Statistician Dennis Lindley wrote a book called “Making Decisions” which included the stunningly-arrogant sentence: “The main conclusion [of this book] is that there is essentially only one way to reach a decision sensibly.” He justifies this outrageous claim, contrary to all human experience and a moment’s reflection, by saying that, “any deviation from the precepts is liable to lead the decision-maker into procedures which are demonstrably absurd — or as we shall say, incoherent.” (page vii, second edition, 1985). There follows an account of maximum-expected utility decision theory, which is justified in the standard way using Dutch Book arguments (considerations of certain infinite gambles).

I have never trusted these Dutch Book arguments, first because we all live in a finite world, and so games in which one party is guaranteed to win after an infinitely-large time strike me as games selling pie-in-the-sky. Everyone is rich eventually when investing in a Ponzi scheme, also. And second, gambling is such a socially- and culturally-embedded practice that I cannot possibly conceive how it could be used to justify decision-making procedures claiming universal validity. (For a start, to gamble you need to believe that events in the universe are not pre-determined, something which perhaps half of humanity does not currently believe.) The statistician Cosma Shalizi over at Three-Toed Sloth has a nice parody of the advice of decision-theory ideologues here.

A: Hey, you over there, the one walking! You’re doing it wrong.
B: Excuse me?
A: You’re only using two feet! You should keep at least three of your six in contact with the ground at all times.
B: …
A: Look, it’s easily proved that’s the optimal way to walk. Otherwise you’d be unstable, and if you were walking past a Dutchman he could kick one of your legs with his clogs and knock you over and then lecture you on how to make pancakes.
B: What? Why a Dutchman?
A: You can’t trust the Dutch, they’re everywhere! Besides, every time you walk it’s really just like running the gauntlet at Schiphol.
B: It is?
A: Don’t change the subject! Walking like that you’re actually sessile!
B: I don’t seem to be rooted in place…
A: It’s a technical term. Look, it’s very simple, these are all implications of the axioms of the theory of optimal walking and you’re breaking them all. I can’t get over how immobile you are, walking like that.
B: “Immobile”?
A: Well, you’re not walking properly, are you?
B: Your theory seems to assume I have six legs.
A: Yes, exactly!
B: I only have two legs. It doesn’t describe what I do at all.
A: It’s a normative theory.
B: For something with six legs.
A: Yes.
B: I have two legs. Does your theory have any advice about how to walk on two legs?
A: Could you try crawling on your hands and knees?

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