3. Cohen’s conceptual reject-the-norm argument

Perhaps the best known response from a philosopher to the HB program

is L. J. Cohen’s article ‘‘Can human irrationality be experimentally demonstrated?’’

(1981). Cohen’s thesis is that it is impossible for empirical

evidence to show that normal, adult humans are irrational. Although

Cohen’s article is more than two decades old, it still reflects the views of at

least some analytic philosophers. For example, Pollock and Cruz briefly

discuss the HB literature and state that their reading ‘‘is pretty much the

same as the assessment of the irrationality literature offered by Jonathan

Cohen’’ (1999, 130 n. 110).

Cohen begins by asking two questions: What would a normative

theory that describes how we ought to reason look like? And what would a descriptive theory that describes our reasoning competence look like?

Cohen’s strategy is to argue that these theories would be identical: A theory

of our reasoning competence just is a theory of how we ought to reason.

Cohen puts the point bluntly. ‘‘[O]rdinary human reasoning—by which I

mean the reasoning of adults who have not been systematically educated

in any branch of logic or probability theory—cannot be held to be faultily

programmed: it sets its own standards’’ (1981, 317). Cohen does not suggest

that normal human adults never reason poorly. But his explanation of

reasoning failures depends essentially on a performance-competence distinction.

A normal adult’s reasoning flaws are performance errors; her

reasoning competence is flawless—and necessarily so.

Cohen’s performance-competence distinction is familiar from linguistics.

The idea in linguistics is that we possess a cognitive system that

stores a rich body of grammatical information. A central goal of linguistics

is to infer linguistic rules from intuitions that cognitive system produces.

So linguists build theories of grammar. Such a theory for English would

accurately capture the grammatical competence of speakers of English. In

order to find out about this competence, we investigate the grammatical

judgments of English speakers (e.g., judgments about whether particular

sentences are grammatical). In order to make such judgments, speakers

must employ not only their grammatical competence, but also various

ancillary cognitive systems, such as memory, attention, and perception. As

a result, some judgments of a speaker might fail to reflect her underlying

grammatical competence because of the failure of one of these ancillary

systems. These are performance errors. Because of performance errors, the

linguist is likely to be faced with a situation in which she cannot construct

a theory because her data—speakers’ judgments—are messy or inconsistent.

As a result, the linguist must construct an idealized grammar for the

language. For Cohen, much of this story can be applied directly to the

theory of reasoning competence: We possess a cognitive system that represents

our reasoning competence. A descriptive theory of reasoning

competence will describe the rules of reasoning that make up our reasoning

competence. The data for such a theory will consist of subjects’

intuitions about particular reasoning problems. For Cohen, ‘‘an intuition

that p is . . . an immediate and untutored inclination, without evidence or

inference, to judge that p’’ (1981, 318). Such intuitions might not reflect a

subject’s reasoning competence, however, because of the potential for

performance errors. As a result, subjects’ intuitions might well be messy or

inconsistent. So the theorist must construct an idealized theory of reasoning

competence.

What about a normative theory of how we ought to reason? Here again,

we start with subjects’ intuitions about particular reasoning problems:

In order to discover what criteria of probability are appropriate for the

evaluation of lay reasoning we have to investigate what judgments of

probability are intuitively acceptable to lay adults and what rational constraints

these judgments are supposed to place on one another. (1981, 319)

Because of the possibility of performance errors, some amount of idealization

will be necessary in constructing a normative theory. According to

Cohen, we achieve an idealized normative theory through a process of

narrow reflective equilibrium: a coherent reconstruction of the subject’s

reasoning principles. Nelson Goodman describes this process as follows:

[R]ules and particular inferences alike are justified by being brought into

agreement with each other. A rule is amended if it yields an inference we are

unwilling to accept; an inference is rejected if it violates a rule we are unwilling

to amend. The process of justification is the delicate one of making

mutual adjustments between rules and accepted inferences; and in the

agreement achieved lies the only justification needed for either. (1965, 67)

An implication of Cohen’s view is that ‘‘Nothing can count as an

error of reasoning among our fellow adults unless even the author of the

error would, under ideal conditions, agree that it is an error’’ (1981, 322).

