Judgment under Uncertainty: Heuristics and Biases
Amos Tversky; Daniel Kahneman
Science, New Series, Vol. 185, No. 4157. (Sep. 27, 1974), pp. 1124-1131.
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occupation from a list of possibilities( f o r example, farmer, salesman, airline
pilot, librarian, or physician)? How d opeople order these occupat~oas frommost to least likely? In the representativenes> heuristic, the probability that
Steve is a I~brarian, for example, IS
assessed by the degree to which he isrepresentative of, or similar to, thestereotype of a librarian. Indeed, reBiases in judgments reveal some heuristics ofsearch with problems of this type has
shown that people order the occupathinking under uncertainty.
tions by probability and by similarity
in exactly the same way ( I ) . This approach to the j i ~ d g ~ ~ i eofn t probability
Amos Tversky and Daniel Kahnemanleads to serious errors, because similarity, or representativeness, is not 1t1fluenced by several factors that should
affect judgments of probability.
Many decisions are based on beliefs mated when visibility is good because
l1zrer7ritivity to prior probability ofconcerning the likelihood of uncertain the objects are seen sharply. Thus, the outcomer. One of the factors that haveevents such as the outcome of an elec- reliance on clarity as an indication of no effect on representat~veness buttion, the guilt of a defendant, or the distance leads to common biases. Such should have a major effect on probabilfuture value of the dollar. These beliefs biases are also found in the intuitive ~ t yis the prior probability, or base-rate
are usually expressed in statements such judgment of probability. This article frequency, of the outcomes. In the caseas "I think that . . . ," "chances are describes three heuristics that are em- of Steve, for example, the fact that. . . ," "it is unlikely that . . . ," and ployed to assess probabilities and to there are many more farmers than liso forth. Occasionally, beliefs concern- predict values. Biases to which these brarians in the population should entering iuncertain events are expressed in heuristics lead are enumerated, and the into any reasonable estimate of thenumerical form as odds o r subjective applied and theoretical implications of probabil~ty that Steve is a librarianprobabilities. What determines such be- these observation5 are discussed.
rather than a farmer. Considerations ofliefs? How do people assess the probbase-rate frequency, however, do notability of an uncertain event or theaffect the similarity of Steve to thevalue of an uncertain quantity? This Representativenessstereotypes of librarians and farmers.
article shows that people rely on aIf people evaluate probability by repMany of the probabilistic questions resentativeness, therefore, prior probalimited number of heuristic principles
which reduce the complex tasks of as- with which people are concerned belong bilities will be neglected. This hypothesis
sessing probabilities and predicting val- to one of the following types: What is was tested in an experiment where priorues to simpler judgmental operations. the probability that object A belongs to probabilities were manipulated ( I ) .
In general, these heuristics are quite class B? What is the probability that Subjects were shown brief personality
useful, but sometimes they lead to severe event A originates from process B? descriptions of several individuals, alWhat is the probability that process R legedly sampled at random from aand systematic errors.
The subjective assessment of proba- w ~ l l generate event A? In answering group of 100 professionals-engineersbility resembles the subjective assess- such questions, people typically rely on and lawyers. The subjects were askcd
ment of physical quantities such as the representativeness heuristic, in to assess, for each description, the probdistance or size. These judgments are which probabilities are evaluated by the ability that it belonged to an engineer
all based on data of limited validity, degree to which A is representative of rather than to a lawyer. In one experiwhich are processed according to heu- B, that is, by the degree to which A mental condition, subjects were told
ristic rules. F o r example, the apparent resembles B. F o r example, when A ib that the group from which the descripdistance of an object is determined in highly representative of B, the proba- tions had been drawn consisted of 7 0
part by its clarity. The more sharply the bility that A originates from B is judged engineers and 30 lawyers. Tn anotherobject is seen, the closer it appears to to be high. On the other hand, if A is condition, subjects were told that thebe. This rule has some validity, hecaust: not similar to B, the probability that A group consisted of 30 engineers and 7 0
in any given scene the more distant originates from B is judged to be low. lawyers. The odds that any particularF o r an illustration of judgment by description belongs to an engineer
objects are seen less sharply than nearer
objects. However, the reliance on this representativeness, consider an indi- rather than to a lawyer should berule leads to systematic errors in the vidual who has been described by a higher in the first condition, where there
estimation of distance. Specifically, dis- former neighbor as follows: "Steve is is a majority of engineers, than in thetances are often overestimated when very shy and withdrawn, invariably second condition, where there is a
visibility is poor because the contours helpful, but with little interest in peo- majority of lawyers. Specifically, it canof objects are blurred. O n the other ple, or in the world of reality. A meek be shown by applying Bayes' rule that
hand, distances are often underesti- and tidy soul, he has a need for order the ratio of these odds should be (.7/.312,
and structure, and a passion for detail." o r 5.44, for each description. In a sharp
The authors are tncmbers of the department ofHo w do people assess the probability violation of Bayes' rule, the subjects
psychology at the Hebt'cw University, Jerusalem,that Steve is engaged in a particular in the two conditions produced essenI~rael.

