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V_V comments on JFK was not assassinated: prior probability zero events - Less Wrong
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The oracle can infer that there is some back channel that allows the message to be transmitted even it is not transmitted by the designated channel (e.g. the users can "mind read" the oracle). Or it can infer that the users are actually querying a deterministic copy of itself that it can acausally control. Or something.
I don't think there is any way to salvage this. You can't obtain reliable control by planting false beliefs in your agent.
I am not planting false beliefs. The basic trick is that the AI only gets utility in worlds in which its message isn't read (or, more precisely, in worlds where a particular stochastic event happens, which would almost certainly erase the message before reading). It's fully aware that in most worlds, its message is read; it just doesn't care about those worlds.
But in the real world the stochastic event that determines whether the message is read has a very different probability than what you make the AI think it has, therefore you are planting a false belief.
It may care about worlds where the message doesn't meet your technical definition of having been read but nevertheless influences the world.
If I'm understanding Stuart's proposal correctly, the AI is not deceived about how common the stochastic event is. It's just made not to care about worlds in which it doesn't happen. This is very similar in effect to making it think the event is common, but (arguably, at least) it doesn't involve any false beliefs.
(I say "arguably" because, e.g., doing this will tend to make the AI answer "yes" to "do you think the event will happen?", plan on the basis that it will happen, etc., and perhaps making something behave exactly as it would if it believed X isn't usefully distinguishable from making it believe X.)
The problem is that the definition of the event not happening is probably too strict. The worlds that the AI doesn't care about don't exist its decision-making purposes, and in the world that the AI cares about, the AI assigns high probability to hypotheses like "the users can see the message even before I send it through the noisy channel".