So it is not possible to empirically demonstrate that people are incompetent

reasoners, and the reason is that it is impossible for people to be

incompetent reasoners (i.e., it is impossible for people’s reasoning competence

to be defective). When we make mistakes, it is due to contingent

barriers like pesky distractions or memory failures that hamper our (in

principle) flawless execution.

Cohen believes that the primary data for our normative theory are subjects’

intuitions—their immediate, untutored inclinations—about reasoning

problems. What justifies this premise? Cohen seems to suggest that this is the

only possibility unless one invokes the standards of a Higher Power.

[I]f you claim no special revelation in matters of logic or probability, you

will have to be content there too to accept the inherent rationality of your

fellow adults. (1981, 321)

One may be tempted to ask: ‘‘how do we know that any intuition of the

relevant kind is veridical?’’ . . . The best that normative theorists can hope for

in this field (and also what they need to achieve), if they do not claim any

special revelation, is that the contents of all relevant intuitions—suitably

sifted or qualified, if necessary—can be made to corroborate one another by being exhibited as the consequences of a consistent and relatively simple set

of rules or axioms that also sanctions other intuitively acceptable, but

previously unremarked, patterns of reasoning. (1981, 322)

Keep in mind, however, that for Cohen, intuitions are immediate and

untutored inclinations to judge, derived without evidence or inference.

There are surely many other possibilities, even if one is inclined to construct

a normative theory on the basis of the judgments of reasoners. For

example, one might construct a normative theory on the basis of people’s

well-considered judgments (as opposed to their immediate judgments).

Cohen, however, rejects such possibilities by insisting that ‘‘[t]he judgments

of everyday reasoning must be evaluated in their own terms and by

their own standards’’ (1981, 320).

What does Cohen say about base rate neglect? He argues that, at best,

this is an example of subjects being ignorant of a mathematical truth.

However, he rejects even this possibility by offering a number of arguments

to the effect that ‘‘it is doubtful whether the subjects have made any

kind of mathematical error at all’’ (1981, 328). Here is one of Cohen’s

arguments:

You are suffering from a disease that, according to your manifest symptoms,

is either A or B. For a variety of demographic reasons disease A happens to

be nineteen times as common as B. The two diseases are equally fatal if

untreated, but it is dangerous to combine the respectively appropriate

treatments. Your physician orders a certain test which, through the operation

of a fairly well understood causal process, always gives a unique diagnosis

in such cases, and this diagnosis has been tried out on equal

numbers of A- and B-patients and is known to be correct on 80% of those

occasions. The tests report that you are suffering from disease B.

Let’s pause here to consider how someone might reason who was not

neglecting base rates: For every hundred patients who have either A or B in

this population, on average five will have B and 95 will have A. Of those

who test positive for B, four will have B (80% of 5) and 19 will have A

(20% of 95). So for the 23 who test positive for B, 4 actually have B. Now

back to Cohen:

Should you nevertheless opt for the treatment appropriate to A, on the

supposition . . . that the probability of your suffering from A is 19/23? Or

should you opt for the treatment appropriate to B, on the supposition

. . . that the probability of your suffering from B is 4/5? It is the former

option that would be the irrational one for you, qua patient, not the

latter. . . . Indeed, on the other view, which is the one espoused in the literature, it would be a waste of time and money even to carry out the tests,

since whatever their results, the base rates would still compel a more than

4/5 probability in favour of disease A. So the literature under criticism is

propagating an analysis that could increase the number of deaths from a

rare disease of this kind. (1981, 329)

This is a stunning line of argument. (As is Cohen’s defense of the gambler’s

fallacy [1981, 327–28].) While Cohen is right that the literature he is

criticizing defends a position that would lead to a greater number of

deaths from (rare) disease B, he recognizes that his own position would

lead to a greater number of total deaths—indeed, four times as many—

from both diseases A and B. Out of 100 people, Cohen’s strategy can be

expected to lead to 20 deaths (1 person dies from B, 19 die from A), while

the other strategy can be expected to lead to 5 deaths (all of those with

disease B). Cohen grants that ‘‘[t]he administrator who wants to secure a

high rate of diagnostic success for his hospital at minimal cost would be

right to seek to maximize just that probability, and therefore to dispense

altogether with the tests.’’ Note also that Cohen admits that in order not

to violate Bayes’ Rule, the subject must ignore the given base rate and

‘‘suppose equal predispositions’’ (1981, 329).