Judgment under Uncertainty:
Heuristics and Biases

SCIENCE, VOL. 185

tially the same probability judgments.
Apparently, subjects evaluated the likelihood that a particular description belonged to an engineer rather than to alawyer ,by the degree to which thisdescription was representative of thetwo stereotypes, with little or no regard
for the prior probabilities of the categories.
T h e subjects used prior probabilities
correctly when they had no other information. I n the absence of a personality
sketch, they judged the probability thatan unknown individual is an engineer
to be .7 and .3, respectively, in the twobase-rate conditions. However, priorprobabilities were effectively ignored
when a description was introduced,
even when this description was totally
uninformative. T h e responses to thefollowing description illustrate this phenomenon:
Dick is a 30 year old man. He is married with no children. A man of highability and high motivation, he promises
to be quite successful in his field. He iswell liked by his colleagues.
This description was intended to convey
no information relevant to the questionof whether Dick is a n engineer or alawyer. Consequently, the probability
that Dick is a n engineer should equal
the proportion of engineers in thegroup, as if no description had been
given. T h e subjects, however, judged
the probability of Dick being an engineer to be .5 regardless of whether thestated proportion of engineers in thegroup was .7 o r .3. Evidently, people
respond differently when given no evidence and when given worthless evidence. When no specific evidence isgiven, prior probabilities are properly
utilized; when worthless evidence isgiven, prior probabilities are ignored(1).

Insensitivity to sample size. T o evaluate the probability of obtaining a particular result in a sample drawn froma specified population, people typically
apply the representativeness heuristic.
That is, they assess the likelihood ofa sample result, f o r example, that the
average height in a random sample often men will be 6 feet (180 centimeters), by the similarity of this result
to the corresponding parameter (thatis, to the average height in the population of men). T h e similarity of a sample statistic to a population parameter
does not depend o n the size of thesample. Consequently, if probabilities
are assessed by representativeness, thenthe judged probability of a sample statistic will be essentially independent of
27 SEPTEMBER 1974

sample size. Indeed, when subiects
assessed the distributions of averageheight for samples of various sizes,
they produced identical distributions.
F o r example, the probability of obtaining an average height greater than 6feet was assigned the same value forsamples of 1000, 100, and 1 0 men ( 2 ) .
Moreover, subjects failed to appreciate
the role of sample size even when it
was emphasized in the formulation of
the problem. Consider the following
question:
A certain town is served by two hospitals. In the larger hospital about 45
babies are born each day, and in $hesmaller hospital about 15 babies are borneach day. As you know, about 50 percent
of all babies are boys. However, the exact
percentage varies from day to day. Sometimes it may be higher than 50 percent,sometimes lower.
For a period of 1 year, each hospitalrecorded the days on which more than 60
percent of the babies born were boys.
Which hospital do you think recorded
more such days?
b The larger hospital ( 2 1 )b The smaller hospital (21)b A'bout the same (that is, within 5
percent of each other) (53)T h e values in parentheses are the number of undergraduate students whochose each answer.
Most subjects judged the probabilityof obtaining more than 6 0 percent boys
to be the same in the small and in thelarge hospital, presumably because these
events are described by the same statistic and are therefore equally representative of the general population. I ncontrast, sampling theory entails thatthe expected number of days on whichmore than 60 percent of the babies areboys is much greater in the small hospital than in the large one, because alarge sample is less likely to stray from
5 0 percent. This fundamental notionof statistics is evidently not part ofpeople's repertoire of intuitions.
A similar insensitivity to sample sizehas been reported in judgments of posterior probability, that is, of the probability that a sample has been drawn
from one population rather than fromanother. Consider the following example:
Imagine an urn filled with balls, ofwhich % are of one color and 1/3 ofanother. One individual has drawn 5 balls'from the urn, and found that 4 were redand 1 was white Another individual has
drawn 20 balls and found that 12 were
red and 8 were white. Which of the two
individuals should feel more confident thatthe urn contains 2/3 red balls and 95 whiteballs, rather than the opposite? What odds
should each individual give?

I n this problem, the correct posterior
odds are 8 to 1 for the 4 : 1 sample
and 1 6 to 1 for the 12 : 8 sample, assuming equal prior probabilities. However, most people feel that the firstsample provides much stronger evidence
for the hypothesis that the urn is predominantly red, because the proportionof red balls is larger in the first than in
the second sample. Here again, intuitive
judgments are dominated by the sample
proportion and are essentially unaffectedby the size of the sample, which plays
a crucial role in the determination of
the actual posterior odds ( 2 ) . I n addition, intuitive estimates of posterior
odds are far less extreme than the correct values. T h e underestimation of the
impact of evidence has been observed
repeatedly in problems of this type (3, 4).
I t has been labeled "conservatism."
Misconceptions o f chance. People expect that a sequence of events generated
by a random process will represent theessential characteristics of that processeven when the sequence is short. I n
considering tosses of a coin for headso r tails, for example, people regard thesequence H-T-H-T-T-H to be more
likely than the sequence H-H-H-T-T-T,
which does not appear random, andalso more likely than the sequence H-HH-H-T-H, which does not represent thefairness of the coin ( 2 ) . Thus, people
expect that the essential characteristicsof the process will be represented, notonly globally in the entire sequence,but also locally in each of its parts. A
locally representative sequence, however, deviates systematically from chance
expectation: it contains too many alternations and too few runs. Anotherconsequence of the belief in local representativeness is the well-known gambler's fallacy. After observing a longrun of red on the roulette wheel. forexample, most people erroneously believe that black is now due, presumably
because the occurrence of black will
result in a more representative sequencethan the occurrence of an additional
red. Chance is commonly viewed as aself-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore
the equilibrium. I n fact, deviations arenot "corrected" as a chance processunfolds, they are merely diluted.
Misconceptions of chance are notlimited to naive subjects. A study ofthe statistical intuitions of experienced
research psychologists ( 5 ) revealed alingering belief in what may be called
the "law of small numbers," according
to which even small samples are highlyrepresentative of the populations fromwhich they are drawn. The responsesof these investigators reflected the expectation that a valid hypothesis about
a population will be represented by astatistically significant result in a sample-withlittle regard for its size. As
a consequence, the researchers put too
much faith in the results of small samples and grossly overestimated thereplicability of such results. In theactual conduct of research, this bias
leads to the selection of samples of
inadequate size and to overinterpretationof findings.
Insensitivity to predictability. People
are sometimes called upon to make such
numerical predictions as the future valueof a stock, the demand for a commodity, or the outcome of a football game.
Such predictions are often made byrepresentativeness. F o r example, suppose one is given a description of acompany and is asked to predict its
future profit. If the description of thecompany is very favorable, a very
high profit will appear most representative of that description; if the description is mediocre, a mediocre performance will appear most representative.
The degree to which the description isfavorable is unaffected by the reliabilityof that description o r by the degree towhich it permits accurate prediction.
Hence, if people predict solely in termsof the favorableness of the description,
their predictions will be insensitive tothe reliability of the evidence and to
the expected accuracy of the prediction.
This mode of judgment violates thenormative statistical theory in which
the extremeness and the range of predictions are controlled by considerationsof predictability. When predictability
is nil, the same prediction should bemade in all cases. F o r example, if thedescriptions of companies provide no
information relevant to profit, then thesame value (such as average profit)
should be predicted for all companies.
If predictability is perfect, of course,
the values predicted will match theactual values and the range of predictions will equal the range of outcomes.
In general, the higher the predictability,
the wider the range of predicted values.
Several studies of numerical prediction have demonstrated that intuitive
predictions violate this rule, and that
subjects show little o r no regard forconsiderations of predictability ( I ) . I n
one of these studies, subjects were presented with several paragraphs, each
describing the performance of a stu-

