Decision analysis, Penrose style

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I appreciated the comments on my recent entry on decision analysis and Schroedinger’s cat.

Some comments

Chris sent some general links, and Simon and Dsquared referred to some specific desicion problems in finance–an area I know nothing about but certainly seems like a place where formal decision analysis would be useful.

Deb referred to the expected value of information (a concept I remember from teaching classes in decision analysis) and wonders why I have to bring quantum mechanics and Roger Penrose into the picture.

Why bring in quantum mechanics?

I bring up quantum mechanics for two reasons. First, making a decision has the effect of discretizing a continuous world. (Just as, in politics, a winner-take-all election converts a divided populace into a unidirectional mandate.) I see a strong analogy here to the collapsing of the wave function. To bring in a different physics analogy, decision-making crystallizes a fluid world into a single frozen choice.

The second connection to quantum mechanics connection arises because decisions are not made in isolation, and when we wait on a decision, it tends to get “entangled” with other decisions, producing a garden of forking paths that is a challenge to analyze. At some point–even, possibly, before the “expected value of additional information” crosses the zero line–decisions get made, or decision-making gets forced upon us, because it’s just to costly for all concerned to live with all the uncertainty. (I wouldn’t say this is true of all decisions or even most decisions, but it can arise, especially I think in decisions which are loosely coupled to other decisions–for example, a business decision that affects purchasing, hiring in other divisions, planning, etc.) This is the Penrose connection–that quantum states (or decisions) get resolved when they are entangled with enough mass.

P.S.

The other thing I learned is that links don’t always work. Chris sent me this link, Simon sent this, and Dsquared sent this. My success: 0/3. 1 broken link and 2 with password required.

6 thoughts on “Decision analysis, Penrose style”

  1. Andrew, your line of reasoning is very interesting and quite consistent with my business experiences. Your notion how the continuous become discete is very astute

  2. AG: Two reasons for applying QM to situation where you need to decide whether and when to act:

    1. discretizing a continuous world

    2. entangling of decisions (Penrose's explanation of Schroedinger's cat)

    Gotcha. That makes sense. But the "binarization of a continuousness " analogy applies to every single decision we ever make. As does the entanglement point, actually.

    There is one other valid reasons for applying QM to DM:

    3. act of measurement can affect "reality"

    If A=action

    B=beliefs

    C=consequences

    decision theory says A=f(B,C)

    But:

    a. C at time 2 is a function of A at time 1.

    b. C=f(A) cognitive dissonance

    c. C=f(B) lemons from lemonade, sour grapes

    d. B=f(C) wishful thinking

    e. B=f(A) cognitive dissonance

    etc.

    So another physics analogy:

    F=ma is a useful approximation even though it ignores friction.

    A "is better than" B iff EU(A)>EU(B) is a useful and dangerous approximation because:

    a. it ignores MUCH more than "friction" AND

    b. the world it represents changes as a function of how it is represented.

    There's that tricky pussycat again.

  3. Ach, of course, it's now copyright Blackwells.

    http://www.cs.unibo.it/~fioretti/ is Fioretti's homepage; I think he says that you can email him for the password if you want it.

    But Chris is dead right; what you're talking about is the decision to exercise an American option. The value of waiting in real options theory is twofold; you have the value of information, plus the value of the possibility that the deal might get better (it might also get worse, but you don't care as much about that since you have the option, not the obligation to do the deal).

    Quantum probability, I think, clouds the issue since the problem here is not so much that the probability is a complex number but that it's a classical probability over an ill-defined information set. I don't think that the imaginary part of the quantum probability maps onto "entangledness" all that well? Although my knowledge of quantum probability is pretty rudimentary so I might be totally wrong.

  4. "The act of measurement interacts with that which is measured."

    Am I missing something or that's a classical Hawthorne effect? (Penrose, OUP edition, rests on my bookshelf, untouched but ready for hours of hard page-turning on the beach).

  5. Francois: Am I missing something or that's a classical Hawthorne effect?

    Excellent point. There are many examples in psychology that have the quantum feature where the act of measuring affects the thing being measured. Hawthorne effect, framing effects, preference reversal and probably others.

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