From Wiki:
The broken windows theory is a criminological theory of the norm-setting and signaling effect of urban disorder and vandalism on additional crime and anti-social behavior. The theory states that maintaining and monitoring urban environments to prevent small crimes such as vandalism, public drinking, and toll-jumping helps to create an atmosphere of order and lawfulness, thereby preventing more serious crimes from happening.
Blue Bloods had an episode focusing on this very issue. NYC Police Commissioner found it to be a very useful tool in their arsenal and refused to give up the program. Great program addressing real life police situations. We always have it on the TV in the office for their all day Thursday marathon on ION.
Another aspect to “broken windows” is that they found that criminals commit lots of crimes, large and small. Many who were brought in for fare jumping turned out to be wanted for other offences.