Cohen suggests that base rate neglect is superior to a Bayesian reasoning

strategy because, although base rate neglect will lead to more

overall deaths, it will lead to fewer deaths from a rare disease. This is a real

head-scratcher. Philosophers and their loved ones, after all, get sick too. If

you have the same symptoms as 200 other people and there are two

treatments, one with a survival rate of 95% and the other with a survival

rate of 80%, Cohen’s argument implies that the rational person will

choose the treatment with the lower survival rate. If that’s what rationality

dictates, we don’t want it. Cohen’s optimism is the result of an a priori

attachment that exacts a heavy price so that we may save cognitive face.

But then any conceptual reject-the-norm argument is by its very nature

deeply antithetical to the scientific spirit that animates not just Ameliorative

Psychology but all inquiry about the natural world.

Like with Gigerenzer’s conceptual reject-the-norm argument, Cohen

is defending a rather eccentric normative category. Cohen’s conception of

what it is to be ‘‘rational’’ is distinctly Protagorean—‘‘man is the measure

of all things.’’ But subjects who neglect the base rate might well be ‘‘rational’’

in a Protagorean sense and yet reason extraordinarily badly. In fact, in

chapter 9, we will argue that most subjects who neglect base rates are

reasoning badly. To see this intuitively, consider someone whose behavior makes him a very low risk for HIV, who takes a very reliable HIV test, and

who tests positive. What is an AIDS counselor supposed to tell this patient?

Should the counselor ignore the fact that the subject is low risk and

advise him that there is a 99% chance he has HIV? Or should the counselor

take that fact into account and tell the subject that the chances are

more like 50-50? How to reason about this situation has literally life-anddeath

consequences: ‘‘Former Senator Lawton Chiles of Florida reported

at an AIDS conference in 1987 that of 22 blood donors in Florida who

were notified that they tested HIV-positive with the ELISA test, seven

committed suicide. In the same medical text that reported this tragedy, the

reader is informed that ‘even if the results of both AIDS tests, the ELISA

and WB (Western blot), are positive, the chances are only 50-50 that the

individual is infected’ (Stine, 1996, 333, 338)’’ (Gigerenzer, Hoffrage, and

Ebert 1998). Now consider the AIDS counselor who ignores the base rate

and tells his clients that they have a 99% chance of having HIV, when in

fact only about 50% of his clients who test positive have HIV. Ignoring the

base rate in this situation may well be ‘‘rational’’ in Cohen’s sense. But it

would be lousy reasoning—the sort of reasoning that would quite properly

haunt one the rest of one’s days.

Cohen is surely right to suggest that there is some sort of a distinction

between our performance and the cognitive capacities that make it possible.

But it is not the distinction seen in linguistics. It is the distinction

familiar from any activity that requires skill and dedication. People who

have the competence to sing Weber’s desperate aria ‘‘Wo berg ich mich’’

might on occasion perform it badly, but even at our best, most of us really

can’t perform it at all. In this case, no one is inclined to suppose that

everyone’s capacities are similar or that everyone’s contingent collection of

capacities just is the measure of excellence. Some people sing better than

others. Further, everyone recognizes that there are differences in people’s

native mathematical and logical abilities. And both of these are crucial to

reasoning competence. So surely it is not too much of a stretch to suppose

that some people reason better than others. But Cohen denies that different

normal adults might have different reasoning competences; he

insists that any apparently different intuitions about particular reasoning

problems must always be resolvable.

No doubt two different people, or the same people on two different occasions,

may sometimes have apparently conflicting intuitions. But such an apparent

conflict always demands resolution. The people involved might come to

recognize some tacit misunderstanding about the terms of the problem, so that there is no real conflict; or they might repudiate a previously robust

intuition, perhaps as a result of becoming aware that an otherwise preferred

solution has unacceptable implications; or they might conclude that different

idiolects or conceptions of deducibility are at issue. (1981, 319)

This is an empirical speculation, and we will now turn to some fascinating

evidence that suggests that it is false.

