Your usual sensory information is inadequate data. You’re dealing with that every day. This seems a good starting point to generalize from; brains in vats seem like overkill to approach the question.
Agreed. Brains-in-vats was one of the original questions that I was pondering and the specific questions were narrowed into goofy sensory data. Narrowing that down provided the two scenarios.
Should they act differently ? There’s nothing in the information you’ve provided that seems to break the symmetry in uncertainty, so I’d say no.
What I find interesting is that Bob has more information than Alice but is stuck with the same problem. I found it counter-intuitive that more information did not help provide an action. Is it better to think of Bob as having no more information than Alice?
Adding a memory of Blue to Alice seems like adding information and provides a clear action. Additionally adding a memory of Red removes the clear action. Is this because there is now doubt in the previous information? Or… ?
Should they circle more than one color ? … And other variants—you’ve given no reasons to prefer one outcome to another, so in general we can’t say how they should act.
Why wouldn’t Bob circle both Red and Blue if given the option?
What I find interesting is that Bob has more information than Alice but is stuck with the same problem
Yes, it seems that Bob has more information than Alice.
This is perhaps a good context to consider the supposed DIKW hierarchy: data < information < knowledge < wisdom. Or the related observation from Bateson that information is “a difference that makes a difference”.
We can say that Bob has more data than Alice, but since this data has no effect on how Bob may weigh his choices, it’s a difference that makes no difference.
Is this because there is now doubt in the previous information ?
“Doubt” is data, too (or what Jaynes would call “prior information”). Give Alice a memory of a blue ball, but at the same time give her a reason (unspecific) to doubt her senses, so that she reasons “I recall a blue ball, but I don’t want to take that into account.” This has the same effect as giving Bob conflicting memories.
We can say that Bob has more data than Alice, but since this data has no effect on how Bob may weigh his choices, it’s a difference that makes no difference.
Okay, that makes sense to me.
Give Alice a memory of a blue ball, but at the same time give her a reason (unspecific) to doubt her senses, so that she reasons “I recall a blue ball, but I don’t want to take that into account.” This has the same effect as giving Bob conflicting memories.
Ah, okay, that makes a piece of the puzzle click into place.
In DIKW terms, what happens when we add Blue to Alice? When we later add Red? My hunch is that the label on the data simply changes as the set of data becomes useful or useless.
Also, would anything change if we add “Green” to Bob’s choice list? My guess is that it would because Bob’s memories of Red and Blue are useful in asking about Green. Specifically, there is no memory of Green and there are a memories of Red and Blue.
What I find interesting is that Bob has more information than Alice but is stuck with the same problem. I found it counter-intuitive that more information did not help provide an action. Is it better to think of Bob as having no more information than Alice?
The way you’ve set the question up Bob doesn’t have any more relevant/useful information than Alice. They are both faced with only two apparently mutually exclusive options (red or blue) and you have not provided any information about how the test is scored or why either should have any reason to prefer to answer it over not answering it. Since Bob has two logically inconsistent memories he does not actually have any more relevant information than Alice and so there should not be anything counter-intuitive about the fact that the information doesn’t change his probabilities.
Adding a memory of Blue to Alice seems like adding information and provides a clear action. Additionally adding a memory of Red removes the clear action. Is this because there is now doubt in the previous information? Or… ?
There’s other information implicit in the decision that you are not accounting for. Alice has a set of background beliefs and assumptions, one of which is probably that her memory is generally believed to correlate with true facts about external reality. In the case of discovering logical inconsistencies in her memory she has to revise her beliefs about the reliability of her memory and change how she weights remembered facts as evidence. You can’t just ignore the implicit background knowledge that provides the context for the agents’ decision making when considering how they update in the light of new evidence.
Why wouldn’t Bob circle both Red and Blue if given the option?
You haven’t given enough context for anyone to provide an answer to this question. When confronted with the multiple choice question Bob may come up with a theory about what the existence of this question implies. If he hasn’t been given any specific reason to believe there are any particular rules applied to the scoring of the answer he gives then he will have to fall back on his background knowledge about what kinds of agents might set him such a question and what their motivations and agendas might be. That will play into his decision about how to act.
Agreed. Brains-in-vats was one of the original questions that I was pondering and the specific questions were narrowed into goofy sensory data. Narrowing that down provided the two scenarios.
What I find interesting is that Bob has more information than Alice but is stuck with the same problem. I found it counter-intuitive that more information did not help provide an action. Is it better to think of Bob as having no more information than Alice?
Adding a memory of Blue to Alice seems like adding information and provides a clear action. Additionally adding a memory of Red removes the clear action. Is this because there is now doubt in the previous information? Or… ?
Why wouldn’t Bob circle both Red and Blue if given the option?
Yes, it seems that Bob has more information than Alice.
This is perhaps a good context to consider the supposed DIKW hierarchy: data < information < knowledge < wisdom. Or the related observation from Bateson that information is “a difference that makes a difference”.
We can say that Bob has more data than Alice, but since this data has no effect on how Bob may weigh his choices, it’s a difference that makes no difference.
“Doubt” is data, too (or what Jaynes would call “prior information”). Give Alice a memory of a blue ball, but at the same time give her a reason (unspecific) to doubt her senses, so that she reasons “I recall a blue ball, but I don’t want to take that into account.” This has the same effect as giving Bob conflicting memories.
Okay, that makes sense to me.
Ah, okay, that makes a piece of the puzzle click into place.
In DIKW terms, what happens when we add Blue to Alice? When we later add Red? My hunch is that the label on the data simply changes as the set of data becomes useful or useless.
Also, would anything change if we add “Green” to Bob’s choice list? My guess is that it would because Bob’s memories of Red and Blue are useful in asking about Green. Specifically, there is no memory of Green and there are a memories of Red and Blue.
Interesting.
The way you’ve set the question up Bob doesn’t have any more relevant/useful information than Alice. They are both faced with only two apparently mutually exclusive options (red or blue) and you have not provided any information about how the test is scored or why either should have any reason to prefer to answer it over not answering it. Since Bob has two logically inconsistent memories he does not actually have any more relevant information than Alice and so there should not be anything counter-intuitive about the fact that the information doesn’t change his probabilities.
There’s other information implicit in the decision that you are not accounting for. Alice has a set of background beliefs and assumptions, one of which is probably that her memory is generally believed to correlate with true facts about external reality. In the case of discovering logical inconsistencies in her memory she has to revise her beliefs about the reliability of her memory and change how she weights remembered facts as evidence. You can’t just ignore the implicit background knowledge that provides the context for the agents’ decision making when considering how they update in the light of new evidence.
You haven’t given enough context for anyone to provide an answer to this question. When confronted with the multiple choice question Bob may come up with a theory about what the existence of this question implies. If he hasn’t been given any specific reason to believe there are any particular rules applied to the scoring of the answer he gives then he will have to fall back on his background knowledge about what kinds of agents might set him such a question and what their motivations and agendas might be. That will play into his decision about how to act.