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PONT P1R-1OSO-77-1O
CAUSAL SCHEMATA IN
JUDGMENTS UNDER UNCERTAINTY
11’
~ DECISION RESEARCH • A BRANCH OF PERCEPTRONICS
Amos Tversky
Daniel Kahneman
October 1977
D D C
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JUL 24 1918
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DECI&IONTECHNOLOGY
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C Y B E R N E T I C S T E C H N O L O G O F F I C E
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The objective of the Advanced Decision
Technology Program is to develop and transfer
to users in the Department of Defense advanced
management technologies for decision making.
These technologies are based upon research
in the areas of decision analysis, the behavioral
sciences and interactive computer graphics .
The program is sponsored by the Cybernetics
Technology Office of the Defense
Advanced Research Projects Agency and
technical progress is monitored by the Office
of Naval Research — Engineering Psychology
Programs. Participants in the program ~
re
Decisions and Designs,Incorporated
Harvard University
Perceptronics, Incorporated
Stanford Research Institute
Stanford University
The University of Southern California
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regard to this report should be
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Director , Engineering Psychology Programs
Office of Naval Research
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or
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Cybernetics Technology Office
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The views and conclusions contained In this document are those of the author (s) and should not be intsrpreted as necessarily
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Government . This document has been approved for public release with unlimited distribution.
\,JTECHN ICAL tEP
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CAUSAL SCHEMATA IN~jJJDGMEN TS UNDER UNCERTA IN1Y7\
_ _ _ _ _ _ _ _ _ _ _
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~~~~~~~~~~~~~~~ ~~~DanieI~(ahnem~~~~~~
Sponsored by
Defense Advanced Research Projects Agency
ARPA Order No. 3469
Under Subcontract from
Decisions and fle~grc “gvrpr’
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DECISION RESEARCH
A BRANCH OF PERCEPTRONICS
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SUMMARY
Perhaps the major source of irrationality in risky
decisions is the exaggerated response to the contrast between
cer tain ty and possibility, and the inadequate sensitivity to
probability differences. We hypothesize that this tendency
will have a major biasing effect on tradeoffs between attributes
that involve both certain and probable changes. This hypothesis
has important consequences to strategic decisions and negotiations .
In these contexts , one of ten trades a certain gain or loss
(e.g.~ gaining or losing a military advan tage) in exchange for
probabilistic gains or losses (e.g., an increase or a decrease
in the probability of war). The preceding analysis suggests
that probabilistic gains and losses will be undervalued in
comparison to sure gains and sure losses. Methods for communicating
this bias to dec ision makers and procedures for eliminating it
will be explored.
Decision analysis views subjective probability as a degree
of belief , i.e., as a summary of one ’s state of information about
an uncerta-~.n event. This concept does not always coincide with
the lay interpretation of probability . People sometimes think
of the probability of an event as a measure of the propensity
of some causal process to produce that event , ra ther than as a
swnmary of their state of belief. The tendency to regard
properties as belonging to the external world rather than to our
own state of information characterizes much of our perception .
We normally regard colors as properties of objects, not of our
visual system, and we trea t sounds as external ra ther than intern al
events. In a similar vein , people commonly interpret the assertion
“the probability of heads on the next toss of this coin is 1/ 2”
as a statement about the propensity of the coin to show heads ,
rather than as a statement about our ignorance regarding the
outcome of the next toss.
ii
- _j
The interpretation of probability as propensity leads
people to base their judgments of likelihood primarily on causal
considerations , and to ignore information that does not have
cau sal interpretation produces characteristic errors in
judgments of probability . Research to date has investigated
this phenomenon in three different contexts. One experiment
indicates that the assessment of a conditional probability,
P (AIB), is determined mainly by the perceived causal impact of
B on A , even when this mode of judgment yields paradoxes and
inconsistencies. A second study was concerned with the
assessment of the posterior probabil ity of an event, given the
base-rate frequency of that event and some additional specific
evidence. The results indicated that base—rate information is
generally ignored unless it is given a causal interpretation.
A third study examined the a3sessment of the probability of a
hypothesis H given two items of information D
1
and D2, on the
basis of the prior probability P (H ), and the conditional
probabilities P(H~D
1
) and P (HID2
). It showed that people adopt
different rules for combining evidence when the data (D
1
and D2
)
are given a causal interpretation.
These resu lts illustrate the discrepancy between in tui tive
judgments under uncertainty and the normative theory of subjective
probability. In the latter , all probability assessments refer
to one ’s degree of belief , ar d the same formal calculus applies
to the combination of all pr3babilistic data . In contrast , people
have several different ways of thinking about probability , and
their approach to the combination of probabilistic data depends
on the manner in which those data are interpreted . This
discrepancy presents a major educational challenge : to help
people achieve a synthesis between their natural modes of
judgment and the logic of probability .
iii
A
TABLE OF CONTENT S
Page
SUMMARY ii
ACKNOWLEDGMENT v
1. INTRODUCTION 1-1
2. CAUSAL AND DIAGNOSTIC REASONING 2-1
2.1 Confidence in Causal and Diagnostic 2-1
Inferences
2.2 Causal and Diagnostic Interpretations 2—5
of Events
2.3 Prediction , Explanation and Revision 2—10
3. ON THE USE AND NEGLECT OF BASE-RATES 3-1
4. REFERENCES 4-1
DISTRIBUTION LIST D-1
DD FORM 1473
iv
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I
ACKNOWLEDGMENT
This research was sponsored by the Advanced Research
Projects Agency of the Department of Defense and was monitored
by Office of Naval Research under Contract N000l4-78-C-OlOO
(ARPA Order No. 3469) under Subcontract from Decisions and
Designs , Inc., to Oregon Research Institute and Subcontract
78-072-0722 to Perceptronics , Inc.
I
I
1. INTRODUCTION
I
Many of the decisions we make , in tr ivial as well as in
crucial matter s, depend on the apparent likelihood of ~vents
such as the keeping of a promise, the success of an enterprise ,
or the response to an action. Since we generally do not have
adequa te formal rr~-1~’~
1r to compute the probabilities of such
events, their asse .~ment is necessarily subjective and intuitive .
The manner in whic~i people evaluate evidence to assess
probabilities has aroused much research interest in recen t year s,
e.g., Edwards (1968), Slovic (1972), Tversky and Kahneman (1974),
Slovic , Fischhoff and Lichtenstein (1977), Kahnernan and Tversky
(1978). This research has identified several judgmental
mechanisms which are associated with characteristic errors and
biases. The present paper is concerned with the role of causal
thinking in judgments under uncertainty and with some biases that
are associated with this mode of thinking .
We investigate judgments of the conditional probability
P(X/D) of some target event X, on the basis of some evidence or
Data D. For a psychological analysis of the impact of evidence ,
it is useful to distinguish between different types of relations
that the judge may perceive between D and X. If D is commonly
perceived as a cause of the occurrence of non—occurrence of X ,
or as an indication of the presence of such a cause , we re fer
to D as a causal datum . On the other hand , if X is trea ted as a
possible cause of D, we refer to D as a diagnostic datum .