Perhaps the best known response from a philosopher to the HB program

is L. J. Cohen’s article ‘‘Can human irrationality be experimentally demonstrated?’’

(1981). Cohen’s thesis is that it is impossible for empirical

evidence to show that normal, adult humans are irrational. Although

Cohen’s article is more than two decades old, it still reflects the views of at

least some analytic philosophers. For example, Pollock and Cruz briefly

discuss the HB literature and state that their reading ‘‘is pretty much the

same as the assessment of the irrationality literature offered by Jonathan

Cohen’’ (1999, 130 n. 110).

Cohen begins by asking two questions: What would a normative

theory that describes how we ought to reason look like? And what would a descriptive theory that describes our reasoning competence look like?

Cohen’s strategy is to argue that these theories would be identical: A theory

of our reasoning competence just is a theory of how we ought to reason.

Cohen puts the point bluntly. ‘‘[O]rdinary human reasoning—by which I

mean the reasoning of adults who have not been systematically educated

in any branch of logic or probability theory—cannot be held to be faultily

programmed: it sets its own standards’’ (1981, 317). Cohen does not suggest

that normal human adults never reason poorly. But his explanation of

reasoning failures depends essentially on a performance-competence distinction.

A normal adult’s reasoning flaws are performance errors; her

reasoning competence is flawless—and necessarily so.

Cohen’s performance-competence distinction is familiar from linguistics.

The idea in linguistics is that we possess a cognitive system that

stores a rich body of grammatical information. A central goal of linguistics

is to infer linguistic rules from intuitions that cognitive system produces.

So linguists build theories of grammar. Such a theory for English would

accurately capture the grammatical competence of speakers of English. In

order to find out about this competence, we investigate the grammatical

judgments of English speakers (e.g., judgments about whether particular

sentences are grammatical). In order to make such judgments, speakers

must employ not only their grammatical competence, but also various

ancillary cognitive systems, such as memory, attention, and perception. As

a result, some judgments of a speaker might fail to reflect her underlying

grammatical competence because of the failure of one of these ancillary

systems. These are performance errors. Because of performance errors, the

linguist is likely to be faced with a situation in which she cannot construct

a theory because her data—speakers’ judgments—are messy or inconsistent.

As a result, the linguist must construct an idealized grammar for the

language. For Cohen, much of this story can be applied directly to the

theory of reasoning competence: We possess a cognitive system that represents

our reasoning competence. A descriptive theory of reasoning

competence will describe the rules of reasoning that make up our reasoning

competence. The data for such a theory will consist of subjects’

intuitions about particular reasoning problems. For Cohen, ‘‘an intuition

that p is . . . an immediate and untutored inclination, without evidence or

inference, to judge that p’’ (1981, 318). Such intuitions might not reflect a

subject’s reasoning competence, however, because of the potential for

performance errors. As a result, subjects’ intuitions might well be messy or

inconsistent. So the theorist must construct an idealized theory of reasoning

competence.

What about a normative theory of how we ought to reason? Here again,

we start with subjects’ intuitions about particular reasoning problems:

In order to discover what criteria of probability are appropriate for the

evaluation of lay reasoning we have to investigate what judgments of

probability are intuitively acceptable to lay adults and what rational constraints

these judgments are supposed to place on one another. (1981, 319)

Because of the possibility of performance errors, some amount of idealization

will be necessary in constructing a normative theory. According to

Cohen, we achieve an idealized normative theory through a process of

narrow reflective equilibrium: a coherent reconstruction of the subject’s

reasoning principles. Nelson Goodman describes this process as follows:

[R]ules and particular inferences alike are justified by being brought into

agreement with each other. A rule is amended if it yields an inference we are

unwilling to accept; an inference is rejected if it violates a rule we are unwilling

to amend. The process of justification is the delicate one of making

mutual adjustments between rules and accepted inferences; and in the

agreement achieved lies the only justification needed for either. (1965, 67)

An implication of Cohen’s view is that ‘‘Nothing can count as an

error of reasoning among our fellow adults unless even the author of the

error would, under ideal conditions, agree that it is an error’’ (1981, 322).

