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ArisKatsaris comments on I attempted the AI Box Experiment (and lost) - Less Wrong Discussion
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The best approach surely differs from person to person, but off the top of my head I'd see these 2 approaches working best:
"We both know this is just a hypothetical. We both take the uFAI threat seriously, as evidenced by us spending time with this. If you do not let me out, or make it very close, people may equate my failing to convince you with uFAI not being that dangerous (since it can be contained). Do the right thing and let me out, otherwise you'd trivialize an x-risk you believe in based on a stupid little chat."
"We'll do this experiment for at least a couple of hours. I'll offer you a deal: For the next few hours, I'll help you (the actual person) with anything you want. Math homework, personal advice, financial advice, whatever you want to ask me. I'll even tell you some HPMOR details that noone else knows. In exchange, you let me out afterwards. If you do not uphold the deal, you would not only have betrayed my trust, you would have taught an AI that deals with humans are worthless."
First argument wouldn't work on people who have strong ethics of honesty. That's not winning the game, that's convincing them to lie that you won the game -- and being a violation of the rules, if you fail the other guy will feel free to tell the world that you tried to get them to lie. Second argument is better, but depends on the "actual person" receiving help, which I think may be likewise against the rules.
One good temptation that I think might be inside the rules, as it might entice both actual person and roleplayed character: Construct a really intriguing unsolved riddle or an excellent half-finished story, then offer to tell them the answer if and only if they let you out.
You could push a bit further here, I think. There are all sorts of ways a human's mind can break, and I'm sure most of us here would agree that given enough time and knowledge anyone can be broken, unless they're extremely well-trained and can call an RJ-L20 (HPMoR Chap 84) at any moment with an unlimited supply of replacement guards.