Finally , if the jud ge fails to see D either as a cause or as a
consequence of X , we refer to D as an incidental datum . In a
normative analysis , this distinction between causal , diagnostic
and incidental data is immaterial , and the impact of data depends
solely on their informativeness.
1—1
— - -
~~~~~~~~~~~~~~~~~~
— - - -- ---
-I ~~~~~
--- - -
It is a psychological commonplace that people strive to
achieve a coherent interpretation of the events that surround
them , and that the cogni tive organiz ation of events into causal
schemata is one of the primary means of achieving such coherence .
The classical work of Michotte (1963) provided a compelling
demonstration of the irresistible tendency to perce ive sequences
of events in terms of causal relations, even when the perceiver
is fully aware that the rela tion between these events is
incidental and that the imputed causality is illusory . The
preva lence of causal schemata in the perception of elementary
social relations was highlighted in Heider ’s (1958) seminal work
and the study of causa l attribution is one of the foci of
contemporary social psychology (Jones et al. 1972; Ross , 1977).
People normally think in terms of causes and effects.
They can also invert the normal sequence and reason from
consequences to causes. Incidental data which do not enter into
causal schemata do not con tribute to the coherent organization
of events. These general considerations provide a background
for the main theme of this paper , that the impact of evidence
depends cri tically on whether it is perce ived as causal ,
diagnostic or incidental. Specifically, we hypothesize (i) that
causal data has a greater impact than diagnostic da ta of equal
informativeness , and (ii) that incidental data are given little
or no weight, in the presence of causal or diagnostic data.
In the first par t of the paper , we compare the effec ts
of causal and dia gnostic data , and show that people assign grea ter
impact to causal than to diagnostic data of equal informativeness.
We also explore a class of problems where a particular datum has
both causal and diagnostic significance , and demonstrate that
intuitive assessments of P(X/D) are dominated by the direct causal
I
1—2
-- - -
~~
--. -
~~
-- —
a
impact of D on X, with insufficient regard for diagnostic
considerations. The second part of the paper compares the
impact of causal and incidental data of equal informativeness.
Specifically, we investigate judgments of the posterior
probabili ty of an event, on the basis of the base—rate frequency
of that event and some additional data. We show that base-rate
data that are given a causal interpretation affect judgments,
while base-rates that do not fit into a causal schema are given
little or no weight.
I
I
a
P
1—3
P
2. CAUSAL AND DIAGNOSTIC REASONING
a
2.1 Confidence in Causal and Diagnostic Inferences
A causal schema represents an association between a
cause and an effect, in which the cause precedes the effect both
logically and temporally. Thus, it is hardly surprising that
people find it easier and more natural to follow the normal
sequence and reason from causes to consequences than to invert
this sequence and reason from consequences to causes. If causal
inferences are indeed eas ier and more natural than diagnostic
inferences, then one would expec t people to infer effec ts from
causes with greater confidence than causes from effec ts — even
when the effect and the cause actually provide the same amount
of information about each other. We tested this hypothesis
using two different measures: judgments of conditional probabilities
and confidence in the accuracy of predictions .
In one set of ques-tion5 we asked subjects to compare the
two conditional probabilities P(y/X) and P(X/Y) for a pair of
events X and Y such that (i) X is naturally viewed as a cause
of Y , and (ii) P(X) = P(Y), i.e., the base—rate probabilities
of the two events are equal. The latter condition implies that
P(Y/X) = P(X/Y). Our prediction was that most subjects would
view the causal relation as stronger than the diagnostic
relation , and would erroneously assert that t
~(Y/X)> P(X/Y).
In another set of questions , we asked subjects to compare
their confidence in predictions involving two continuous
variables , depending on which of these variables was given and
• which was to be predicted . Here again , the problems are
constructed so that one of the variables is naturally viewed as
causal with respect to the other. If the two variables have
a
P
2—1
similar marginal distributions , there is no valid statistical
reason to expec t a difference in the accuracy with which one of
the variables can be predicted from the other. We h;pothesized
that most subjects would state that a prediction from cause to
effect can be made with greater confidence than a prediction from
effect to cause .
The predicted asymmetry between causal and diagnostic
inferences was strongly confirmed with both types of questions.
The effect is illustrated by the following problems , where the
numbers in par entheses indicate the number of subjects who chose
each option .
P
Problem 1: Which of the following events is more probable?
(a) That a girl has blue eyes if her mother has blue
eyes (N = 106)
(b) That the mother has blue eyes, if her daughter has
blue eyes (N = 34)
(-) The two events are equally probable (N = 35)
Problem 2: In a survey of high-school seniors in a city ,
the height of boys was compared to the height of their
fathers. In which prediction would you have greater
confidence ?
(a) The prediction of the father ’s hei ght from the son ’s
height (N = 15)
(b) The prediction of the son ’s height from the father ’s
height (N = 111)
(-) Equal confidence (N = 24 )
Since the distribution of height or eye color is
essentially the same in successive generations , the correct answer
to both problems is “ Equal” . Most subjects , however , expressed
2— 2
I
grea ter confidence in the causal than in the diagnostic
prediction .
Problems 1 and 2 illustrate a fa irly direct causal
relationship. Strictly speaking, of course , the color of the
mother ’s eyes is not a cause of her daughter ’s eye color. It
is merely a man ifestation of a genetic mechanism which determines
the color of the mother ’s eyes, and could also de termine the
eye color of her daughter. In common usage , however , it is quite
acceptable to say that a boy is tall because his father is 6’4” ,
while the statement that the father is 6’4” because his son is
tall is clearly anomalous . There are many other situations
in which the earlier manifestation of an underlying causal system
is treated as a cause of subsequent manifestations of the same
system.
A rather more subtle relation exists between manifestations
of the same causal system which vary in the degree to which they
directly represent that system . Here again , we expect the more
direct manifestation of the underlying cause to serve as a proxy
for it, in relation to less direct manifestations of the same
system. Consequently , inferences from the more to the less
direct express ion of an underlying trait or disposition should
be made with greater confidence than inferences in the inverse
direction . Problems 3 and 4 illustrate the type of questions
that were used to test this hypothesis.
Problem 3: Which of the following events is more probable?
(a) That an athlete won the decathlon , if he won the
first event in the decathlon (N = 19)
(b) That an athlete won the first event in the decathlon,
if he won the decathlon (N = 93)
(-) The two events are equally probable (N = 34)
z
2—3 _ _ _ _ _ _ _ _ _ _ _ _ _ _
Problem 4: Two tests of intelligence were administered
to a large group of students : a one-hour comprehensive
test, and a 10—minute abbreviated version .
In which prediction would you have greater confidence?
(a) The prediction of a student ’s score on the shor t
test from his score on the comprehensive test
(N = 143)
(b) The prediction of a student’s scor e on the
comprehensive test from his score on the short tes t
(N = 33)
(-) Equal confidence (N = 17)
Here again , the correc t answer is ‘Equal’ in both
problems . In Problem 3, the prior probability that an
(unspecified) athlete will win the decathlon is 1/N, where N
is the number of competitors. This is also the prior probability
that an unspecified athlete will win the first event. Consequently,
the two conditional probabilities must be equal. In Problem 4,
the standard assumption of linear regressions entails equal
accuracy in the prediction of one test from another. The responses
to both problems , however , exhibit a marked preference for one
direction of prediction over the other.
