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Morendil comments on Reacting to Inadequate Data - Less Wrong
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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.