dent teacher during a particular practice lesson. Some subjects were asked
to evaluate the quality of the lesson
described in the paragraph in percentile
scores, relative to a specified population.
Other subjects were asked to predict,also in percentile scores, the standingof each student teacher 5 years after
the practice lesson. The judgments madeunder the two conditions were identical.
That is, the prediction of a remotecriterion (success of a teacher after 5
years) was identical to the evaluationof the information on which the prediction was based (the quality of thepractice lesson). The students who madethese predictions were undoubtedly
aware of the limited predictability ofteaching competence on the basis of asingle trial lesson 5 years earlier; nevertheless, their predictions were as extreme as their evaluations.
The illu~iono f validity. As we haveseen, people often predict by selecting
the outcome (for example, an occupation) that is most representative of the
input (for example, the description ofa person). The confidence they havein their prediction depends primarilyon the degree of representativeness(that is, on the quality of the match
between the selected outcome and the
input) with little o r no regard for thefactors that limit predictive accuracy.
Thus, people express great confidence
in the prediction that a person is alibrarian when given a description ofhis personality which matches thestereotype of librarians, even if thedescription is scanty, unreliable, or outdated. The unwarranted confidence
which is produced by a good fit between
the predicted outcome and the input
information may be called the illusionof validity. This illusion persists evenwhen the judge is aware of the factorsthat limit the accuracy of his predictions. It is a common observation thatpsychologists who conduct selection
interviews often experience considerable
confidence in their predictions, evenwhen they know of the vast literaturethat shows selection interviews to behighly fallible. The continued relianceon the clinical interview for selection,
despite repeated demonstrations of its
inadequacy, amply attests to the strengthof this effect.
The internal consistency of a patternof inputs is a major determinant of
one's confidence in predictions basedon these inputs. F o r example, people
express more confidence in predicting thefinal grade-point average of a student

whose first-year record consists entirelyof B's than in predicting the gradepoint average of a student whose firstyear record includes many A's and C's.
Highly consistent patterns are mostoften observed when the ~ n p u t variables are highly redundant o r correlated.
Hence, people tend to have great confidence in predictions based on redundant input variables. However, anelementary result in the statistics of correlation asserts that, given input variables of stated validity, a prediction
based on several such inputs canachieve higher accuracy when they are
independent of each other than when
they are redundant o r correlated. Thus,
redundancy anlong inputs decreases
accuracy even as it increases confidence,and people are often confident in predictions that are quite likely to be off
the mark ( I ) .
Misconceptions o f regression. Supposea large group of children has been
examined on two equivalent versions ofan aptitude test. If one selects ten children from among those who did best on
one of the two versions, he will usuallyfind their performance on the second
version to be somewhat disappointing.
Conversely, if one selects ten children
from among those who did worst on
one version, they will be found, on the
average, to do somewhat better on theother version. More generally, consider
two variables X and Y which have thesame distribution. If one selects individuals whose average X score deviatesfrom the mean of X by k units, thenthe average of their Y scores will usually deviate from the mean of Y by lessthan k units. These observations illustrate a general phenomenon known as
regression toward ;he mean, which was
first documented by Galton more than
100 years ago.
In the normal course of life, one
encounters many instances of regression
toward the mean, in the comparisonof the height of fathers and sons, ofthe intelligence of husbands and wives.
or of the performance of individuals
on consecutive examinations. Nevertheless, people do not develop correct intuitions about this phenomenon. First,
they do not expect regression in many
contexts where it is bound to occur.
Second, when they recognize the occurrence of regression, they often invent
spurious causal explanations for it ( I ) .
We suggest that the phenomenon of regression remains elusive because it is incompatible with the belief that thepredicted outcome should be maximally
SCIENCE, VOL. 185