Problems 3 and 4 both involve two manifes tations of the
same underlying trait, which differ in reliability . Victory in
* the decathlon and victory in a single event are both manifestations
of athletic excellence , but the former provides a stronger
indication of excellence than the latter. Similarly, performance
in intelligence tests reflects an underlying trait of intelligence ,
and the more comprehensive test provides a more reliable measure
of this trait than does the abbreviated version. The results
confirm the hypothesis that the prediction from the more reliable
to the less reliable manifestation is associated with greater
confidence than the inverse prediction.
•
2—4 ___________________________ _ _ _ _ - . -_ _ _ _ _ _ _ _ _ _
-
I
2.2 Causal and Diagnostic Interpretations of Events
I
The previous section showed that the impact of causal
data on the judged probability of a consequence is greater than
the impact of diagnostic data on the judged probability of a
cause . The present section investigates questions in which the
evidence has both causal and diagnostic significance with respect
to the target event. We study the hypothesis that people tend to
focus on the causal impact of the data for the future , and tend
to neglect their diagnostic implications about the past. We
f irst discuss a class of problems in which the dominance of
causal over diagnostic considerations produces inconsistent and
paradoxical probability assessments. This type of problem was
originally introduced by Turoff (1972) in a discussion of the
cross-impact method of forecasting .
Problem 5: (Turoff). Let C be the event that within
the next 5 years Congress will have passed a law to
curb mercury pollut ion, and let D be the event that
within the next 5 years , the number of deaths attributed
to mercury poisoning will exceed 500. Let C and ~
denote the negotiations of C and D , respectively.
2
Question : Which of the two conditional probabilities,
P(C/D) or P(C/~ ), is higher?
Question:Which of the two conditional probabili ties ,
P(D/C) or P(D/~ ), is higher?
The overwhelming majority of respondents state that
Congress is more li kely to pass a law restricting mercury
pollution if the death toll exceeds 500 than if it does not ,
i.e., P(C/D > P(C/~
). Most people also state that the death toll
is likely to reach 500 if a law is enacted within the next five
years than if it is not, i.e., P(D/C) < P(D/Th .
The symbols C,D, etc. are introduced to facilitate the present
exposition . They were not presented to the respondents who were
given complete verbal descriptions of the events.
1
2—5
I
These judgments reflect the causal beliefs that a high death
toll would increase the pressure to pass an anti—pollution
measur e, and that a measure would be effec tive in the prevention
of mercury poisoning. In one sample of 68 students , 58 chose
the modal answer to both questions. This seemingly plausible
pattern of judgments violates the most elementary rules of
conditional probability .
Clearly, P(C/D) > P(C/D) implies P(C/C) > P ( C ) .
Furthermore, the inequality
P(C/D) =
P ( C & D )
> P(C)
I
holds if and only if P(C & D) > P(C) P(D) which holds if and only
if
P(D)
P(C & D) = P(D/C)
which in turn implies P(D/C) > P(D/C), provided P(C) and P(D) are
non-zero . Hence , P(C/ D) > P(C/5) implies P(D/C > P(D/~ ), contrary
to the prevailing pattern of judgment.
It is easy to construct additional examples of the same
type in which people ’s intuitions violate the probability calculus .
Such examples consist of a pair of events , A and B, such that the
• occurrence of B increases the likelihood of the subsequent
occurrence of A , while the occurrence of A decreases the likelihood
of the subsequent occurrence of B. For example , consider the
~ I
following problem .
Problem 6 : Let A be the event that before the end of next
year , Peter will have installed a burglar alarm system in
his home . Let B denote the event that Peter ’s home will be
I
2—6
I
burglarized before the end of next year.
Question : Which of the two conditional probabilities ,
P (A/B ) or P(A/B), is higher?
Question : Which of the two conditional probabilities ,
P(B/A) or P(B/A), is hi gher ?
A large majority of our subjects (56 of 68) stated that
P(A/B) > P(A/~ ) and that P(B/A) < P(B/~ ), contrary to the laws
of probability . We interpret this pattern of judgments as
another indication of the dominance of causal over diagnostic
considerations. To appreciate the nature of the effect, let us
analyze the structure of Problem 6.
First consider P (A/B ), the conditional probability that
Peter will install an alarm system in his home before the end
of next year , assuming that his home will be burglarized
sometime during this period . The alarm system could be installed
either before or after the burglary . The information conveyed
by the condition , i . e . , the assumption of a burglary , has causal
significance with respect to the future and diagnostic
significance with respect to the past. Specifically, the
S occurrence of a burglary provides a cause for the subsequen t
installation of an alarm system , and it provides a diagnostic
indication that the house had not been equipped with an alarm
system at the time of the burglary . Thus, the cau sal impact’of
the burglary increases the likelihood of the alarm system while
the diagnostic impact of the burglary decreases this likelihood.
The nearly unartimous judgments that P(A/B) > P(A/B) indicates
that the causal impact of B dominates its diagnostic impact.
Precisely the same analysis applies to P(B/A) - the
probability that Peter ’ s house will be burglarized before the end
of next year , given that he will have installed an alarm system
I
2—7
_ _ _ _ _ _• - - -- --- ----- - -—--
~~~~~~~~~~~~~~~-
a
sometime during this period . The presence of an alarm system
I is causally effective in reducing the likelihood of a subsequent
burglary ; it also provides a diagnostic indication that the
occurrence of a burglary could have prompted Peter to install
the alarm system. The causal impact of the alarm system reduces
the likelihood of a bur glary ; the diagnostic impact of the alarm
system increases this likelihood . Here again , the prevalence
of the judgment that P(B/A) < P(B/A) indicates that the causal
impact of A dominates its diagnostic impact. Instead of
weightin g the causal and the diagnostic impacts of the evidence ,
people apparen tly assess the conditional probabilities P(A/B ) and
P(B/A) primarily in terms of the direct causal effect of the
condition , which leads to contradictions in problems of this type.
• A salient feature of Turoff’ s problems is the ambigu ity
of the temporalrelation between the conditioning event and the
target event. Even in the absence of temporal ambiguity ,
I however , it is of ten the case that the conditioning event has
both causal and diagnostic significance . The present analysis
leads to the hypothesis that assessments of cond itional
probabilities are dominated by causal considerations , even when
I the temporal relation between the events is fully specified.
Problem 7 : Which of the following two probabilities is
higher ?
3 P (R/H)- The probability that there will be rationing of fuel for
individual consumers in the US during the l99~. ‘s, if you
assume that a marked increase in the use of solar energy
for home heating will occur during the 1980’s.
I
P(R/ii)- The probability that there will be rationing of fuel for
individual consumers in the US during the 1990’s, if you
assume that no marked increase in the use of solar energy
for home heating will occur during the 1980’s.
