I have one personal Localbitcoins story, in this regard. About a year ago, maybe a little less than a year ago, I had conducted a cash transaction for about half of a bitcoin around $7k. For some reason, I had miscalculated and gave the person $600 more than what was the current price (So in that situation I gave the person $3,800 rather than $3,200 - something like that).
I caught the mistake about 10 minutes after the transaction, and after the person already had left the transaction location with the extra $600 that I had given to him. Neither of us had intended such a situation, he acknowledged the mistake, and after I repeatedly texted him, and even offered to go to his location to retrieve the $600, he did not do the right thing of returning the $600 to me.
He also began to call me names in what seemed to be a kind of rationalization for him to keep the $600. Anyhow, I consider that person to have been a regular person, and even that he had rationalized in his own head that he was correct to keep the extra $600 that I had given to him (windfall), but I still believe (my assumption that people who you meet in person are usually honest) only a minority of people would have kept the $600 in that particular situation... but the real test remains getting into the situation, and test of character about whether you personally do the right thing when given an opportunity to nearly anonymously profit.
Perhaps I am cynical. But I think the average provider on LocalBitcoins is, how can I put this delicately, statistically less likely to return $600 than the average person in the street.