clearing the table

Yesterday, we lined up things for Gigerenzer’s first shot.

Okay, to briefly reprise – although to follow this post, you will have to read yesterday’s post: Tversky and Kahnman claim to have shown a pattern of illogical response to problems that transform sets into the language of probability. The conjunction problem, or what’s wrong with Linda, was one of those conundrums.

Here’s the problem as T and K present it:

Linda is 31, outgoing, single. She majored in philosophy in college. As a student she was deeply concerned with issues of discrimination.

Which of the two alternatives is more probable:

Linda is a bank teller
Linda is a bank teller and is active in the feminist movement?

The b is, as Gigerenzer points out, rather like the question Piaget posed to children: here is a picture of flowers, 6 of which are daisies and four of which are not. Are there more daisies or flowers in the picture? In the Piaget case, by the time children are eight, they recognize that the daisies are flowers, and that the confusing thing in the question is really that it makes it falsely appear like daisies are categorially equal to flowers, instead of a subset of them. (well, they realize this in child-brain speech, as in, that’s a trick question). But T and K consistently found that college students would chose b. So what gives?

“I argue that the irrationality is not to be found in adult reasoning but in the logical norm. Consider what the norm is: the probability of an event A is larger than (or equal to) the probability of the events A and B, that is, p(A) > P(AAB). This conjunction rule is used as a
content-blind norm for judgment: the content of the As and Bs is not considered relevant to evaluating good reasoning. All that counts is the mathematical probability p and the logical '^ and correct judgment is attested when people use the English terms probable and and in this and
only this way. This amounts to a purely syntactic definition of rational reasoning, and therefore, of an error in judgment.”

Putting his money on the table, so to speak, Gigerenzer rearranges T and K’s question to this one:

“Consider the following version of the Linda problem. Here the polysemy of the word probable is eliminated by using the phrase how many:

There are 100 persons who fit the description above (that is, Linda's). How many of them are:

Bank tellers?

Bank tellers and active in the feminist movement? '^

This change is sufficient to make the apparently stable cognitive illusion largely disappear. In one experiment, every single participant answered that there are more bank tellers {Hertwig and Gigerenzer, 1999; for similar results see Fiedler, 1988; Tversky and Kahneman, 1983). The
experiment also showed that the majority of participants interpreted how many in the sense of mathematical probability, but more probable as meaning "possible," "conceivable," or one of the other nonmathematical meanings listed in the OED.”

If Gigerenzer is right, he is onto something major – like, Meno style major. Like, maybe education is actually possible – confounding the cynics among you. Alas, T and K have tinkered with rephrasing the question in terms of “how many,” discovering that simply changing the b phrase slightly (to “bank tellers and active feminists”) can again dramatically change the responses.

All of which leads Gigerenzer to ask whether the problem, here, is that T and K are abstracting the mind from our ecology. This is how the Great G puts it:

“What have we learned from some 20 years and hundreds of experiments on the conjunction fallacy? We have leamed more about the limits of logic as norms than about the workings of the mind. In fact, I do not know of any new Insight that this activity has produced. Logical norms distract us from understanding intelligent behavior.”

At this point, LI is tempted to go down the trail, shooting up the Bush age obsession with testing as education, and the foreseeable result (further cretinization of a vulnerable population) by the No Child having anything to think with but their Behind Act. But we will simply lay down a marker for future reference.

To return, however. Our topic, in our last post, was supposed to be the individual, considered as an autonomous thing – the person, in short. Since Kant – at least, that is how the intellectual history story goes, but in actuality Kant simply codified what was in the child-speak of the Western mass mind for a long time – we’ve operated on the assumption that the autonomy of the individual is the bedrock of ethics. Philosophy’s safecrackers – Schopenhauer, Nietzsche, Freud, Heidegger, etc, etc – have found it pretty easy to break into that concept and show up its flaws, just as Marx found it easy to point to the historical trajectory of class interest that produces the “character mask” of the subject under capitalism. Old Kant’s original formulation of the autonomy thesis is notably eccentric, since it excludes the sensibility – the animal collective that howls around the noumenal X that we proudly bear through our trials and temptations. While Gigerenzer is no overt Kantian, his theory does lend credence to the idea that the sensibility can, indeed, breach our autonomy – or, to put it another way, that the way in which we perceive things is so framed by elements given by the sensibility that “logical norms distract us from intelligent behavior.” To illustrate which, Gigerenzer cites a psychological experiment created from a cliché:

“Consider an experiment in which a full glass of water and an empty glass are put in front of a participant (Sher and McKenzie, 2003). The experimenter asks the participant to pour half of the full glass into the other glass, and then asks the participant to hand him the half empty glass. Which one does the participant pick? Most people picked the previously full glass. When they were asked, however, to hand over the half-full glass, most participants picked the previously empty one. This experiment reveals that the two statements are not pragmatically equivalent (see also McKenzie and Nelson, 2003). People extract surplus information from the framing of the question, and this surplus information concems the dynamics or history of the situation, which helps to guess what is meant.”

Okay, one more post on this topic, tomorrow.


et alia said…
Hrm...If I understand the scenarioes presented (which I may not), I think I've noticed this phenomenon before. A person is given two formally equivalent tasks/problems and performs one of them correctly, but the other not.

An example I've noticed with musicians: ask a musician to play a given piece in a different key than the one they're playing it in. A decent musician can usually do this with no problems. Formally, this is equivalent to being able to do addition modulo 12 in quickly your head. But how many musicians, even after an explanation, could easily calculate that 7 + 7 mod 12 is 3?

I'm not sure if I understand your point about education: do you mean that people have many latent skills (like the musicians I mentioned), and that education, as the identification and making manifest of these latent skills, is possible? I agree 100% with that. It seems to me that education in this country (and likely most other Western nations) is nothing but selection. Bad for the kids; bad for the future.
et alia said…
Argh. 7 + 7 mod 12 is 2. . . . .
roger said…
I like this sentence -- "I'm not sure if I understand your point about education: do you mean that people have many latent skills (like the musicians I mentioned), and that education, as the identification and making manifest of these latent skills, is possible?" "Skills" is too specialized a term -- what I really mean is that the division between acts and information is artificial. The talk about frames that is very popular at the moment contains a truth and a misconception -- yes, people are moved to respond in a given way due to a given frame -- but no, the frame doesn't have a special status outside of a set of actions. Meaning that the information one absorbs from framing, say, the Linda scenario shouldn't lead us to automatically think that there is a cognitive, evolved mismatching between the brain probability problems -- as T. and K. claim -- but simply that information can be misleading if it isn't sorted in such a way that the output you want isn't indicated in the problem you present, when you are presenting that problem to information absorbing creatures. And this, I think, is educationally interesting, insofar as it leads one from inferring solely from the output to the way of presenting the problem. I'm no educator, but when I did teach classes in philosophy, I noticed that the selection of information I got from the class by asking a question and calling on a raised hand was a skewed one -- it would often lead me to keep presenting the problem in the wrong way. So I started taking my own samples -- I'd ask x the question, whether x raised his hand or not.
This made it hard for students -- like any herd animal, they depended on a pack leader -- and it made it harder for me -- like any predator, I depended on the herd being organized by pack leaders. But I felt that if I got better at doing that kind of feedback work, I'd get better at educating the students. Gigerenzer's samples make me think I was on the right track.

Although -- for all of that, T and K's work is still groundbreaking, and Gigerenzer is ungracious about that.