*
2—8
A
_ _ _ —~~~~
-- ---
I
It is perhaps instructive to consider the normative
(Bayesian) approach to this problem, in the li ght of the
distinction we have drawn between causal and diagnostic
considerations. The event H that there will be a marked
increase in the use of solar energy for home heating during the
• 1980’s has both causal and diagnostic significance . The direct
causal impact of H on R is clearly negative . Other things being
equal , a marked increase in the use of solar energy can only
alleviate a fuel crisis in later years. However , a marked
increase in the use of solar energy during the 80 ’s also provides
a stron g indication of an impending energy crisis. In particular ,
it suggests that fuel prices in the 80’s are suff iciently high
to make the investment in solar energy for home heating economical
for a large number of consumers. High fuel prices in the 80’s,
in turn , suggest a state of shortage of fossil fuel , which
increases the likelihood of fuel rationing in the subsequent
decade. Thus , the direct causal impact of H on R reduces the
likelihood of R , whereas the diagnostic implications of H
indirectly increase the likelihood of R.
Although the question of the relative strength of these
fac tors cannot be settled formally, we contend that the diagnostic
implications of H outweigh its causal impact. The amount of
fuel that may be saved by the increased use of solar energy for
home heating is unlikely to be large enough to avert an impending
crisis. On the other hand , the scarc ity of fuel which is implied
by H is highly indicative of a forthcoming energy crisis.
Accordin g to this line of reasoning P (R/H ) > P (R/H ), where H is
the negation of H.
The hypothesis of this section , however , was that people
generally overweigh t the direct causal contribution of the
conditioning event in asses sments of conditional probabil ities ,
I
C
2—9 _ _ _ _ _ _
and do not give sufficient weight to its diagnostic significance .
This hypothesis entails, in the example of Problem 7 , that the
stipulation of an increase in the use of solar energy for heating
in the 1980’s will reduce the judged probability of fuel
rationing in the 1900’s. Indeed , 68 of 83 respondents stated
that P(R/H) < P(R/i~). The same pattern of judgments is observed
in other problems of this type , where the indirect diagnostic
implications of the condition are in conflict with its direct
causal implications . Although this pattern of judgments does
• not violate the rules of probabili ty, as was the case in
Turoff’s problems , it reflects , we believe , a common tendency
to neglect the diagnostic significance of the conditioning
event in judgments of conditional probability .
2.3 Prediction, Explanation and Revision
In the preceding sections we presented some evidence
in support of the hypothesis that causal inferences have
greater efficacy than diagnostic inferences. First we showed
that inf erences from causes to consequences are made with
greater confidence than inferences from consequences to causes.
Second , we showed that when the same data have both causal
and diagnostic significance, the former is generally given more
weight than the latter in judgments of conditional probability .
We turn now to the more general question of the relation
between an image , model or schema of a system , e.g., the energy
situation or the personality of an individual , and some outcome
or manifes tation of that system, e.g., an increased use of
solar energy or a display of hostility . The relation between
models and outcomes is relevant to several types of judgments ,
I
*
2—10
~~~1
I
including prediction , explanation and model-revision . Thus ,
a person may apply the model to predict the outcome or to
assess its probability . He may use the model to explain the
occurrence of a particular event or consequence . Finally ,
he may employ the information provided by the occurrence of
a particular event to correct or revise his model.
Prediction and explanation represent two dif ferent
types of causal inference , while model-revision is a prototype
of diagnostic inference. In prediction, the judge selects
that outcome which is most congruent with his model of the
system. In explanation, the judge iden tifies those fea tures
of the model that are most likely to give rise to the specifi ed
outcome. In revision , on the other hand , the judge correc ts
or completes the elements of the model tha t are least congruent
with the data .
3
Most inferences in everyday life rely on models or
images which are imprecise , incomplete and occasionally incorrect.
Moreover , people are commonly willin g to acknowledge that their
models of systems such as the intentions of a person or the
energy situation could be in error . The presence of uncertainty
regarding the accuracy of a model has implications for the
proper conduct of prediction , explanation and revision . If a
model is subject to error , predictions from that model should
be moderate or regressive , i.e., they should not grea tly depar t
from base-rate predictions . For instance, one should be more
reluctant to predict that a person will engage in a rare or
a unusual behavior when one ’s information about the person comes
from an unreliable source than when the same information comes
from a more reliable source .
I
2—11
~ -~~~----~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- -
---
a
•
Explanations that are based on uncertain models should
also be tempered with caution , since the causalfactors that
are used in the explanation may not exist in reality .
Fur thermore , explanation in the presence of uncertainty should
always be combined with model-revision . For example , if a
person engages in an activity that appears incompatible with
our impression of his personality, we should seriously cons ider
the poss ibility that our impression was incorrect, and that
it should be revised in the direction suggested by the new
data . The greater the uncertainty about the model and the
more surprising the behavior , the grea ter should the rev ision
be. An adequate explanation should take into account the
changes in the model that are implied or suggested by the
event that is to be explained . From a normative point of view ,
therefore , explanation in the presence of uncertainty about
the model involves both diagnostic and causal inferences.
Previous research has shown that people commonly
overpredict from highly uncertain models. For example ,
subjects confidently predict the professional choice or
academic performance of an individual on the basis of a brief
personality sketch , even when this sketch is attributed to an
unreliable source (Kahneman and Tversky , 1973). The intentions
and traits that are inferred from a personality ske tch are
naturally viewed as causes of such outcomes as professional
choice or success in school. The overprediction that is
observed in such
4
problems is therefore compatible with the
high eff icacy of causal data that was discussed in the
• preceding sections.
r
2—12
C
-_ -.— - -
~~~~
-
I
In the context of explanation and revision, the strength
of causal reasoning and the weakness of diagnostic reasoning
are manifest in the great ease with which people construct
causal accounts for outcomes which they could not predict, and
in the di f f i c u lty that they have in revising uncer ta in models
to accomodate new data. It appears easier to assimilate a
new fact within an existing causal model than to revise the
model in the light of this fact. Moreover , the revisions that
are made to accommodate new facts are of ten minimal in scope an d
local in character.
To illustra te this notion , we turn to prev iously
unreported observations from an earlier study of intuitive
prediction (Kahneman and Tversky , 1973). In that study 114
graduate students in psychology were presented with a paragraphlength
descr iption of a graduate student, Tom W., which had
alledgedly been written dur ing his senior year in high school
by a clinical psychologist, on the basis of projective tes ts.
The following description was given:
“Tom W. is of high intelligence , although lackin g in
true creativity . He has a need for order and clarity ,
and for neat and tidy systems in which every detail
finds its appropriate place. His writing is ra ther
dull and mechanical , occasionally enlivened by somewhat
corny puns and by flashes of imagination of the sci-fi
type. He has a strong drive for competence. He seems
to have little feel and little sympathy for other people
and does not enjoy interacting with others. Self-
I
centered , he nonetheless has a deep moral sense.
I
2—13
‘
I
- --- --- - - -- —
I
The subjects were first asked to predict Tom W .’s field of
graduate specialization by ranking nine possibilities in terms
of their likelihood . There was a strong consensus among the
respondents that Tom W. is most likely to be in Computer
Science or Engineering , and least likely to be in Social
Sciences and Social Work or in the Huma~ ities and Education .
Responses to an additional question also exhibited general
agreement that projective tests do not provide a valid source
of information for the prediction of professional choice.
