against the Dutch book argument

In continuation of the previous post, here are my slides for this afternoon talk at the 4th BFF conference (with nothing against Dutch people of course!, or anyone actually since this is a “best friends forever” conference):

5 Responses to “against the Dutch book argument”

  1. We should not forget Sir Ronald Fisher. ..a champion of anti-Decision Theory in (whatever he understands as) “scientific “”truth”” “.

    I read him stating that “decision theory fits shoemakers, not scientists”….like 30 years ago. …

    I never found this paper of him again.

    Does anybody know this paper or at least the quote.

    I never understood why he had such a special antipathy against shoe repairers. …

    But then I read about his trouble finding new shoes in Paris and giving such a hard time to his host (Borel ?)…

    Vive la préférence !
    (pas toujours separable de l’opinion. ..see Herman Rubin )

    and Fishburn

  2. I will write with more detail later.
    But I can´t see the point of spanking
    the (gambling nature) of Dutch book arguments.
    because, (1) adding a bit of generality, it´s to derogate
    Utility theories , which in turn are coherently (ah ah) derived
    within pure Set Theory (no money involved).
    And (2), unless there are different definitions fo “coherence”,
    i.e., different *concepts* (not just different presentations) ,
    we are talking about pedagogical tools, nothing else.
    See DeFinetti´s 1931 paper on “gambling”.
    Regards,

    sergio

  3. Jaynes also derogates the Dutch book approach for contaminating (what is to him) foundations for the formal basis for scientific reasoning with gambling and financial gain. My Bayesian roots are Jaynesian but over time I’ve come to a greater appreciation for Dutch book arguments; those who prefer to ground the Bayesian approach in admissibility and decision theory are not so far away from Dutch book arguments as might initially be supposed. If we’re willing to say that a loss function exists (or equivalently, that a utility function exists) then the issue of paying off in dollars is easily dealt with by instead supposing that payoff is linear in utility. As to the framing of the argument in terms of gambling, one notes the truism that getting dressed in the morning and walking out the front door is a gamble in some sense; it’s impossible in life (even in scientific research) to avoid weighing up the expected risks and rewards of various possible courses of action. Since we can’t avoid gambling in this sense, it seems to me to be a very minimal requirement that our choices not expose us to the possibility of sure loss.

    • Thanks, Corey. I did not know about Jaynes’ positions on the Dutch book. What I found hard to understand while preparing the discussion is that the criticism would bear on admissible and possibly Bayes estimators, which should be “safe” from such criticisms. My conclusion was that this approach switches from one loss function to another, which may be reductive wrt the authors really mean.

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