It doesn't always work, that's for sure. I suspect one of the things the admissions committee did was try to filter out the cheaters. Explaining how the honor system worked was part of the freshman orientation camp (held on Catalina Island).
One reason it did work is the students liked being trusted, and they did not like anyone that would threaten the system, and would turn them in.
BTW, that was 50 years ago. I have no information on how the honor system is fairing today.