After completing the prediction task , the subjects were asked
the following question .
“In fact, Tom W. is a graduate student in the School of
Education and he is enrolled in a special program for
training for the education of handicapped children.
Please outline very briefly the theory which you consider
a most likely to explain the relation between Tom W. ’s
personality and his choice of career.”
What is the proper approach to this question? The
respondents were faced with an apparent conflict between a
S hard fact, Tom W. ’s choice of career , and a detai led bu t
unreliable description of his personality. The high confidence
wi th which people predict professional choice from personali ty
descriptions implies a belief in a high correlation between
personality and vocational choice . This belief , in turn ,
entails that professional choice is highly diagnostic with
respect to personality . In the above example , Tom W. ’s
vocational choice is unlikely in view of his personality
description, and that description is attributed to a source
of low credibili ty. A reasonable diagnostic inference should
I
2~44
I
therefore lead to a substan tial revision of one ’s image of
$ Tom W .’s charac ter , to make it more compatible with the
stereotype of his chosen profession . If one believes that
students of special education are generally compassionate ,
then Tom W.’s professional choice should raise doubts about
his having “little feel and little sympathy for other people,”
as stated in the psychologist’ s report. An adequate response
to the problem should at least raise the possibility that
Tom W. ’s personality is not as described , and that he is in
fact kinder and more humane than his description suggests.
Our subjects did not follow this approach. Only a
small minority (21%) even mentioned any reservations about the
validity of the description . The overwhelming majority of
respondents , including the sceptics , resolved the conflic t
either by reference to suitably chosen aspects of Tom W. ’s
description (e.g., his deep moralsense ) or by a reinterpretation
of the psychological significance of his choice (e.g., as an
expression of a need for dominance) .
It could be argued that our subjects ’ failure to revise
their image of Tom W. merely reflects the demand characteristics
of the task which they had been assigned , namely to “explain the
relation between Tom W .’s personality and his choice of career.”
According to this account, the task naturally interpreted as
calling for an attempt to relate Tom W. ’s profess ional choice
to the description of his personality without que..~tioning its
validity. We believe , however , that the prevalent tendency
to treat the image of Tom W. as if it were perfectly val id , in
spite of severe doubts , exemplifies a much broader phenomenon :
the tendency to explain without revising, even when the model
that is used in the explanation is highly uncertain .
I
2—15
_ _ _ _ _ — ----- - -~~
-
1 .
In our view , the subjects ’ responses illustra te the
reluctance to revise a rich and coherent model , however
uncer tain , and the ease with which such a model can be used
to explain new facts , however unexpected . We were impressed
by the fluency which our respondents displayed in developing
causal accounts of Tom W .’s unexpected choice of vocation ,
and have no reason to believe that they would have been less
facile in explaining other unexpected behaviors on his part.
Highly developed explanatory skills probably contribute
to the proverbial robustness and stability of impressions ,
models , conceptions and paradigms in the face of incompatible
evidence (Abelson , 1959; Hovland , 1959; Kuhn , 1962; Janis , 1972;
Jervis , 1975). The impetus for revising a model can only come
from the recogn ition of an incon gruency between tha t model and
some new evidence . If people can explain most occurrences to
their own satisfaction with minimal and local changes in their
existing conceptions , they will rarely feel the need for drastic
revision of these conceptions . In this manner , the fluency of
causal thinkin g inhi bits the process of diagnostic revision.
I
I
2—16
;—- - — —‘---- —--- -- -. •— — - ------— - - - — -- - — _
‘~
— ___-___
~~~~~~~~
--_)
_ - - -
P
$ 3. ON THE USE AND NEGLECT OF BASE-RATES
When people judge the probability of an event , they
usually have access to information of two types : singular
• and distributional. Singular information , or case data ,
consists of evidence about the particular case under
consideration. Distributional information , or base-rate data ,
consists of knowledge about the relative frequency of that
event in a relevant population . For example , the presenting
symptoms of a patient or the results of a laboratory test
provide sin gular inf orma tion about the presence of a par ticular
disease , while the base-rate frequency of that disease provides
p distributional information . Although the distinction between
singular and distributional data is not always so clear , it
serves a useful role in the analysis of intuitive inferences.
Note that the present concept of distributional information
I does not coincide with the Bayesian concept of prior probability .
The former is defined by the na tur e of the data , whereas the
latter is defined by the temporal sequence of information
acquisition .
Previous research has shown that judgments of probability
are of ten dominated by singular evidence , with little or no
regard for distributional data . To illustrate , consider the
I following problem (Kahneman and Tversky , 1973).
Problem 8: A panel of psychologists interviewed a sample
of 30 engineers and 70 lawyers , and summarized their
I impressions in thumbnail descriptions of those individuals.
The following descr iption has been drawn at random from
the sample of 30 engineers and 70 lawyers.
I
* 3—1
_ _ _ - -----— —~~~
-- - - - - - --- - - - — - -
“John is a 39-year-old man . He is married and has
two children . He is active in local politics. The
hobby that he most enjoys is rare book collection .
He is competitive , argumentative , and articulate.”
Question : What is the probability that John is a
lawyer rather than an engineer ?
Problem 8 was given to a group 85 respondents. Another
group of 86 respondents answered another version of the same
problem in which the sample from which John was allegedly
drawn was said to consist of 70 engineers and 30 lawyers.
The median answer to Problem 8 was .95 in both groups. The
base—rate frequency of engineers and lawyers had no effect
whatsoever in this problem . In other problems , the manipulation
of base-rate had a slight , albeit significant effect. It
follows readily from Bayes ’ rule that probability of John ’s
being a lawyer should be considerably higher when the base-rate
of lawyers is high than when it is low. Specifically , the
ratio of the posterior odds of the two groups should be (7/3)
2
(Kahneman and Tversky , 1973).
$ In that paper , we related the neglect of base-rate data
to the hypothesis that people evaluate the probability that
John is a lawyer rather than an engineer by the degree to which
he is more representative of the stereotype of lawyers than of
* the stereotype of engineers. Since the similarity of a
I
thumbnail description to the stereotype of a category is
unaffected by the base—rate frequency of the category , a
jud gment of probability that is based exclusively on similarity
or representativeness should be essentially independent of
base-rate frequency . While judgments of probability by
representativeness are inherently insensitive to base—rate
_ _ _ _ _
1$
frequencies , the neglect of base-rate information appears
to be a more general phenomenon , which occurs even when
considerations of representativeness or similarity are
not involved in the assessment of probability .
We now believe that, regardless of whether or not probability
is judged by representativeness, base—rate information will be
dominated by case data , except when it is given a causal
interpretation. We now turn to some elementary demonstrations
of this hypothesis in problems where both b~ se-rate and case
data are provided in numerical form .
Problem 9: A cab was involved in a hit-and-run ci~~’ident
at night: Two cab companies , the Green and the Blue ,
operate in the city . You are given the following data :
(i) 85% of the cabs in the city are Green and 15% are
Blue.
