Ya know, the funny thing about students - if you presume they are honest, they tend to be honest. The students loved it, I loved it. If anyone cheated, the students would turn him in. Nobody ever bragged about cheating, 'cuz they would have been ostracized.
Besides, I actually wanted to learn the stuff.
I think if you look at the 2012 Harvard cheating scandal, it's clear that this isn't true. There, the professor presumed honest students, hundreds cheated, and no student reported.
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.