You have to be pretty careful when looking at popular accounts of scientific work. The authors usually employ more controls than journalists have the space (or audiences have the patience) to process. While I would love to be able to say that all the behavioral econ experiments are bunk, they aren’t. Recurring patterns of bounded rationality (cognitive biases, framing effects, and computational limits) at the individual level have been established over a vast number of experiments using a wide range of techniques. Even professional decision analysts, trained in probability and decision theory and primed to be careful, are subject to some of these patterns. So the doubters about this particular experiment ought to keep their powder dry–framing effects are pretty robust and can be shown to occur even when there is nothing remotely ambiguous about the question. Whether and when these limits on rationality have real impacts on economic phenomena is a harder question and one that is just beginning to be addressed by empiricists.

Peter and Grant are asking a different question: How do we know that the described behavior is not “rational?” I am well aware of the problems associated with applying Bayesian rationality (also very popular with artificial intelligence types, I should note) to situations with “large worlds” where the set of alternatives is too big to describe and map or to situations where persistent disagreement across agents seems natural. Neither of those problems are at issue in the example given, however.

I can find philosophers who will tell you that measurements are problematic, that common sense is problematic, and that not being a solipsist is problematic. David Hume made a very compelling argument against belief in causality. Making things problematic is what philosophers do, but this enterprise often has little to do with the progress of understanding. When you can reverse people’s choices about lotteries by stating the exact same proposition in terms of losses rather than gains (as has been shown many times), we are well beyond the niceties of philosophical definitions–we are faced with the equivalent of optical illusions. And when we can see how someone could exploit these inconsistencies to take money from the agent in question, no philosopher can rescue these illusions from the category of “mistakes” or “errors.”

As for the problems of going from natural language to formal language, I heartily agree–that’s why we pay people who know how to structure problems formally (it is a learned skill for most). To the extent that the process of formalization reveals ambiguities in the natural language presentation of a problem, that is usually an important benefit of formalization. Even a statement like “you can fool some of the people all of the time” admits at least two valid interpretations–either there is a fixed set of gullible people who are always fooled or there is a different set of people fooled with each instance of deception–and a formal analysis may help tease such things out. Such ambiguities in experimental questions posed to test subjects are errors by the experimenter, and while this sort of bad technique does occur and even slips past peer review sometimes, the literature as whole is not shot through with it.

In short, if the experiment cited by Grant were performed correctly with due concern for eliminating ambiguities and included appropriate controls and checks to make sure that subjects’ errors were not due to such ambiguities, then there is nothing a philosopher could say to credibly rescue the responses from a claim of irrationality. Maybe an anthropologist has a different sort of life preserver, however, and I await a description of that with some interest.

That’s a completely ridiculous conclusion to draw from the experiment – even statistically. You could replace ‘bank teller’ with ‘bartender’ or ‘lawyer’ and the result would be the same. Having primed somebody with the suggestion that Linda is socially conscious, it is actually more likely for them to think that she’s active in the feminist movement than that she’s a bank teller or school bus driver, because, statistically, someone likely to be be concerned with discrimination is also likely to be concerned with feminism. (This is the ‘prior information’ that steve postrel talks about).

Consider this re-wording of the question:

“Li Shen is 19 and earns passing grades in college. As a child, he used to draw with crayons, and played with his classmates. Which is more probable? (a) Li is studying law; (b) Li is studying law and has friends”

This is a question that is disconnected from the premise supplied (okay, that is debatable, but it is still a tenuous connection). Given that the intent of the experiment is to determine whether people will pick the more probable (read larger) set of two, it must be demonstrable that (a) the conclusion does not follow from the premise; and (b) that one of the sets is larger than the other (presumably there are law students somewhere without any friends – but this requires interpretation). Any other experimental design induces interpretation on the behalf of the subject. Let’s try again:

“Which is more probable? (a) Li is studying law; (b) Li is studying law and has brown hair”

Better. But completely pointless. In fact, the experiment could have been written with the choices like this:

“Which is more probable? (a) Linda is active in the feminist movement and a bank teller; (b) Linda is a bank teller”

or even:

“Which is more probable? (a) Linda is active in the feminist movement; (b) Linda is active in the feminist movement and has red hair”

I’m willing to bet that with the last formulation, the subjects would have picked option (a) – the correct, ‘rational’ answer. One does not have to resort to a discussion of the context of definitions to see that this is an experiment that proves absolutely nothing.

Do Kahneman & Tversky have any excuse for having wasted perfectly good grant money on such a badly designed experiment?

The first point — which should be obvious to anyone who deals professionally with probability, but often seems not — is that the answer to a problem involving uncertainty depends very crucially on its mathematical formulation. We are given a situation expressed in ordinary English words and asked to use it to make a judgement. The probability theorists have arrived at a way of translating such situations from natural human language into a formal mathematical language, and using this formalism, to arrive at an answer to the situation which they deem correct. However, natural language may be imprecise (as in the example, as gek notes). Imprecision of natural language is a key reason for attempting a translation into a formal language, since doing so can clarify what is vague or ambiguous. But imprecision also means that there may be more than one reasonable translation of the same problem situation, even if we all agreed on what formal language to use and on how to do the translation. There may in fact be more than one correct answer.