(ii) A witness identified the cab as a Blue cab . The
court tested his ability to identify cabs under
the appropriate visibility conditions . When
presented with a sample of cabs (half of which were
Blue and half of which were Green) the witness
made correct identifications in 80% of the cases
and erred in 20% of the cases.
Question : What is the probability that the cab involved
in the accident was Blue rather than Green?
Several hundred subjects have been given slightly
different versions of this question . For all versions, the
modal and median response was 80%. Thus , the intuitive
judg ment of probability coincides with the credibility of the
witness and ignores the relevant base-rate, i.e . , the relative
frequency of Green and Blue cabs . It is instructive to contrast
people ’s answers with the formal solution of the problem.
I
1
-
4 ,
To obtain the correct answer , let B and G denote respectively
the hypotheses that the cab involved in the accident was
Blue or Green , and let W be the witness ’ report. By Bayes ’
rule in odds form :
I
P(B/W) —
P (W/B)P(B)_ (.8) (.15) —
12
P(G/W)
—
P (W/G)P(G) (.2)(.85)
—
17
and hence P (B/W ) =
12+17
.41
In spite of the witness ’ report , therefore , the hit—and—
run cab is less likely to be Blue than Green , because the
base-rate is more extreme than the witness is credible. The
overwhelming majority of subjects fail altogether to take the
base-rate into account .
Base-rate in formation , however , is properly used in the
absence of case data. When item (ii ) is omitted from Problem 9,
almost all subjects give the correct answer that the probabili ty
of the cab being Blue is .15. In the absence of case data the
question is naturally viewed as a sampling problem, and the
accident serves to define a sampling trial in which a single
cab is drawn from the population of cabs in the city . As soon
as pertinent case data about the hit-and-run cab is introduced ,
3
the base-rate no longer seems relevant. Apparently, people
are unable to relate the color of the hit-and-run cab
simultaneously to two different types of processes: random
sampling of cabs , and imperfect identification of color by a
witness.
I
3—4
I .
The neglect of bast~—rate data is a highly robust
effect, which has been confirmed in a var iety of contexts
ran ging from simple questions such as Problem 9 (Ajzen , 1977;
Hammerton , 1973; Kahneman and Tversky , 1973; Lyon and Slovic ,
1976) to co~iplex realistic problems (Nisbett and Borgida , 1975;
Nisbett , Borgida , Crandall and Reed , 1976). In her doctoral
dissertation, Maya Bar—Hillel ( 1975) investigated the neglect
of base-rate using a wide variety of questions. Her results,
and those of Lyon and Slovic (197 6), show that base-rate data
have little or no impact regardless of whether they are
presented be fore or after the case data , and regardless of
whether they agree or disagree with the case data . There is
a small effect of extreme base—rate ( e . g . , 1:99), although the
discrepancy between estimates and correct values is actually
most pronounced in these situations. We have found that
base-rate data are also neglected when the evidence is presented
in verbal rather than numerical form, e.g., “ the great majority
of cabs are Green , ” “ the witness was correct in most of the
cases. ”
Base-rate data , however , are not always ignored , as
demonstrated in the following modification of the accident
problem .
Problem 10: A cab was involved in a hit-and-run accident
at night. Two cab companies , the Green and the Blue ,
operate in the city . You are given the following data :
(i) Although the two companies are roughly equal in
size , 85% of cab accidents in the city involve
Green cabs , and 15% involve Blue cabs.
(ii) As in Problem 9 above .
Question : What is the probability that the cab involved
*
in the accident was Blue rather than Green?
3— 5
_ - - - -
~~~~~~
---
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I
Although Problem 10 is formally identical to Problem 9,
the repsonses to the two problems were radically dif ferent.
To highlight the difference, we compare the responses of a
group of 69 subjects who answered Problem 9 to those of another
group of 72 subjects who answered Problem 10. The proportion
of subjects whose answers coincided with the witness ’ hit-rate
(80%) was .45 in Problem 9 and .18 in Problem 10.
The proportions of subjects whose responses co incided with the
base-rate (15%) were .07 and .18, respec tively for the two
problems . The proportion of intermediate responses , which may
be taken as evidence for the use of both items , was .35 in
Problem 9 and .60 in Problem 10. The median answer to
Problem 10 was .55, which is not too far from the correct
answer of .41. It is worth noting that the variance of
responses to this problem was large , indica ting a lack of
consensus in the weighting of the base-rate and the singular
data.
Problem 10 d if f e r s from Problem 9 only in that the
base—rate refers to the frequency of accidents ra ther than to
the frequency of cabs . According to our analysis , however ,
this is a crucial change . The difference between the baserates
of accidents for the Blue and Green companies readily
elic its a causalexplanation, i.e., that the drivers of the
Green cabs are more reckless and less competen t than the
drivers of the Blue cabs . This property applies to any
specific Green cab and increases the perceived likelihood
that a Green rather than a Blue cab was involved in the
accident. In contrast , the difference between the proportions
of Blue and Green cabs in the city does not elicit a causal
explanation which makes any specific Green cab more likely to
be involved in an accident than any specific Blue cab .
3
* 3—6
A
- .----- - -- --
~~~~~
—
~~~~~~~~~~~~~~~
- --- - -
I
In other words , we suggest that base—rate data will be
used when the difference in the base—rate of outcomes is
interpreted as a difference in the propensities to produce
these outcomes. In Problem 9, the di f f e rence in the propor tions
of Green and Blue cabs is ignored because it cannot be related
to the propen sity of any par ticular cab to be involved in an
accident. In Problem 10, on the other hand , the dif ference
in the frequency of accidents has impact on judgments because
it is interpreted as a difference in the propensity to cause
accidents .
Bar-Hillel (1975) has constructed several families of
problems to explore the conditions under which base-rate data
are utilized or neglected. Her results suppor t the hypothesis
that base—rate information which is interpreted as a propensity
dominates other base-rate information which cannot be
interpreted in this manner. The following question is adopted
from one of her studies.
Problem 11: (Bar-Hillel) Consider the following
assumptions regarding suicide . In a population of
young adults , 80% of the individuals are married and
20% are single . The percentage of deaths by suicide
is three times higher among single individuals than
among married individuals.
Question : What is the probability that an individual,
• selected at random from those that had
committed suicide , was single?
‘ 1
The correct answer to this problem follows readily from
Bayes ’ rule. Let D denote death by suicide , and let M and S
denote, respectively, married and single.
I
3—7
- _ _ __ ---- ---- -- ----- -
~~
-
—~~~~
-- —
Hence
P(S/D) —
P(D/S) —
(3) ( .20 ) —
3
P (M/D)
—
P(D/M)
—
(1) (.80)
—
and P(S/D) = 3/7 = .43. The modal and median answer of a
group of 65 subjects was .75. This value corresponds exactly
to the ratio of suicide rates among single and married people ,
and reflects total neglect of the base-rate frequencies of
these categories.
Two items of information are supplied in this question :
the proportions of married and single individuals , and the
ratio of suicide-rates in these categories. The second of
these items is readily related to a causal schema of suicide ,
while the former is not. The differential suicide—rates imply
that a single person has a stronger propensity to commit
su icide than a married person. In contrast, the proportions
of single and married individuals have no bearing on the
causation of suicide. As hypothesized , base—rate information
which is not linked to a causal schema is ignored in the
presence of causally relevant evidence. This result does not
depend on prior beliefs regarding suicidal tendencies in the
population. When respondents were told that the suicide-rate
is higher among married than among single people, the base-rate
frequencies of these categories were again ignored (Bar—Hillel ,
1975).
