When do you think Clippy is planning to start defecting?
If Clippy decides the same way as I do, then I expect he starts defecting at the same turn as I do. The result is 100x C,C. There is no way how identical deterministic algorithms with the same input can result in different outputs, so in each turn, C,C or D,D are the only possibilities. It’s rational to C.
However, “realistic” Clippy uses different algorithm which is unknown to me. Here I genuinely don’t know what to do. To have some preference to choose C over D or conversely, I would need at least some rough prior probability distribution on the space of all possible decision algorithms suitable for Clippy. But I can hardly imagine such a space.
Reminds me a bit the problem of two envelopes where you know that one of them has 10 times greater amount of money than the second, but otherwise these amounts are random. (V.Nesov, do you know the canonical name of this paradox?) You open the first, find some amount, and then have to choose between accepting it or taking the second envelope. You cannot resolve that without having some idea about what “random” here means, how the amounts of money were distributed into the envelopes. If you don’t know anything about the process, you face questions like “what is the most natural probability distribution on the interval (0,\infty)?”, that I don’t know how to answer.
Anyway, I think these dilemmas are typical illustration of insufficient information for any rational decision. Without information any decision is ruled by bias.
Actually, there is something you can do to improve the outcome over always accepting or always switching, without knowing the distribution of money.
All you need to do is define your probability of switching according to some function that decreases as the amount of money in the envelope increases. So for example, you could switch with probability exp(-X), where X is the amount of money in the envelope you start with.
Of course, to have an exactly optimal strategy, or even to know how much that general strategy will benefit you, you would need to know more about the distribution.
Zubon,
When do you think Clippy is planning to start defecting?
If Clippy decides the same way as I do, then I expect he starts defecting at the same turn as I do. The result is 100x C,C. There is no way how identical deterministic algorithms with the same input can result in different outputs, so in each turn, C,C or D,D are the only possibilities. It’s rational to C.
However, “realistic” Clippy uses different algorithm which is unknown to me. Here I genuinely don’t know what to do. To have some preference to choose C over D or conversely, I would need at least some rough prior probability distribution on the space of all possible decision algorithms suitable for Clippy. But I can hardly imagine such a space.
Reminds me a bit the problem of two envelopes where you know that one of them has 10 times greater amount of money than the second, but otherwise these amounts are random. (V.Nesov, do you know the canonical name of this paradox?) You open the first, find some amount, and then have to choose between accepting it or taking the second envelope. You cannot resolve that without having some idea about what “random” here means, how the amounts of money were distributed into the envelopes. If you don’t know anything about the process, you face questions like “what is the most natural probability distribution on the interval (0,\infty)?”, that I don’t know how to answer.
Anyway, I think these dilemmas are typical illustration of insufficient information for any rational decision. Without information any decision is ruled by bias.
Actually, there is something you can do to improve the outcome over always accepting or always switching, without knowing the distribution of money.
All you need to do is define your probability of switching according to some function that decreases as the amount of money in the envelope increases. So for example, you could switch with probability exp(-X), where X is the amount of money in the envelope you start with.
Of course, to have an exactly optimal strategy, or even to know how much that general strategy will benefit you, you would need to know more about the distribution.