The memory example is interesting. I now think my rejection of (*) (from my previous comment) was too strong but I haven’t figured out what to make of this more precisely. I feel like there is something valuable to be said about different ways that options can exist or be available and how relevant they are to maximality or other decision rules. I’ve always thought of menus as very unambiguous objects, so this is difficult to wrap my head around. I have more specific thoughts about the example below.
I share your intuition for B being impermissible. Having witnessed B being dominated makes it very hard to say that it would be permissible. I am, however, skeptical of my intuition because it needs to make assumptions that I’m not convinced of.
The situation has two conditions: (1) I’m sure that if I remembered what C was, it would be a valid option at the current situation and that it dominates B. Being sure in this way without knowing what C is requires the situation to be the same in every way that could affect these. (2) I’m unable to generate the same options as the other time. I think this can happen in three ways: (i) the inputs to that generation are different, (ii) the generation process is different or (iii) the generation process is just nondeterministic (or possible to run incompletely). Both (i) and (ii) make fully trusting the similarity of the situation implausible so (iii) must be true to satisfy the conditions. As far as I can tell, for the intuition of deferring to a different run of the process to make sense, these assumptions need to be made:
A common reference menu (not necessarily objective/true) must exist, and the process must sample it.
Knowledge of dominance relations on the reference menu is authoritative over relations on samples of it.
I notice that if I consciously deny these, I don’t get the intuitive verdict.
Another example to test the second assumption in isolation: An undeniably trustworthy oracle tells me that an option exists that would dominate B but not A[1]. My intuitive verdict again is that it would be pretty incredible to take B. I feel this intuition is somewhat weaker than in the memory example but still clear.
I read “an option exists” as it being in my menu (because that is at least intuitively what being an option means) and then give it similar privileges as real options. Thinking about it more critically, I have a hard time accepting objects that I cannot choose to play in my decision rule for my objects of choice. In terms of the assumptions, I take the oracle to have access to relations on the reference menu but I’m still unsure if I’m willing to let those be authoritative.
Or similarly: It is a logical implication of my information. This is the case with mixed options over nowhere-optimal options vs somewhere-uniquely-optimal options.
Thanks for the reply!
The memory example is interesting. I now think my rejection of (*) (from my previous comment) was too strong but I haven’t figured out what to make of this more precisely. I feel like there is something valuable to be said about different ways that options can exist or be available and how relevant they are to maximality or other decision rules. I’ve always thought of menus as very unambiguous objects, so this is difficult to wrap my head around. I have more specific thoughts about the example below.
I share your intuition for B being impermissible. Having witnessed B being dominated makes it very hard to say that it would be permissible. I am, however, skeptical of my intuition because it needs to make assumptions that I’m not convinced of.
The situation has two conditions: (1) I’m sure that if I remembered what C was, it would be a valid option at the current situation and that it dominates B. Being sure in this way without knowing what C is requires the situation to be the same in every way that could affect these. (2) I’m unable to generate the same options as the other time. I think this can happen in three ways: (i) the inputs to that generation are different, (ii) the generation process is different or (iii) the generation process is just nondeterministic (or possible to run incompletely). Both (i) and (ii) make fully trusting the similarity of the situation implausible so (iii) must be true to satisfy the conditions. As far as I can tell, for the intuition of deferring to a different run of the process to make sense, these assumptions need to be made:
A common reference menu (not necessarily objective/true) must exist, and the process must sample it.
Knowledge of dominance relations on the reference menu is authoritative over relations on samples of it.
I notice that if I consciously deny these, I don’t get the intuitive verdict.
Another example to test the second assumption in isolation: An undeniably trustworthy oracle tells me that an option exists that would dominate B but not A[1]. My intuitive verdict again is that it would be pretty incredible to take B. I feel this intuition is somewhat weaker than in the memory example but still clear.
I read “an option exists” as it being in my menu (because that is at least intuitively what being an option means) and then give it similar privileges as real options. Thinking about it more critically, I have a hard time accepting objects that I cannot choose to play in my decision rule for my objects of choice. In terms of the assumptions, I take the oracle to have access to relations on the reference menu but I’m still unsure if I’m willing to let those be authoritative.
Or similarly: It is a logical implication of my information. This is the case with mixed options over nowhere-optimal options vs somewhere-uniquely-optimal options.