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the independence of the two factors in the value of information

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  • Jim Davies
    I m teaching decision making now, and the students have this question about information value that I m having trouble answering. RN2 p602 says that information
    Message 1 of 2 , Jan 27, 2006
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      I'm teaching decision making now, and the students have this question
      about information value that I'm having trouble answering.

      RN2 p602 says that information has value to the extent that it is
      likely to cause a chagne of plan and to the extent that the new plan
      will be significantly better than the old plan. Are these independent?

      I'm trying to come up with a intuitive example of this, and I'm having
      trouble coming up with a situation in which the information is
      unlikely to affect your decision, but the information might result in
      a significantly better decision.

      I came up with the idea of buying a DVD player, choosing between going
      to get it at best buy (A) and circuit city (B). The information in
      question is the exact prices at these stores. The agent knows the
      price ranges.

      Situation 1:
      A: $10-80
      B: $15-98

      In this case, it's likely to affect your decision and you could save a
      lot of money because of it. The information is worth most in this case.

      Situation 2:
      A: $48-51
      B: $49-53

      It's likely to affect your decision, but the difference is not big, so
      the decision doesn't really matter, so the information is not worth as
      much.

      Situation 3:
      A: $30-50
      B: $48-60

      Unlikely to affect decision, because A is so much more likely to be
      cheaper, AND the price ranges are so close that you don't save much
      money. Information worth the least in this case.

      Situation 4:
      A: ??
      B: ??

      I want an example in which it's unlilkely to affect your decision but
      the decision could be significantly better given the information. I
      was thinking
      A: $10-51
      B: $68-98
      but it seems with such a little overlap it's hard to say that the
      change in decision will be important. How can it not affect your
      decision and also result in a significantly better outcome?

      Or am I thinking about this in the wrong way?
    • The Geek
      It s not really about whether or not the information would change your decision, it s that the answer is **unlikely** to change your decision. It s tough to
      Message 2 of 2 , Jan 29, 2006
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        It's not really about whether or not the information
        would change your decision, it's that the answer is
        **unlikely** to change your decision. It's tough to
        illustrate when you have a pretty flat probability
        distribution as implied by your DVD example.

        Instead try this:

        Harry's Bargain Electronics sells the DVD players for
        $99, but they're running a special promotion where
        every 1000th customer who buys one gets it for free.
        Crazy Ron's sells the same DVD player for $50, but
        everyone has to pay. In this example the
        "information" is whether or not you would be one of
        the lucky customers at Harry's to get it for free.

        Madame Trelawney the psychic is able to tell you with
        100% certainty whether or not you will be one of the
        lucky ones to get a freebie if you buy from Harry's.
        How much would you pay her for that knowledge?

        While the information could cause a significant
        difference in the relative expected values of the two
        choices ($99-$50 vs. $0-$50), it's **unlikely** that
        you're going to get a freebie, so the information
        itself isn't terribly valuable. It's **very**
        valuable **if** you're going to be the winner. But,
        999 times out of 1000 you'll find out you're not going
        to be a winner. In that case you'd just go to Crazy
        Ron's, which is the same decision you'd make without
        the information.

        Rob G.


        --- Jim Davies <jim.davies@...> wrote:

        > I'm teaching decision making now, and the students
        > have this question
        > about information value that I'm having trouble
        > answering.
        >
        > RN2 p602 says that information has value to the
        > extent that it is
        > likely to cause a chagne of plan and to the extent
        > that the new plan
        > will be significantly better than the old plan. Are
        > these independent?
        >
        > I'm trying to come up with a intuitive example of
        > this, and I'm having
        > trouble coming up with a situation in which the
        > information is
        > unlikely to affect your decision, but the
        > information might result in
        > a significantly better decision.
        >
        > I came up with the idea of buying a DVD player,
        > choosing between going
        > to get it at best buy (A) and circuit city (B). The
        > information in
        > question is the exact prices at these stores. The
        > agent knows the
        > price ranges.
        >
        > Situation 1:
        > A: $10-80
        > B: $15-98
        >
        > In this case, it's likely to affect your decision
        > and you could save a
        > lot of money because of it. The information is worth
        > most in this case.
        >
        > Situation 2:
        > A: $48-51
        > B: $49-53
        >
        > It's likely to affect your decision, but the
        > difference is not big, so
        > the decision doesn't really matter, so the
        > information is not worth as
        > much.
        >
        > Situation 3:
        > A: $30-50
        > B: $48-60
        >
        > Unlikely to affect decision, because A is so much
        > more likely to be
        > cheaper, AND the price ranges are so close that you
        > don't save much
        > money. Information worth the least in this case.
        >
        > Situation 4:
        > A: ??
        > B: ??
        >
        > I want an example in which it's unlilkely to affect
        > your decision but
        > the decision could be significantly better given the
        > information. I
        > was thinking
        > A: $10-51
        > B: $68-98
        > but it seems with such a little overlap it's hard to
        > say that the
        > change in decision will be important. How can it not
        > affect your
        > decision and also result in a significantly better
        > outcome?
        >
        > Or am I thinking about this in the wrong way?
        >
        >
        >
        >
        >
        >
        >


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