representative of the input, and, hence,that the value of the outcome variable
should be as extreme as the value ofthe input variable.
The failure to recognize the importof regression can have pernicious consequences, as illustrated by the following observation ( I ) . I n a discussionof flight training, experienced instructors noted that praise for an exceptionally smooth landing is typically followed
by a poorer landing o n the next try,
while harsh criticism after a roughlanding is usually followed by an improvement on the next try. T h e instructors concluded that verbal rewards are
detrimental to learning, while verbal
punishments are beneficial, contrary to
accepted psychological doctrine. Thisconclusion is unwarranted because of
the presence of regression toward themean. As in other cases of repeatedexamination, an improvement will usually follow a poor performance anda deterioration will usually follow an
outstanding performance, even if the
instructor does not respond to thetrainee's achievement on the first attempt. Because the instructors had
praised their trainees after good landings and admonished them after poor
ones, they reached the erroneous andpotentially harmful conclusion that punishment is more effective than reward.
Thus, the failure to understand theeffect of regression leads one to overestimate the effectiveness of punishment and to underestimate the effectiveness of reward. In social interaction,
as well as in training, rewards are typically administered when performanceis good, and punishments are typicallyadministered when performance ispoor. By regression alone, therefore,
behavior is most likely to improve after
punishment and most likely t o deteriorate after reward. Consequently, thehuman condition is such that, by chancealone, one is most often rewarded forpunishing others and most often punished for rewarding them. People are
generally not aware of this contingency.
In fact, the elusive role of regression
in determining the apparent consequences of reward and punishment
seems to have escaped the notice of students of this area.

Availability

There are situations in which people
assess the frequency of a class or the
probability of an event by the ease with
27 SEPTEMBER 1974

which instances or occurrences can bebrought to mind. F o r example, one mayassess the risk of heart attack among
middle-aged people by recalling suchoccurrences among one's acquaintances.
Similarly, one may evaluate the probability that a given business venture will
fail by imagining various difficulties it
could encounter. This judgmental heuristic is called availability. Availability
is a useful clue for assessing frequency
o r probability, because instances oflarge classes are usually recalled betterand faster than instances of less frequent classes. However, availability isalliected by factors other than frequency
and probability. Consequently, the reliance on availability leads to predictable biases, some of which are illustrated
below.
Biases due to the retrievabitity o f instances. When the size of a class isjudged by the availability of its instances, a class whose instances areeasily retrieved will appear more numerous than a class of equal frequency
whose instances are less retrievable. I n
a n elementary demonstration of this effect, subjects heard a list of well-known
personalities of both sexes and were
subsequently asked to judge whether thelist contained more names of men thanof women. Different lists were presented
to different groups of subjects. In someof the lists the men were relatively morefamous than the women, and in others
the women were relatively more famousthan the men. In each of the lists, thesubjects erroneously judged that theclass (sex) that had the more famous
personalities was the more numerous(6).

In addition to familiarity, there areother factors. such as salience, which
affect the retrievability of instances. F o r
example, the impact of seeing a houseburning o n the subjective probability ofsuch accidents is probably greater than
the impact of reading about a fire in
the local paper. Furthermore, recent occurrences are likely to be relatively
more available than earlier occurrences.
It is a common experience that the
subjective probability of traffic accidentsrises temporarily when one sees a car
overturned by the side of the road.
Biases drte to the eflectiveness of asearch set. Suppose one samples a word(of three letters o r more) at random
from a n English text. Is it more likelythat the word starts with r o r thatr is the third letter? People approach
this problem by recalling words thatbegin w ~ t hr (road) and words thathave r in the third position (car) andassess the relative frequency by theease with which words of the two types
come to mind. Because it is much easierto search for words by their first letter
than by their third letter, most people
judge words that begin with a given
consonant to be more numerous thanwords in which the same consonant appears in the third position. They do soeven for consonants, such as r o r k,that a r e more frequent in the third
position than in the first (6).
Different tasks elicit different searchsets. F o r example, suppose you are
asked to rate the frequency with which
abstract words (thought, love) and concrete words (door, water) appear in
written English. A natural way toanswer this question is to search forcontexts in which the word could appear. It seems easier to think ofcontexts in which a n abstract concept
is mentioned (love in love stories) than
to think of contexts in which a concrete
word (such as door) is mentioned. If
the frequency of words is judged by theavailability of the contexts i n which
they appear, abstract words will b e
judged as relatively more numerous thanconcrete words. This bias has been observed in a recent study (7) whichshowed that the judged frequency ofoccurrence of abstract words was muchhigher than that of concrete words.
equated in objective frequency. Abstract
words were also judged to appear in amuch greater variety of contexts thanconcrete words.
Binses of irnaginnbility. Sometimes
one has to assess the frequency of aclass whose instances are not stored inmemory but can be generated according to a given rule. In such situations,
one typically generates several instancesand evaluates frequency o r probabilityby the ease with which the relevant instances can be constructed. However,
the ease of constructing instances does
not always reflect their actual frequency,
and this mode of evaluation is prone
to biases. T o illustrate, consider a groupof 10 people who form committees ofk members, 2 k 8. H o w manydifferent committees of k members canbe formed? T h e correct answer to thisproblem is given by the binomial coefw hich reaches a maximum
ficient (If)of 2.52 for k = 5. Clearly, the numberof committees of k members equals
the number of committees of (10 - k)members, because any committee of k< <members defines a unique group of(10 - k) nonmembers.
One way to answer this question without computation is to mentally construct committees of k members andto evaluate their number by the easewith which they come to mind. Cornmittees of few members, say 2, aremore available than committees of manymembers, say 8. The simplest scheme
for the construction of committees is apartition of the group into disjoint sets.
One readily sees that it is easy to construct five disjoint committees of 2
members, while it is impossible to generate even two disjoint committees of
8 members. Consequently, if frequency is assessed by imaginability, o r
by availability for construction, thesmall committees will appear more numerous than larger committees, in contrast to the correct bell-shaped function. Indeed, when naive subjects wereasked to estimate the number of distinct
committees of various sizes, their estimates were a decreasing monotonic
function of committee size (6). F o r
example, the median estimate of thenumber of committees of 2 members
was 70, while the estimate for committees of 8 members was 20 (the correct answer is 45 in both cases).
Tmaginability plays an important rolein the evaluation of probabilities in reallife situations. The risk involved in anadventurous expedition, for example, isevaluated by imagining contingencies
with which the expedition is not
equipped to cope. If many such difficulties are vividly portrayed, the expedition can be made to appear exceedingly
dangerous, although the ease with which
disasters are imagined need not reflect
their actual likelihood. Conversely, therisk involved in an undertaking may begrossly underestimated if some possible
dangers are either difficult to conceiveof, or simply do not come to mind.
Illlrsory correlation. Chapman andChapman ( 8 )have described an interesting bias in the judgment of the frequency with which two events co-occur.
They presented naive judges with information concerning several hypothetical mental patients. The data for eachpatient consisted of a clinical diagnosis
and a drawing of a person made by
the patient. Later the judges estimatedthe frequency with which each diagnosis(such as paranoia o r suspiciousness)had been accompanied by various features of the drawing (such as peculiareyes). T h e subjects markedly overestimated the f r e q ~ ~ e n ofc y co-occurrence of

