Define "crime". Is all reported crime to be recorded as such? Police cannot take the word of everyone who reports, and often well-meaning people report things that are not in fact crimes. Police do not investigate all crimes witnessed or reported by the public. No force in the world has such resources. But they cannot honestly record alleged crimes as actual crimes, nor can we hold them responsible for counting all the crime that the public doesn't report to them. So it is normal for public surveys to be different than those from police reports.