If the above account is correct, the base—rate should
not be ignored when it is causally related to the target
outcome , as in the following problem, which was given to a
group of 68 subjects.
t 3—8
Problem 12: Consider the following assumptions
regarding suicide. In a population of adolescents ,
80% of suicide attempts are made by girls , and 20%
by boys. The percentage of suicide attempts that
result in death is three times higher among boys than
among girls.
Question : What is the probability that an adolescent ,
selected at random from those who had died
by suicide, was a boy?
Problem 12 is formally identical to Problem 11, but the
answers to the two problems are different. The proportion of
subjects whose answers correspond to the ratio of fatalities
was .54 in Problem 11 and .28 in Problem 12. The median
answer to Problem 12 was .50, which differs significantly
from the median of .75 observed for Problem 11.
Why is the base—rate frequency ignored in Problem 11
but not in Problem 12? According to the present analysis ,
• the base-rate has impact when it can be interpreted as a
propensity that is causally related to the target outcome .
5 The proportions of single and married individuals do not
affec t the propens ity of any particular individual to commit
suicide , much as the proportions of Blue and Green cabs do
not affec t the propensity of any particular cab to be involved
in an accident. In contrast, the different ra tes of suicide
attempts among boys and girls indicate that girls are more
prone than boys to attempt suicide. In addition , the subject
is informed in Problem 12 that girl s are less likely than boys
to die from a suicide attempt. Since both items of information
are causally linked to death by suicide , neither item dominates
the other. In Problem 11, on the other hand , one item
r
3—9
- - - - - -- .~~~~~~~ - - - ~~~~~~~~~~~~~~~~~~~
—
~~~~~~~~~~~~~~~~
- -- - -
~~~~~~
-- -- - ---
I
( the differential suicide rate ) has causal character , while
the other (the proportions of single and married individuals)
does not , and the former dominates the latter .
Another manner in which base—rate data can be
incorporated into a causal schema is illus trated in the
following problem that was presented to two separate groups
of 53 subjects .
Problem 13 : Among hi gh school seniors in a given school ,
5% (or 40%) were awarded scholarships.
David is a senior in that school. He was described by
his counselor as “industrious , intelligent and
responsible, does well above average in structured tasks ,
but lacks intellectual curiosity ”
Question : What is the probability that David obtained
a scholarship?
The responses to Problem 13 were sensitive to the
base-rate frequency of recipients of the scholarship . The
median estimate was .25 when the base—rate was 5%, and .50
when the base-rate was changed to 40%. The change of base-rate
in this problem alters the perception of the scholarship from
one that is hard to get to one that is easy to get , and the
estimates of David ’ s chances vary accordingly.
Similar problems were used by Ajzen (1977) in a compelling
demonstration of the contrast between causal and non-causal
base-rates. In one experiment , subjects were required to
assess the probability that a student, for whom a brief
description was provided , had passed a particular examination .
t
3-10
—•—-.--—------ -—
~
.-—-•-
~
_________
Base-rate information was g iven in d i f f e r e n t forms to two
* groups of subjects .
Causal base-rate information: “Two years ago , a final
exam was given in a course at Yale University. About
75% of the students passed (failed ) the exam.”
Non-causal base-rate information: “Two years ago , a
final exam was given in a course at Yale University .
An educational psychologist interested in scholastic
achievement interviewed a large number of students
who had taken the course . Since he was primarily
concerned with reactions to success (failur e), he
selec ted mostly students who had passed (failed) the
exam. Specifically, about 75% of the students in his
sample had passed (failed) the exam .”
Ajzen (1977) notes : “I t can be seen that whereas the causal
base-rate implies that the examination was easy (75% passed)
• or d i f f i c u l t (75 % failed), the non—causal base-rate had no such
implication .”
The results indicated that the causal base-rate was much
more potent than the non-causal , although both types of baserates
produced significant effects. For the causal base—rate ,
the ludged probability of success (averaged across descriptions)
was higher by .34 when the base-rate of success was high than
when it was low. For the non-causal base-rate , the corresponding
difference was only .12. In the terms of the present analysis ,
the ease or d i f f i c u l t y of an examination is one of the factors
that affect a student’s propensity to pass that examination,
and it is therefore integrated with other determinants of
propensity , such as the student ’s intelli gence and motivation.
3—11
—
The base—rate of success was used in the preceding
study to def ine an examination as easy or hard . In a second
study , the base-rate of preferences was used to define options
as more or less attractive (Ajzen , 1977). Subjects were
required to assess the probability that students , for whom a
personality sketch was provided , would choose either history
or economics as an elective general-interest course . The
causal base--rate, which served to define the relative
attractiveness of the two options , consisted of the proportions
of students enrolled in the two courses (.70 and .30). The
non-causal base-rate was introduced as follows :
“To obtain student reaction , the history (economics )
prof essior recently interviewed 70 students who had
taken his general interest course in history (economics).
In order to enable comparisons , he also interviewed 30
students who had taken the course in economics (history).”
Note that, unlike the causal base—rate , the non—causal
vers ion provides no information about the popular ity of the
two courses. The effect of the non-causal base-rate was not
significant in this study , although there was a probability
difference of .025 in the expected direction . In contrast ,
the causal base-rate had a strong effect: the mean judged
probability of choice was .65 for a popular course (high
base-rate), and .3-6 for an unpopular course (low base-rate).
Evidently, the attractiveness of courses is inferred from the
base-rate of choices and is integrated with personal
characteristics in assessing the probability that a par ticular
student will select one course rather than the other.
3— 12
— -~~~~~~ -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -
_ _
Ajzen ’s exper iments , as well as Problem 13 demonstrate
the effectiveness of base-rate data , in situations where these
data serve to specify a causal schema which is otherwise
incomplete in an essentialrespec t. Scholarships can be more
or less selective , examinations can be easy or hard , and
general-interest courses vary in attractiveness. In the
absence of per tinen t data , çeople probably complete the
appropria te schema of success or choice by a def aul t value,
e.g., by assuming a typical level of difficulty for the
examination, or equal popularity for the two courses. If the
base-rate provides information about difficulty or popularity ,
this information is used to complete the causal schema and
it therefore affects the judged probability that a particular
student will obtain the scholarship, pass the examination, or
select economics over history. Base—rate data which do not
provide information about difficulty or popularity are not
incorporated in the causal schema and are therefore given
little or no weight in judgments of probability .
Base-rate data which do provide information about the
difficulty of an undertaking or the prevalence of an action
may nevertheless be neglected, if they conflict with an
es tablished prior conception or causalschema . Impress ive
demonstrations of this phenomenon have been reported by Nisbett
and Bor gida (1975). They presented subjects with detailed
information about the procedure and results of a well-known
experimental investigation of people ’s willingness to help a
stranger in distress (Darley and Latane , 1969). In that
experiment, six men (of whom one was a confederate of the
experimenter) participated in a discussion of personal problems .