So it is not possible to empirically demonstrate that people are incompetent

reasoners, and the reason is that it is impossible for people to be

incompetent reasoners (i.e., it is impossible for people’s reasoning competence

to be defective). When we make mistakes, it is due to contingent

barriers like pesky distractions or memory failures that hamper our (in

principle) flawless execution.

Cohen believes that the primary data for our normative theory are subjects’

intuitions—their immediate, untutored inclinations—about reasoning

problems. What justifies this premise? Cohen seems to suggest that this is the

only possibility unless one invokes the standards of a Higher Power.

[I]f you claim no special revelation in matters of logic or probability, you

will have to be content there too to accept the inherent rationality of your

fellow adults. (1981, 321)

One may be tempted to ask: ‘‘how do we know that any intuition of the

relevant kind is veridical?’’ . . . The best that normative theorists can hope for

in this field (and also what they need to achieve), if they do not claim any

special revelation, is that the contents of all relevant intuitions—suitably

sifted or qualified, if necessary—can be made to corroborate one another by being exhibited as the consequences of a consistent and relatively simple set

of rules or axioms that also sanctions other intuitively acceptable, but

previously unremarked, patterns of reasoning. (1981, 322)

Keep in mind, however, that for Cohen, intuitions are immediate and

untutored inclinations to judge, derived without evidence or inference.

There are surely many other possibilities, even if one is inclined to construct

a normative theory on the basis of the judgments of reasoners. For

example, one might construct a normative theory on the basis of people’s

well-considered judgments (as opposed to their immediate judgments).

Cohen, however, rejects such possibilities by insisting that ‘‘[t]he judgments

of everyday reasoning must be evaluated in their own terms and by

their own standards’’ (1981, 320).

What does Cohen say about base rate neglect? He argues that, at best,

this is an example of subjects being ignorant of a mathematical truth.

However, he rejects even this possibility by offering a number of arguments

to the effect that ‘‘it is doubtful whether the subjects have made any

kind of mathematical error at all’’ (1981, 328). Here is one of Cohen’s

arguments:

You are suffering from a disease that, according to your manifest symptoms,

is either A or B. For a variety of demographic reasons disease A happens to

be nineteen times as common as B. The two diseases are equally fatal if

untreated, but it is dangerous to combine the respectively appropriate

treatments. Your physician orders a certain test which, through the operation

of a fairly well understood causal process, always gives a unique diagnosis

in such cases, and this diagnosis has been tried out on equal

numbers of A- and B-patients and is known to be correct on 80% of those

occasions. The tests report that you are suffering from disease B.

Let’s pause here to consider how someone might reason who was not

neglecting base rates: For every hundred patients who have either A or B in

this population, on average five will have B and 95 will have A. Of those

who test positive for B, four will have B (80% of 5) and 19 will have A

(20% of 95). So for the 23 who test positive for B, 4 actually have B. Now

back to Cohen:

Should you nevertheless opt for the treatment appropriate to A, on the

supposition . . . that the probability of your suffering from A is 19/23? Or

should you opt for the treatment appropriate to B, on the supposition

. . . that the probability of your suffering from B is 4/5? It is the former

option that would be the irrational one for you, qua patient, not the

latter. . . . Indeed, on the other view, which is the one espoused in the literature, it would be a waste of time and money even to carry out the tests,

since whatever their results, the base rates would still compel a more than

4/5 probability in favour of disease A. So the literature under criticism is

propagating an analysis that could increase the number of deaths from a

rare disease of this kind. (1981, 329)

This is a stunning line of argument. (As is Cohen’s defense of the gambler’s

fallacy [1981, 327–28].) While Cohen is right that the literature he is

criticizing defends a position that would lead to a greater number of

deaths from (rare) disease B, he recognizes that his own position would

lead to a greater number of total deaths—indeed, four times as many—

from both diseases A and B. Out of 100 people, Cohen’s strategy can be

expected to lead to 20 deaths (1 person dies from B, 19 die from A), while

the other strategy can be expected to lead to 5 deaths (all of those with

disease B). Cohen grants that ‘‘[t]he administrator who wants to secure a

high rate of diagnostic success for his hospital at minimal cost would be

right to seek to maximize just that probability, and therefore to dispense

altogether with the tests.’’ Note also that Cohen admits that in order not

to violate Bayes’ Rule, the subject must ignore the given base rate and

‘‘suppose equal predispositions’’ (1981, 329).

