With respect to question 1, Aumann’s Agreement Theorem would require that if they are acting rationally as you stated and with common knowledge, they would have to agree. That being the case, according to the formalism, question 2 is ill-posed.
Your proposed state of affairs could hold if they lack common knowledge (including lack of common knowledge of internal utility functions despite common knowledge of otherwise external facts and including differing prior probabilities). To resolve question 2 in that case you would have to assign probabilities to the various forms that the shared and unshared knowledge could take, to determine which state of affairs most probably prevails. For example, you may use your best estimation and determine that the state of affairs that prevails in Faerie is similar to the state of affairs that prevails in your own world/country/whatever, in which case you should weight the evidence provided by each person similar to how you would rate it if you were surveying your fellow countrymen. This is all fairly abstract because approaching such a thing formally is currently well outside our capabilities.
Thanks. I am of course assuming they lack common knowledge. I understand what you are saying, but I am interested in a qualitative answer (for #2): does the fact they have updated their knowledge according to this meta-reasoning process affect my own update of the evidence, or not?
With respect to question 1, Aumann’s Agreement Theorem would require that if they are acting rationally as you stated and with common knowledge, they would have to agree. That being the case, according to the formalism, question 2 is ill-posed.
Your proposed state of affairs could hold if they lack common knowledge (including lack of common knowledge of internal utility functions despite common knowledge of otherwise external facts and including differing prior probabilities). To resolve question 2 in that case you would have to assign probabilities to the various forms that the shared and unshared knowledge could take, to determine which state of affairs most probably prevails. For example, you may use your best estimation and determine that the state of affairs that prevails in Faerie is similar to the state of affairs that prevails in your own world/country/whatever, in which case you should weight the evidence provided by each person similar to how you would rate it if you were surveying your fellow countrymen. This is all fairly abstract because approaching such a thing formally is currently well outside our capabilities.
Thanks. I am of course assuming they lack common knowledge. I understand what you are saying, but I am interested in a qualitative answer (for #2): does the fact they have updated their knowledge according to this meta-reasoning process affect my own update of the evidence, or not?
I read this as the two consultants being basically rational, but not perfect Bayesians, and not sharing common priors.