There is much of background relevance here that may not be known to everyone, First, note that it took about 250 years from the first mathematical formulations of uncertainty using probability (in the 1660s) to reach a sort-of consensus on a set of mathematical axioms for probability theory (the standard axioms, due to Andrei Kolmogorov, in the 1920s). By contrast, the differential calculus, invented about the same time, was already rigorously formalized by the mid-19th century. Dealing formally with uncertainty is hard, and intuitions differ greatly, even for the mathematically adept.

Second, even now, the Kolmogorov axioms are not uncontested. Although it often comes as a suprise to statisticians and mathematicians, there is a whole community of intelligent, mathematically-adept, people in Artificial Intelligence who prefer to use alternative formalisms to probability theory, at least for some problem domains. These alternatives (such as Dempster-Shafer theory and possibility theory) are preferred to probability theory because they more are expressive (more situations can be adequately represented) and because they are easier to manipulate for some types of problems than probability theory. Let no one believe, then, that probability theory is accepted by every mathematically-adept expert who works with uncertainty.

Historical aside: In fact, ever since the 1660s, there has been a consistent minority of people dissenting from the standard view of probability theory, a minority which has mostly been erased from the textbooks. Typically, these dissidents have tried unsuccessfully to apply probability theory to real-world problems, such as those encountered by judges and juries (eg, Leibniz in the 17th century), doctors (eg, von Kries in the 19th), business investors (eg, Shackle in the 20th), and now intelligent computer systems (since the 1970s). One can have an entire university education in mathematical statistics, as I did, and never hear mention of this dissenting stream. A science that was confident of its own foundations would surely not need to suppress alternative views.

Third, intelligent, expert, mathematically-adept people who work with uncertainty do not even yet agree on what the notion of “probability” means, or to what it may validly apply. Donald Gillies, a professor of philosophy at the University of London, wrote a nice book called, “Philosophical Theories of Probability” (Routledge, London, 2000), which outlines the main alternative interpretations. A key difference of opinion concerns the scope of probability expressions (eg, over which types of natural language statements may one validly apply the translation mechanism). Note that Gillies wrote his book 70-some years after Kolmogorov’s axioms.

In addition, there are other social or cultural factors, usually ignored by mathematically-adept experts, which may inform one’s interpretations of uncertainty and probability. A view that the universe is deterministic, or that one’s spiritual fate is pre-determined before birth, may be inconsistent with any of these interpretations of uncertainty, for instance. I have yet to see a Taoist theory of uncertainty, but I am sure it would differ from anything developed so far.

I write this comment to give some context to our discussion. Mainstream economists and statisticians are fond of castigating ordinary people for being confused or for acting irrationally when faced with situations involving uncertainty, merely because the judgements of ordinary people do not always conform to the Kolmogorov axioms and the deductive consequences of these axioms. It is surely unreasonable to cast such aspersions when experts themselves disagree on what probability is, to what statements probabilities may be validly applied, and on how uncertainty should be formally represented.

I note that none of the anti-economists here has proposed any definition of rationality that encompasses logical inconsistency–probably because it would sound and would be inconsistent with how ordinary people understand the term. Maybe anthropologists have their own peculiar jargon where “rational” people don’t know that the set of all bank tellers is bigger than the set of bank tellers with red hair, or where people ignore relevant facts in coming to conclusions, but it’s peculiar to imagine these terms as corresponding to the ordinary meaning of the word.

Personally, I try not to use the word. I’m not at all convinced by an account of the world that separates something “rational” called “thought” from something called “emotion” – that doesn’t sound anything like my experience of the world.

that could be a problem! If economists don’t mean the same thing we do, how are we going to understand them?

How can they be sure they understand each other?

Public understanding can’t ever be served by disciplines using their own jargon. The situation is surely made worse when the jargon involves hijacking words we often use and giving them substantially different meanings.

I guess that over the next few years this will get sorted out. Either people like DK will force other economists to change the way they use the term or we will all get used to the idea that economists don’t mean the same thing that we do.

Peter: The notion of rationality employed by Kahneman here is weaker than Lange’s definition (which really isn’t that strong itself if you think about it). There is no suggestion of choice in this problem, just probability assessment. (I suppose you could say that the agent is picking beliefs to maximize his accuracy, but that just shows how weak, malleable, and nonrestrictive the maximization definition is.) All we ask of the agent is that he know the difference in size between a set and a proper subset of that set. It’s hard to see how any definition of rationality (or common sense) worth the name wouldn’t include such a principle. Otherwise we’re in the realm of Doestoyevsky’s Underground Man who rebelled against the proposition that twice two makes four–hardly a paragon of rationality by his own lights.