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I attended Caltech in the 70s when it had an honor system. An anecdote on how it worked:

A fellow student of mine, "Bob", was taking Ama95, a required class that was one of the hardest classes. All exams were take home, open book, open note, but with a time limit of 2 hours. There was no proctoring, and nobody would know if one took extra time or not.

Bob took the exam to his dorm room, closed the door, and set the timer at 2 hours. He had been up late studying, and fell asleep. The timer woke him. He figured he'd been asleep for an hour. So he drew a line in his blue book, and continued taking the test for another hour. He then wrote an explanation of the line and what had happened, and turned it in.

He received an F. The professor was very apologetic, but explained that he had no choice.

Bob received the news with equanimity, and signed up to take the class again next year. He related this story in a matter of fact manner to a group of us in the dorm library.

The thing about the honor system is it turned the students and professors into collaborators rather than adversaries. The students liked the honor system very much. If their best friend cheated, they'd turn him in. Hence, any attempt at organized cheating meant ostracism. I never saw any of that in my time there.

Nobody stole anything in the dorm that I was aware of.

For contrast, I attended a class at a local college. One of the other students befriended me, and it turned out he did that to convince me to help him cheat. (I declined.) A friend of mine attended another university, and the day he moved into his freshman dorm room it was looted.