natural associates, such as suspiciousness and peculiar eyes. This effect waslabeled illusory correlation. I n their erroneous judgments of the data to which
they had been exposed, naive subjects"rediscovered" much of the common,but unfounded, clinical lore concerning the interpretation of the draw-aperson test. The illusory correlation
ctrect was extremely resistant to contradictory data. It persisted even when
the correlation between symptotn anddiagnosis was actually negative, and it
prevented the judges from detecting
relationships that were in fact present.
Availability provides a natural account for the illusory-correlation effect.
The judgment of how frequently twoevents co-occur could be based on thestrength of the associative bond between
them. When the association is strong,
one is likely to conclude that the events
have been frequently paired. Consequently. strong associates will be judged
to have occurred together frequently.
According to this view, the illusory
correlation between suspiciousness andpeculiar drawing of the eyes, for example, is due to the fact that suspiciousness is more readily asqociatcd withthe eyes than with any other part ofthe body.
Lifelong experience has taught us
that, in general, instances of large
classes are recalled better and fasterthan instances of less frequent classes;that likely occurrences are easier toimagine than unlikely ones; and thatthe associative connections between
events are strengthened when the events
frequently co-occur. As a result, man
has at his disposal a procedure (theavailability heuristic) for estimating thenumerosity of a class, the likelihood ofan event, or the frequency of co-occurrences, by the ease with which therelevant mental operations of retrieval,construction, o r association can be
performed. However, as the preceding
examples have demonstrated, this valuable estimation procedure results insystematic errors.

Adjustment and Anchoring

In many situations, people make estimates by starting from an initial valuethat is adjusted to yield the final answer.
The initial value, or starting point, may
be suggested by the formulation of the
problem, or it may be the result of apartial computation. In either case,adjustments are typically insufficient (4).

That is, different starting points yield
different estimates, which are biased
toward the initial values. We call thisphenomenon anchoring.
InsufJicierlt adju~ttnent.In a demonstration of the anchoring effect, subjects
were asked to estimate various quantities, stated in percentages (for example,
the percentage of African countries in
the United Nations). F o r each quantity,
a number between 0 and 100 was determined by spinning a wheel of fortune
in the subjects' presence. T h e subjects
were instructed to indicate first whether
that number was higher or lower thanthe value of the quantity, and then to
estimate the value of the quantity bymoving upward or downward from thegiven number. Different groups were
given different numbers for each quantity, and these arbitrary numbers had amarked effect on estimates. F o r example,
the median estimates of the percentagc
of African countries in the United Nations were 25 and 4 5 for groups that received I0 and 65, respectively, as startlng points. Payoffs for accuracy did not
reduce the anchoring effect.
Anchoring occurs not only when thestarting point is given to the subject,
but also when the subject bases his
cstimate o n the result of some incomplete computation. A study of intuitive
numerical estimation illustrates this effect. Two groups of high school students
estimated, within 5 seconds, a numericalexpression that was written on theblackboard. One group estimated the
product

while another groupproduct

estimated theT o rapidly answer such questions, people may perform a few steps of computation and estimate the product byextrapolation or adjustment. Because adjustments are typically insufficient, thisprocedure should lead to underestimation. Furthermore, because the result of
the first few steps of multiplication (performed from left to right) is higher inthe descending sequence than in theascending sequence, the former expression should b e judged larger than thelatter. Both predictions were confirmed.
The median estimate for the ascending
sequence was 512, while the medianestimate for the descending sequence
was 2,250. The correct answer is 40,320.
Bia~esin the evaluation o f conjunctive and disjlrnctive events. I n a recent
SCIENCE, VOL. 185

