Hi Hirashin. The problem, in my opinion, is that because it uses the countable "crimes", it is explicitly saying people actually, directly prevent crimes, as in a person stopping a bank robbery while in progress, or catching someone touching a woman on a train. This is not what the idea of Crime Prevention is though, it is an intangible, overall, general reduction in crime. It's not having people act like policemen (who very rarely catch criminals in the act either)
I would make it general, or passive and say something like
"The more people know each other, the more crime goes down."
As it says later in the text, it is the effects that are important, not direct intervention.