the general appearance of the neighborhood down. As the neighborhood declines, those who are inclined towards more serious crime (burglary, mugging, rape, etc.) are more likely to commit those crimes, since it appears that nobody cares. Making sure that the broken window gets fixed lowers the overall rate of crime.
I agree that the solution should be community-based, and non-coercive, if possible. Pride begets pride. If my lawn is well kept, and my neighbor's lawn is well kept, there is a peer pressure effect that encourages the other neighbors to keep their lawn up.