Nicht Sehr Gut29 July 2008
I have been reading Gut Feelings: The Intelligence of the Unconscious by Gerd Gigerenzer. Gut Feelings seeks to explain — and in large part to vindicate — some of the processes of intuïtive thinking.
Years ago, I became something of a fan of Gigerenzer when I read a very able critique that he wrote of some work by Kahneman and Tversky. And there are things in Gut Feelings that make it worth reading. But there are also a number of active deficiencies in the book.
Gigerenzer leans heavily on undocumented anecdotal evidence, and an unlikely share of these anecdotes are perfectly structured to his purpose.
Gigerenzer writes of how using simple heuristics in stock-market investment has worked as well or better than use of more involved models, and sees this as an argument for the heuristics, but completely ignores the
efficient-markets hypothesis. The efficient-markets hypothesis basically says that, almost as soon as relevant information is available, profit-seeking arbitrage causes prices to reflect that information, and then there isn't much profit left to be made, except by luck — unpredictable change. (And one can lose through such change as easily as one might win.) If this theory is correct, then one will do as well picking stocks with a dart board as by listening to an investment counselor. In the face of the efficient-markets hypothesis, the evidence that he presents might simply illustrate the futility of any sort of deliberation.
Gigerenzer makes a point of noting where better decisions seem often to be made by altogether ignoring some information, and provides some good examples and explanations. But he fails to properly locate a significant part of the problem, and very much appears to mislocate it. Specifically, a simple, incorrectly-specified model may predict more accurately that a complex, incorrectly-specified model. Gigerenzer (who makes no reference to misspecification) writes
In an uncertain environment, good intuitions must ignore information
but uncertainty (as such) isn't to-the-point; the consequences of misspecification are what may justify ignoring information. It's very true that misspecification is more likely in the context of uncertainty, but one system which is intrinsically less predictable than another may none-the-less have been better specified.
I am very irked by the latest chapter that I've read,
Why Good Intuitions Shouldn't Be Logical. In note 2 to this chapter, one reads
Tversky and Kahneman, 1982, 98. Note that here and in the following the term logic is used to refer to the laws of first-order logic.
The peculiar definition has been tucked behind a bibliographical reference. Further, the notes appear at the end of the volume (rather than as actual foot-notes), And this particular note appears well after Gigerenzer has already begun using the word
logic (and its adjectival form) baldly. If Gigerenzer didn't want to monkey dance, then he could have found an better term, or kept
logic (and derivative forms) in quotes. As it is, he didn't even associate the explanatory note with the chapter title.
Further, Gigerenzer again mislocates errors. Kahneman and Tversky (like many others) mistakenly thought that natural language
probable simply map to logical conjunction, logical disjunction, and something-or-another fitting the Kolmogorov axiomata; they don't. Translations that presume such simple mappings in fact result in absurdities, as when
She petted the cat and the cat bit her.
is presumed to mean the same thing as
The cat bit her and she petted the cat.
because conjunction is commutative. Gigerenzer writes as if the lack of correspondence is a failure of the formal system, when it's instead a failure of translation. Greek
δε should sometimes be translated
and, but not always, and vice versa; likewise,
∧ shouldn't always be translated as
and nor vice versa. The fact that such translations can be in error does not exhibit an inadequacy in Greek, in English, nor in the formal system.
first-order logic refers not to a comprehensive notion of abstract principles of reasoning, but to a limited formal system. Perhaps the simplest formal system to be called a
logic is propositional logic, which applies negation, conjunction, and disjunction to propositions under a set of axiomata. First-order logic adds quantifiers (
for some) and rules therefor to facilitate handling propositional functions. Higher-order logics extend the range of what may be treated as variable.
That is to say that