This generalizes nicely. The asteroid problem provides a nice partitioning into two pieces, such that either piece alone has no effect, but the two pieces together have an effect. But most problems won’t have such a partition built in.
If we want the answer to a yes/no question, the first instinct would be that no such partitioning is possible: if two AIs each provide less than 1 bit of information, then combining them won’t produce a reliable answer. But we can make it work by combining the yes/no question with some other problem, as follows.
Suppose you want the answer to a question Q, which is a yes-or-no question. Then pick a hard problem H, which is an inconsequential yes-or-no question that AIs can solve reliably, but which humans can’t, and for which P(H)=0.5. Take two AIs X and Y. The first AI outputs X=xor(Q,H), and believes that the second AI will output a coin flip. The second AI outputs Y=H, and believes that the first AI will output a coin flip. Then the answer can be obtained by combining the two outputs, xor(X,Y).
This generalizes nicely. The asteroid problem provides a nice partitioning into two pieces, such that either piece alone has no effect, but the two pieces together have an effect. But most problems won’t have such a partition built in.
If we want the answer to a yes/no question, the first instinct would be that no such partitioning is possible: if two AIs each provide less than 1 bit of information, then combining them won’t produce a reliable answer. But we can make it work by combining the yes/no question with some other problem, as follows.
Suppose you want the answer to a question Q, which is a yes-or-no question. Then pick a hard problem H, which is an inconsequential yes-or-no question that AIs can solve reliably, but which humans can’t, and for which P(H)=0.5. Take two AIs X and Y. The first AI outputs X=xor(Q,H), and believes that the second AI will output a coin flip. The second AI outputs Y=H, and believes that the first AI will output a coin flip. Then the answer can be obtained by combining the two outputs, xor(X,Y).
Interesting generalisation.
The next step is to allow more interaction between AI and world, while still minimising impact safely…