If I (the builder/writer) really couldn’t decide which mathematical intuition function to use, then the agent won’t come to exist in the first place.
You don’t pick the output of mathematical intuition in a particular case, mathematical intuition is a general algorithm that works based on world programs, outcomes, and your proposed decisions. It’s computationally intensive, its results are not specified in advance based on intuition, on the contrary the algorithm is what stands for intuition. With more resources, this algorithm will produce different probabilities, as it comes to understand the problem better. And you just pick the algorithm. What you can say about its outcome is a matter of understanding the requirements for such general algorithm, and predicting what it must therefore compute. Absolute certainty of the algorithm, for example, would imply that the algorithm managed to logically infer that the outcome would be so and so, and I don’t see how it’s possible to do that, given the problem statement. If it’s unclear how to infer what will happen, then mathematical intuition should be uncertain (but it can know something to tilt the balance one way a little bit, perhaps enough to decide the coordination problem!)
There is a single ideal mathematical intuition, which, given a particular amount of resources, and a particular game, determines a unique function M mapping {inputs} x {outputs} x {execution histories} --> [0,1] for a UDT1 agent in that game. This ideal mathematical intuition (IMI) is defined by the very nature of logical or mathematical inference under computational limitation. So, in particular, it’s not something that you can talk about choosing using some arbitrary tie-breaker like lexicographic order.
Now, maybe the IMI requires that the function M be binary in some particular game with some particular amount of resources. Or maybe the IMI requires a non-binary function M for all amounts of computational resources in that game. Unless you can explain exactly why the IMI requires a binary function M for this particular game, you haven’t really made progress on the kinds of questions that we’re interested in.
More or less. Of course there is no point in going for a “single” mathematical intuition, but the criteria for choosing one shouldn’t be specific to a particular game. Mathematical intuition primarily works with the world program, trying to estimate how plausible it is that this world program will be equivalent to a given history definition, under the condition that the agent produces given output.
You don’t pick the output of mathematical intuition in a particular case, mathematical intuition is a general algorithm that works based on world programs, outcomes, and your proposed decisions. It’s computationally intensive, its results are not specified in advance based on intuition, on the contrary the algorithm is what stands for intuition. With more resources, this algorithm will produce different probabilities, as it comes to understand the problem better. And you just pick the algorithm. What you can say about its outcome is a matter of understanding the requirements for such general algorithm, and predicting what it must therefore compute. Absolute certainty of the algorithm, for example, would imply that the algorithm managed to logically infer that the outcome would be so and so, and I don’t see how it’s possible to do that, given the problem statement. If it’s unclear how to infer what will happen, then mathematical intuition should be uncertain (but it can know something to tilt the balance one way a little bit, perhaps enough to decide the coordination problem!)
Okay, I understand you to be saying this:
There is a single ideal mathematical intuition, which, given a particular amount of resources, and a particular game, determines a unique function M mapping {inputs} x {outputs} x {execution histories} --> [0,1] for a UDT1 agent in that game. This ideal mathematical intuition (IMI) is defined by the very nature of logical or mathematical inference under computational limitation. So, in particular, it’s not something that you can talk about choosing using some arbitrary tie-breaker like lexicographic order.
Now, maybe the IMI requires that the function M be binary in some particular game with some particular amount of resources. Or maybe the IMI requires a non-binary function M for all amounts of computational resources in that game. Unless you can explain exactly why the IMI requires a binary function M for this particular game, you haven’t really made progress on the kinds of questions that we’re interested in.
Is that right?
More or less. Of course there is no point in going for a “single” mathematical intuition, but the criteria for choosing one shouldn’t be specific to a particular game. Mathematical intuition primarily works with the world program, trying to estimate how plausible it is that this world program will be equivalent to a given history definition, under the condition that the agent produces given output.