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.

Reacting to Inadequate Data

by MrHen 1 min read18th Dec 200921 comments

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Two Scenarios

Alice must answer the multiple-choice question, "What color is the ball?" The two choices are "Red" and "Blue." Alice has no relevant memories of The Ball other than she knows it exists. She cannot see The Ball or interact with it in any way; she cannot do anything but think until she answers the question.

In an independent scenario, Bob has the same question but Bob has two memories of The Ball. In one of the memories, The Ball is red. In the other memory, The Ball is blue. There are no "timestamps" associated with the memories and no way of determining if one came before the other. Bob just has two memories and he, somehow, knows the memories are of the same ball.

If you were Alice, what would you do?

If you were Bob, what would you do?

Variations

More questions to ponder:

  • Should they do anything at all?
  • Should Alice and Bob act differently?
  • If Alice and Bob could circle more than one color, should they?
  • Would either answer change if the option "Green" was added to the choice list?
  • If the question was fill-in-the-blank, what should they write?
  • If Bob's memories were of different balls but he didn't know which ball was The Ball, should his actions change?
  • If Alice and Bob could coordinate, should it affect their answers?

Further Discussion

The basic question I was initially pondering was how to resolve conflicting sensory inputs. If I were a brain in a vat and I received two simultaneous sensory inputs that conflicted (such as the color of a ball), how should I process them?

Another related topic is whether a brain in a vat with absolutely no sensory inputs should be considered intelligent. These two questions were reduced into the above two scenarios and I am asking for help in resolving them. I think they are similar to questions asked here before but their relation to these two brain-in-a-vat questions seemed relevant to me.

Realistic Scenarios

These scenarios are cute but there are similar real-world examples. When asked if a visible ball was red or green and you happened to be unable to distinguish between red and green, how do you interpret what you see?

Abstracting a bit, any input (sensory or otherwise) that is indistinguishable from another input can really muck with your head. Most optical illusions are tricks on eye-hardware (software?).

This post is not intended to be clever or teach anything new. Rather, the topic confuses me and I am seeking to learn about the correct behavior. Am I missing some form of global input theory that helps resolve colliding inputs or missing data? When the data is inadequate, what should I do? Start guessing randomly?

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