study by Bar-Hillel (9) subjects were
given the opportunity to bet on one of
two events. Three types of events wereused: (i) simple events, such as drawing
a red marble from a bag containing 50
percent red marbles and 50 percent
white marbles; (ii) conjunctive events,
such as drawing a red marble seventimes in succession, with replacement,from a bag containing 90 percent red
marbles and 10 percent white marbles;and (iii) disjunctive events, such as
drawing a red marble at least once inseven successive tries, with replacement,from a bag containing 10 percent red
marbles and 90 percent white marbles.
In this problem, a significant majorityof subjects preferred to bet on the conjunctive event (the probability of whichis .48) rather than o n the simple event(the probability of which is .50).Subjects also preferred to bet on the simple
event rather than on the disjunctive
event, which has a probability of .52.
Thus, most subjects bet on the less likely
event in both comparisons. This patternof choices illustrates a general finding.
Studies of choice among gambles andof judgments of probability indicatethat people tend to overestimate theprobability of conjunctive events (10)and to underestimate the probability of
disjunctive events. These biases arereadily explained as effects of anchoring. The stated probability of theelementary event (success at any one
stage) provides a natural starting point
for the estimation of the probabilities ofboth conjunctive and disjunctive events.
Since adjustment from the starting point
is typically insufficient, the final estimates remain too close to the probabilities of the elementary events in bothcases. Note that the overall probabilityof a conjunctive event is lower thanthe probability of each elementary
event, whereas the overall probability ofa disjunctive event is higher than theprobability of each elementary event.
As a consequence of anchoring, theoverall probability will be overestimatedin conjunctive problems and underestimated in disjunctive problems.
Biases in the evaluation of compound
events are particularly significant in thecontext of planning. The successful
completion of an undertaking, such as
the development of a new product, typically has a conjunctive character: forthe undertaking to succeed, each of aseries of events must occur. Even wheneach of these events is very likely, theoverall probability of success can bequite low if the number of events is
27 SEPTEMBER 1974

large. The general tendency to overestimate the probability of conjunctive
events leads to unwarranted optimism in
the evaluation of the likelihood that aplan will succeed or that a project will
be completed on time. Conversely, disjunctive structures are typically encountered in the evaluation of risks. A complex system, such as a nuclear reactor
or a human body, will malfunction if
any of its essential components fails.
Even when the likelihood of failure ineach component is slight, the probabilityof an overall failure can be high if
many components are involved. Because of anchoring, people will tend tounderestimate the probabilities of failure
in complex systems. Thus, the direction of the anchoring bias can sometimes be inferred from the structure of
the event. The chain-like structure of
conjunctions leads to overestimation, thefunnel-like structure of disjunctions
leads to underestimation.
Anchoring in the assessment o f subjective probability distributions. I n decision analysis, experts are often required
to express their beliefs about a quantity,
such as the value of the Dow-Jones
average on a particular day, in theform of a probability distribution. Sucha distribution is usually constructed byasking the person to select values of
the quantity that correspond to specified
percentiles of his subjective probability
distribution. For example, the judge
may be asked to select a number, X,,,
such that his subjective probability that
this number will be higher than thevalue of the Dow-Jones average is .90.
That is, he should select the value X,,
so that he is just willing to accept 9 to
1 odds that the Dow-Jones average will
not exceed it. A subjective probability
distribution for the value of the DowJones average can be constructed fromseveral such judgments corresponding todifferent percentiles.
By collecting subjective probability
distributions for many different quantities, it is possible to test the judge forproper calibration. A judge is properly(or externally) calibrated in a set ofproblems if exactly I
I percent of thetrue values of the assessed quantities
falls below his stated values of Xn. For
example, the true values should fall
below X,, for 1 percent of the quantities and above X,, for 1 percent of thequantities. Thus, the true values should
fall in the confidence interval between
X,,, and X,, on 98 percent of the problems.
Several investigators (11) have ob-tained probability distributions for many
quantities from a large number ofjudges. These distributions indicatedlarge and systematic departures fromproper calibration. In most studies, theactual values of the assessed quantities
are either smaller than X,, or greaterthan X,, for about 30 percent of the
problems. That is, the subjects state
overly narrow confidence intervals whichreflect more certainty than is justified bytheir knowledge about the assessed
quantities. This bias is common tonaive and to sophisticated subjects, and
it is not eliminated by introducing proper scoring rules, which provide incentives
for external calibration. This effect is attributable, in part at least, to anchoring.
T o select X,, for the value of the
Dow-Jones average, for example, it isnatural to begin by thinking about one's
best estimate of the Dow-Jones and toadjust this value upward. If this adjustment-like most others-is insufficient,then X,, will not be sufficiently extreme.
A similar anchoring effect will occur inthe selection of XI,, which is presumably
obtained by adjusting one's best estimate downward. Consequently, the confidence interval between X,, and X,,
will be too narrow, and the assessedprobability distribution will be too tight.
In support of this interpretation it canbe shown that subjective probabilities
are systematically altered by a procedure in which one's best estimate does
not serve as an anchor.
Subjective probability distributions
for t given quantity (the Dow-Jones
average) can be obtained in two different ways: (i) by asking the subject toselect values of the Dow-Jones that
correspond to specified percentiles ofhis probability distribution and (ii) byasking the subject to assess the probabilities that the true value of the
Dow-Jones will exceed some specified
values. The two procedures are formallyequivalent and should yield identical
distributions. However, they suggest different modes of adjustment from differcent anchors. In procedure (i), thenatural starting point is one's best estimate of the quantity. In procedure (ii),on the other hand, the subject may beanchored on the value stated in thequestion. Alternatively, he may be anchored on even odds, or 50-50 chances,which is a natural starting point in theestimation of likelihood. In either case,procedure (ii) should yield less extreme
odds than procedure (i).
T o contrast the two procedures, a
set of 24 quantities (such as the air dis-tance from New Delhi to Peking) waspresented to a group of subjects who
assessed either XI, or X,, for each problem. Another group of subjects received the median judgment of the firstgroup for each of the 24 quantities.
They were asked to assess the odds thateach of the given values exceeded thetrue value of the relevant quantity. In
the absence of any bias, the second
group should retrieve the odds specified
to the first group, that is, 9 : 1. However, if even odds or the stated value
serve as anchors, the odds of the second group should be less extreme, thatis, closer to 1 : 1. Indeed, the medianodds stated by this group, across all
problems, were 3 : 1. When the judgments of the two groups were tested
for external calibration, it was foundthat subjects in the first group were too
extreme, in accord with earlier studies.
The events that they defined as having
a probability of .10 actually obtained in
24 percent of the cases. In contrast,
subjects in the second group were tooconservative. Events to which they assigned an average probability of .34
actually obtained in 26 percent of thecases. These results illustrate the manner in which the degree of calibration
depends on the procedure of elicitation.