Cohen suggests that base rate neglect is superior to a Bayesian reasoning

strategy because, although base rate neglect will lead to more

overall deaths, it will lead to fewer deaths from a rare disease. This is a real

head-scratcher. Philosophers and their loved ones, after all, get sick too. If

you have the same symptoms as 200 other people and there are two

treatments, one with a survival rate of 95% and the other with a survival

rate of 80%, Cohen’s argument implies that the rational person will

choose the treatment with the lower survival rate. If that’s what rationality

dictates, we don’t want it. Cohen’s optimism is the result of an a priori

attachment that exacts a heavy price so that we may save cognitive face.

But then any conceptual reject-the-norm argument is by its very nature

deeply antithetical to the scientific spirit that animates not just Ameliorative

Psychology but all inquiry about the natural world.

Like with Gigerenzer’s conceptual reject-the-norm argument, Cohen

is defending a rather eccentric normative category. Cohen’s conception of

what it is to be ‘‘rational’’ is distinctly Protagorean—‘‘man is the measure

of all things.’’ But subjects who neglect the base rate might well be ‘‘rational’’

in a Protagorean sense and yet reason extraordinarily badly. In fact, in

chapter 9, we will argue that most subjects who neglect base rates are

reasoning badly. To see this intuitively, consider someone whose behavior makes him a very low risk for HIV, who takes a very reliable HIV test, and

who tests positive. What is an AIDS counselor supposed to tell this patient?

Should the counselor ignore the fact that the subject is low risk and

advise him that there is a 99% chance he has HIV? Or should the counselor

take that fact into account and tell the subject that the chances are

more like 50-50? How to reason about this situation has literally life-anddeath

consequences: ‘‘Former Senator Lawton Chiles of Florida reported

at an AIDS conference in 1987 that of 22 blood donors in Florida who

were notified that they tested HIV-positive with the ELISA test, seven

committed suicide. In the same medical text that reported this tragedy, the

reader is informed that ‘even if the results of both AIDS tests, the ELISA

and WB (Western blot), are positive, the chances are only 50-50 that the

individual is infected’ (Stine, 1996, 333, 338)’’ (Gigerenzer, Hoffrage, and

Ebert 1998). Now consider the AIDS counselor who ignores the base rate

and tells his clients that they have a 99% chance of having HIV, when in

fact only about 50% of his clients who test positive have HIV. Ignoring the

base rate in this situation may well be ‘‘rational’’ in Cohen’s sense. But it

would be lousy reasoning—the sort of reasoning that would quite properly

haunt one the rest of one’s days.

Cohen is surely right to suggest that there is some sort of a distinction

between our performance and the cognitive capacities that make it possible.

But it is not the distinction seen in linguistics. It is the distinction

familiar from any activity that requires skill and dedication. People who

have the competence to sing Weber’s desperate aria ‘‘Wo berg ich mich’’

might on occasion perform it badly, but even at our best, most of us really

can’t perform it at all. In this case, no one is inclined to suppose that

everyone’s capacities are similar or that everyone’s contingent collection of

capacities just is the measure of excellence. Some people sing better than

others. Further, everyone recognizes that there are differences in people’s

native mathematical and logical abilities. And both of these are crucial to

reasoning competence. So surely it is not too much of a stretch to suppose

that some people reason better than others. But Cohen denies that different

normal adults might have different reasoning competences; he

insists that any apparently different intuitions about particular reasoning

problems must always be resolvable.

No doubt two different people, or the same people on two different occasions,

may sometimes have apparently conflicting intuitions. But such an apparent

conflict always demands resolution. The people involved might come to

recognize some tacit misunderstanding about the terms of the problem, so that there is no real conflict; or they might repudiate a previously robust

intuition, perhaps as a result of becoming aware that an otherwise preferred

solution has unacceptable implications; or they might conclude that different

idiolects or conceptions of deducibility are at issue. (1981, 319)

This is an empirical speculation, and we will now turn to some fascinating

evidence that suggests that it is false.