Dope

LI moves slowly but surely � admittedly, sometimes we go off the track all together, but it is all in the interest of the Grand Plan. Not to worry, gents and ladies. Our consideration of Bishop Butler, in the next to the last post, was meant to tie in to the our criticism of Christopher Hitchens � hard as that may be to see.

What Butler�s Analogy has to do with the upcoming war in Iraq, or at least the arguments that are being made about it in the American and English press, will become clear in good time.

Let�s go back to the Butler quote, with its play on likelihood. What Butler is doing here is at the heart of one of the great controversies about probability. Is probability about events themselves, or is it a measure of the observer�s consciousness of events? Is it true that, in some non-subjective sense, tomorrow�s sunrise will be like today�s � insofar as it is a sunrise? Are conditions of identity dependent on a likeness of events in nature, or is this likeness merely the impression of an observer that is unconsciously projected onto nature? The latter question is complicated by the slight bias infiltrated into the problem by the word �nature� � as if the consciousness itself were somehow extra-natural. Let�s naturalize the consciousness � by fiat � and make it this question: is there something in the consciousness that makes likenesses, or does it make sense to say that even for sunsets that are not observed, one is like the other?

This is the question posed by the work of Kahneman and Amos Tversky. In 1998, when Tversky died, the editors of Cognitive Psychology brought together a special issue in his honor, that has some interesting essays � although not, alas, available on the web. We�d especially recommend Eldar Shafir�s overview of Tversky�s work. He introduces it adducing four axioms of probability theory:

�The normative approach to probabilistic reasoning is constrained by the
same rules that govern the classical, set-theoretic conception of probability.
Probability judgments are said to be �coherent�, if and only if they satisfy
some simple conditions: (1) no probabilities are negative, (2) the probability
of a tautology is 1, (3) the probability of a disjunction of two logically exclusive
statements equals the sum of their respective probabilities, and (4) the
probability of a conjunction of two statements equals the probability of the
first assuming that the second is satisfied, times the probability of the second.�

The reason the emphasis is on normativity, here, is that Kahneman and Tversky were concerned with how closely the assumptions of utility theory, which depend upon judgments of probability in order to calculate the maximum benefits attendent upon actions, correlate to what we know about how human beings really do form Bishop Butler�s likenesses. This, in turn, provides a nice twist in the debate between the psychological school of probability and the realist school. What Kahneman and Tversky demonstrated is that people make judgments of probability based on the way the likeness situation is framed. Here�s how Shafir puts it:

�Consider a set of propositions each of which a person judges to be
true with a probability of .90. If the person is right about 90% of these, then
the person is said to be well calibrated. If she is right less or more than 90%,
then she is said to be overconfident or underconfident, respectively.
A great deal of empirical work initiated by Tversky and Kahneman has
documented systematic discrepancies between the normative requirements
of probabilistic reasoning and the ways in which people reason about frequencies
and likelihoods. In settings where the relevance of simple probabilistic
rules is made transparent, subjects often reveal appropriate statistical
intuitions. Thus, for example, when a sealed description is pulled at random
out of an urn that is known to contain the descriptions of 30 lawyers and
70 engineers, people estimate the probability that the description belongs to
a lawyer at .30, in line with prior probability. In richer contexts, however,
people often rely on judgmental heuristics that do not obey and can distract
from simple formal considerations and these can lead to judgments that con-
flict with normative requirements.�

One of the most famous of the TK abnormalities has to do with conjunction, and the almost universal tendency to make wobbly judgements about the conjunction of probabilities. In a Discovery Magazine article that lists seven problems with probability judgments (which LI has found on a site that does not cite the author of the article � naughty, naughty � it was by Kevin McKean,) they quote the most famous confusing instance of this:

1. Linda is 31, single, outspoken, and very bright. She majored in philosophy in college. As a student, she was deeply concerned with discrimination and other social issues, and participated in anti-nuclear demonstrations. Which statement is more likely:
2. a. Linda is a bank teller
3. b. Linda is a bank teller and
4. active in the feminist movement.

Most people give a higher probability to the fourth statement than the third statement, even though, if you analyze it, you can see that it has to be less probable � insofar as the set of bank tellers is larger than the set of bank tellers active in the feminist movement. In other words, conjunction here, unlike addition, narrows the set, instead of expanding it. It is hard to get this through one�s head, however. The additional information about Linda moves us to suppose that, if she is a bank teller, surely she is a bank teller in the feminist movement. There�s an essay by Stephan Jay Gould, which, in the course of explaining the miraculousness of Joe Dimaggio's hitting streak, explains how Tversky showed that streaks, or �hot hands,� in baseball or basketball don�t exist � or at least not the way we think they exist. Here's how Gould makes the point about our perception of streaks, and what it says about our perception of the probable and the improbable, using the Linda example.

"Amos Tversky, who studied "hot hands," has performed a series of elegant psychological experiments with Daniel Kahneman.[5] These long-term studies have provided our finest insight into "natural reasoning" and its curious departure from logical truth. To cite an example, they construct a fictional description of a young woman: "Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations." Subjects are then given a list of hypothetical statements about Linda: they must rank these in order of presumed likelihood, most to least probable. Tversky and Kahneman list eight statements, but five are a blind, and only three make up the true experiment:
Linda is active in the feminist movement;
Linda is a bank teller;
Linda is a bank teller and is active in the feminist movement.
Now it simply must be true that the third statement is least likely, since any conjunction has to be less probable than either of its parts considered separately. Everybody can understand this when the principle is explained explicitly and patiently. But all groups of subjects, sophisticated students who ought to understand logic and probability as well as folks off the street corner, rank the last statement as more probable than the second. (I am particularly fond of this example because I know that the third statement is least probable, yet a little homunculus in my head continues to jump up and down, shouting at me�"but she can't just be a bank teller; read the description.")"

Gould also gives a nice summary of Kahneman and Tversky�s conclusions about �natural reasoning.� Gould, of course, like the counter-intuitive feel of the experiment, because he was always, famously, on the lookout for false patterns. Like Gould, LI has read more than his share of Karl Marx, so we have an abiding suspicion of the ulitilitarian definition of rationality and the systems built upon it. TK gives one the feeling that, finally, here's proof that the whole neo-classical economic thing is a hoax. Well, that, too, is a misprision of a pattern. But to continue with Gould:

�Why do we so consistently make this simple logical error? Tversky and Kahneman argue, correctly I think, that our minds are not built (for whatever reason) to work by the rules of probability, though these rules clearly govern our universe. We do something else that usually serves us well, but fails in crucial instances: we "match to type." We abstract what we consider the "essence" of an entity, and then arrange our judgments by their degree of similarity to this assumed type. Since we are given a "type" for Linda that implies feminism, but definitely not a bank job, we rank any statement matching the type as more probable than another that only contains material contrary to the type. This propensity may help us to understand an entire range of human preferences, from Plato's theory of form to modern stereotyping of race or gender.�

Tomorrow we will finally get around to why we think this almost instinctual process of matching to type explains the way the pro-war faction is framing our choices about Iraq.