Discussion
This article has been concerned withcognitive biases that stem from the reliance on judgmental heuristics. These
biases are not attributable to motivational effects such as wishful thinking or
the distortion of judgments by payoffs
and penalties. Indeed, several of thesevere errors of judgment reported
earlier occurred despite the fact that
subjects were encouraged to be accurate
and were rewarded for the correct
answers (2, 6 ) .
The reliance on heuristics and theprevalence of biases are not restricted
to laymen. Experienced researchers arealso prone to the same biases-when
they think intuitively. For example, thetendency to predict the outcome thatbest represents the data, with insufficient
regard for prior probability, has been
observed in the intuitive judgments ofindividuals who have had extensive
training in statistics (1, 5). Although
the statistically sophisticated avoid
elementary errors, such as the gambler's
fallacy, their intuitive judgments areliable to similar fallacies in more intricate and less transparent problems.

It is not surprising that useful heuristics such as representativeness andavailability are retained, even though
they occasionally lead to errors in prediction or estimation. What is perhaps
surprising is the failure of people toinfer from lifelong experience suchfundamental statistical rules as regression toward the mean, or the effect ofsample size on sa.mpling variability. Although everyone is exposed, in the normal course of life, to numerous examples from which these rules could
have been induced, very few people
discover the principles of sampling andregression on their own. Statistical principles are not learned from everyday
experience because the relevant instances are not coded appropriately. For
example, people do not discover thatsuccessive lines in a text differ more in
average word length than do successive
pages, because they simply do not attend to the average word length of individual lines or pages. Thus, people
do not learn the relation between sample
size and sampling variability, although
the data for such learning are abundant.
The lack of an appropriate code also
explains why people usually do notdetect the biases in their judgments ofprobability. A person could conceivably
learn whether his judgments are externally calibrated by keeping a tally of the
proportion of events that actually occur
among those to which he assigns thesame probability. However, it is notnatural to group events by their judged
probability. In the absence of suchgrouping it is impossible far an individual to discover, for example, that only
50 percent of the predictions to which
he has assigned a probability of .9 orhigher actually came true.
The empirical analysis of cognitive
biases has implications for the theoretical and applied role of judged probabilities. Modern decision theory (12, 13)
regards subjective probability as thequantified opinion of an idealized person. Specifically, the subjective probability of a given event is defined by theset of bets about this event that such aperson is willing to accept. An internally consistent, or coherent, subjective
probability measure can be derived for
an individual if his choices among bets
satisfy certain principles, that is, theaxioms of the theory. The derived probability is subjective in the sense thatdifferent individuals are allowed to havedifferent probabilities for the same event.
The major contribution of this approach is that it provides a rigorous

subjective interpretation of probability
that is applicable to unique events andis embedded in a general theory of rational decision.
It should perhaps be noted that, while
subjective probabilities can sometimes
be inferred from preferences among
bets, they are normally not formed inthis fashion. A person bets on team A
rather than on team B because he believes that team A is more likely towin; he does not infer this belief fromhis betting preferences. Thus, in reality,
subjective probabilities determine preferences among bets and are not derived from them, as in the axiomatictheory of rational decision (12).
The inherently subjective nature ofprobability has led many students to thebelief that coherence, or internal consistency, is the only valid criterion bywhich judged probabilities should be
evaluated. From the standpoint of theformal theory of subjective probability,
any set of internally consistent probability judgments is as good as any other.
This criterion is not entirely satisfactory,
because an internally consistent set of
subjective probabilities can be incompatible with other beliefs held by theindividual. Consider a person whose
subjective probabilities for all possible
outcomes of a coin-tossing game reflect
the gambler's fallacy. That is, his estimate of the probability of tails on aparticular toss increases with the number of consecutive heads that precededthat toss. The judgments of such a person could be internally consistent andtherefore acceptable as adequate subjective probabilities according to thecriterion of the formal theory. These
probabilities, however, are incompatible
with the generally held belief that acoin has no memory and is therefore incapable of generating sequential dependencies. For judged probabilities tobe considered adequate, or rational, internal consistency is not enough. The
judgments must be compatible with theentire web of beliefs held by the individual. Unfortunately, there can beno simple formal procedure for assessing the con~patibilityof a set of probability judgments with the judge's total
system of beliefs. The rational judge
will nevertheless strive for compatibility,
even though internal consistency ismore easily achieved and assessed. In
particular, he will attempt to make his
probability judgments compatible withhis knowledge about the subject matter, the laws of probability, and his own
judgmental heuristics and biases.
SCIENCE, VOL. 185

Summary
This article described three heuristics
that are employed in making judgments
under uncertainty: (i) representativeness,
which is usually employed when people are asked to judge the probability
that an object or event A belongs toclass or process B; (ii) availability of instances o r scenarios, which is often employed when people are asked to assess
the frequency of a class or the plausibility of a particular development; and(iii) adjustment from an anchor, which
is usually employed in numerical prediction when a relevant value is available.
These heuristics are highly economical

and usually effective, but they lead tosystematic and predictable errors. A
better understanding of these heuristics
and of the biases to which they lead
could improve judgments and decisions
in situations of uncertainty.
References and Notes
1. D. Kahneman and A. Tversky, Psychol. Rev.
SO, 237 (1973).
2. ---, Cognitive Psychol. 3, 430 (1972).
3. W. Edwards, in Formnl Representation o f
Human Judgment, B. Kleinmuntz, Ed. (Wiley,
New York, 1968), pp. 17-52.
4. P. Slovic and S. Lichtenstein, Organ. Behav.
Hum. Performance 6, 649 (1971).
5. A. Tversky and D. Kahneman, Psychol. Bull.
76, 105 (1971).
6. -,Cognitive Psychol. 5 , 207 (1973).
7. R. C. Galbraith and B. J. Underwood,Mem. Cognition 1, 56 (1973).

Rural Health Care in Mexico?
Present educational and administrative structures must bechanged in order to improve health care in rural areas.
Luis Cafiedo

The present health care structure in
Mexico focuses attention on the urban
population, leaving the rural communities practically unattended. There are
two main factors contributing to thissituation. One is the lack of coordination among the different institutions
responsible for the health of the community and among the educational
institutions. The other is the lack of
information concerning the nature of
the problems in rural areas. In an attempt to provide a solution to these
problems, a program has been designedthat takes into consideration the environmental conditions, malnutrition,
poverty, and negative cultural factorsthat are responsible for the high incidences of certain diseases among rural
populations. It is based on the development of a national information system
for the collection and dissemination of
information related to general, as wellas rural, health care, that will provide
the basis for a national health care system, and depends on the establishmentof a training program for professionals
in community medicine.

The continental and insular area of
Mexico, including interior waters, is
2,022,058 square kilometers (1, 2 ) . In
1970 the population of Mexico was
48,377,363, of which 24,055,305 persons (49.7 percent) were under 15
years of age. The Indian population
made up 7.9 percent of the total (2, 3 ) .
As indicated in Table 1, 42.3 percentof the total population live in communities of less than 2,500 inhabitants, andin such communities public services aswell as means of communication arevery scarce or nonexistent. A large percentage (39.5 percent) of the economically active population is engaged inagriculture (4).
The country's population growth rate
is high, 3.5 percent annually, and it
seems to depend on income, being
higher among the 50 percent of the
population earning less than 675 pesos($50) per family per month (5). The
majority of this population lives in therural areas. The most frequent causesof mortality in rural areas are malnutrition, infectious and parasitic diseases(6, 7), pregnancy complications, and

8. L. J. Chapman and J. P. Chapman, I .
Abnorm. Psvchol. 73. 193 (1967): ibid... 74..
271 (1969).
9. M. Bar-Hillel, Organ. Behav. Hurn. Performance 9, 396 (1973).
10. J. Cohen, E. I. Chesnick, D. Haran, Br. J.
P s ~ c h o l .63. 41 (1972).
11. M: Alpert and H. ~ i i f f a ,unpublished manuscript; C. A. S. von Holstein, Acta Psychol.
35, 478 (1971); R. L. Winkler, J. A m . Slat.
Assoc. 62, 776 (1967).
12. L. J. Savage, The Foirndatior~s o f Statistics(Wiley, New York, 1954).
13. B. De Finetti, in International Encyclopediao f the Social Sciences, D. E . Sills, Ed. (MacmiUan, New York, 1968), vol. 12, pp. 496504.
14. This research was supported by the Advanced
Research Projects Agency of the Departmentof Defense and was monitored by the Oficeof Naval Research under contract N0001473-C-0438 to the Oregon Research Institute,
Eugene. Additional support for this research
was provided by the Research and Development Authority of the Hebrew University,
Jerusalem, Israel.

accidents (2). In 1970 there were 34,107 doctors in Mexico (2). The ratio
of inhabitants to doctors, which is1423.7, is not a representative index
of the actual distribution of resources
because there is a great scarcity ofhealth professionals in rural areas anda high concentration in urban areas(Fig. 1) (7, 8 ) .
In order to improve health at a national level, this situation must bechanged. The errors made in previous
attempts to improve health care must
be avoided, and use must be made of
the available manpower and resourcesof modern science to produce feasible
answers at the community level. Although the main objective of a specialist in community medicine is to control
disease, such control cannot be
achieved unless action is taken against
the underlying causes of disease; it has
already been observed that partial solutions are inefficient (9). As a background to this new program that has
been designed to provide health carein rural communities, I shall first givea summary of the previous attempts
that have been made to provide suchcare, describing the various medical institutions and other organizations thatare responsible for the training of medical personnel and for constructing thefacilities required for health care.
The author is an investigator in the departmentof molecular biology at the Instituto de Investigaciones Biomkdicas, Universidad Nacional Aut6noma de Mexico, Ciudad Universitaria, Mexico
20, D.F. This article is adapted from a paper
presented at the meeting on Science and Man in
the Americas, jointly organized by the Consejo
Nacional de Ciencia y Tecnologia de Mkxico and
the American Association for the Advancementof Science and held in Mexico City, 20 June to
4 July 1973.

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Judgment under Uncertainty: Heuristics and Biases
Amos Tversky; Daniel Kahneman
Science, New Series, Vol. 185, No. 4157. (Sep. 27, 1974), pp. 1124-1131.
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References and Notes
11

The Assessment of Prior Distributions in Bayesian Analysis
Robert L. Winkler
Journal of the American Statistical Association, Vol. 62, No. 319. (Sep., 1967), pp. 776-800.
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