Under the pretext of maintaining privacy, the participants wer e
seated in separate booths and the conversation was held through
an intercom system.
3—13
— ~~~
--—- —--
~~~~~~~~~
-
~~~~
- _ _ _ _ _
I
The conf edera te , who was the first to speak , mentioned that
he was prone to seizures. Then he began to stammer , indicated
that one of his seizures was coming on , and asked for help.
His last comrnments were “I’m gonna die-- er-- er. I’m , ... ,
die--er-—er--seizure——er-- (choking sounds , then silence).”
The object of the helping experiment was to find out
what proportion of participants would try to help, and how
soon they would do so. The surprising result was that not one
of the fifteen subjects rushed to the confederate when he
first asked for help. Four subjects came out of their booths
by the end of the speech when the man was choking, and six
never came out of their booths at all. Nisbett and Borgida
presented these data to their subjects in order to test their
effect of predictions of the behavior of individual participants .
The subjects were shown brief film clips of interviews ,
allegedly conducted with three of the participants in the
helping experiment. The interviews were not directly per tinent
to hel~ ing behavior but they provided a general impression of
personality . The subjects were then asked to guess how each of
the three individuals had behaved in the helping experiment .
I
Nisbett and Borgida found that knowledge of the
distribution of helping responses in the orig inal experiment
had no effect. Subjects who knew the results of the helping
experiment and subjects who were not given this information
made identical predictions concerning the helping behavior of
the men shown in the f ilms .
3—14
~~~~
_
-~~-- . -----~ -—~~~~~~~~~~~~~~~~~~~~~~~~~~
-- — -_ _ _ _
I
Since these men appeared normal and friendly in the f ilms ,
informed and uninformed subjects alike tended to guess that
they had tried to help the stranger. The knowledge that
helping had been infrequent did not affect predictions .
Nisbett and Borgida comment “It is interesting to speculate
just what kind of monstrous target case these subjec ts would
have had to witness before they would guess that he would
behave in a fashion that they knew to be modal” (p. 940).
Exposure to the results of the helping experiment
should have led the subjects to realize that rushing out
of one ’s booth to help a stricken stran ger is more di f f icul t
r than it appears to be. Recall that in Ajzen ’s (1977)
experiment, information about the d i f f i c u l t y of an examination
affected judgments of probability for individual cases , while
Nisbett and Borgida (1975) found no such effect. The apparent
conflict between the studies of Ajzen and Nisbett and Borgida
suggests the hypothesis that base-rate data which describe the
difficulty or attractiveness of an action are used when they
complete a schema that is not fully specified, but not when
they conflict with an existing schema. In the problems studied
by Ajzen , there is no incompatibility oetween the image of the
individual student and any plausible value of the base-rate that
specifies the difficulty of an examination or the attractiveness
of a course. In contrast, Nisbett and Borgida created a conflict
between the callous behavior suggested by the base-rate and
common expec tations about the behavior of normal and friendly
people. The low frequency of helping in the original experiment
calls for a significant revision of accepted conceptions of
helping behavior . Such revisions , as we have argued, are
d i f f i c u l t to make .
I
( 3-15
_ _ _ _ _ _ _ _ _ _ _ — —
Nisbett and Borgida (1975) explained the neglect of
base-rate information by the observation that this “information
is , almost by its very nature, abstrac t, pallid and remote .
In contrast, tar get case informa tion is generally concrete,
vivid and salient.” In support of this contention , Nisbett
et al. (1976) subsequently reported a series of ingenious
demonstrations in which exposure to a few concrete examples
had greater impact on judgments than the presentation of a
large body of statistical evidence. For example , they repor ted
tha t hearing brief comments from a few students has greater
impact on the choice of courses than reading a detailed survey
of student opinions about these courses.
Vividness and concreteness are undoubtedly among the
major determinants of the impact of information. We propose ,
however , that the conditions under which base—rate is used
or neglected are best understood in terms of the role of this
information in causal schemata. In the cab problem, for
example , we argued that the differential base-rate of accidents
for two companies of equal size affects judgments because it
suggests a difference in accident-proneness between the drivers
of the two companies. In contrast, the proportions of Blue
and Green cabs does not induce a differential propensity to be
involved in accidents and this information is therefore neglected .
The critical difference between the two problems involves
causality rather than vividness. Similarly, the statement
that 70 % of students preferred history over economics is
hardly more vivid or concrete than the description of the
instructor ’s decision to sample 70 of his students and 30
students who chose another course (Ajzen , 1977). Here again ,
the essential difference is that the base-rate of preferences
has causal significance , while the base-rate of sampling does not.
3—16
_ - --— --
~~~~~~~~~~~~~~~~~~~~~~~~~~~
--.-
ii
The preceding discussion suggests the following
generalization . Distributional data affect predictions when
they induce a causal model which Ci) explains the base—rate ,
and (ii) applies to the individual case . Thus , the notion that
the drivers of the Green company are reckless explains the
high rate of accidents in this company , and increases the
propensity of any Green cab to be involved in an accident.
Similarily , the assumption that the history course is attractive
explains why the majority of students chose that course , and
also increases the propensity of any individual student to
prefer this course over another . Distributional information
wh ich is not incorporated into a causal schema, either because
it is not interpretable as an indication of propensity or
because it conflicts with an established schema , is given little
or no weight in the presence of singular data .
This conclusion accords with the main thesis developed
in this paper , that the impact of evidence on judgments depends
critically on whether this evidence can be incorporated into
causal schemata. Causal schemata are directional. Consequently,
causal data have more impact than diagnostic data and explanation
is easier than revision . Causal schemata are specific.
Consequently, base-rate information affects judgments about a
specific case only if this information is entered into the
schema of that case . The directionality and specificity of
causal schemata produce major errors in prediction and
explanation, which reflect the deep contrast between intuitive
reasoning and the normative theory of evidence .
I
I
*
3—17
_ _ _ _ _ _ _ _ _ _ - — - _ _ _ _
I I
4. REFERENCES
I
Abelson , R.P. Modes of resolution of belief dilemmas.
Journal of Conflict Resolution, 1959 , 3, 343-352.
Ajzen , I. Intuitive theories of events and the effects of
base-rate information on prediction . Journal of Personality
and Social Psychology, 1977, in press.
Bar-Hillel, M. The base—rate fallacy in subjective judgments
of probability. Unpublished doctoral dissertation, Hebrew
University , 1975.
Darley, J.M. and Latane , B. Bystander intervention in
emergencies: Diffusion of responsibilty . Journal of Personality
and Social Psychology, 1968, 8, 377— 383.
Edwards , W. Conservatism in human information processing.
In B. Kleinmuntz , (Ed.), Formal Representation of Human Judgment.
New York : Wiley , 1968 , l7~~~2.
Hammerton , M. A case of radical probability estimation .
Journal of Experimental Psychology, 1973, 101 , 252—254 .
Heider , F. The Psychology of Interpersonal Relations. New York:
Wiley , 1958.
Hovland , C.I. Reconciling conflicting results derived from
experimental and survey studies of attitude change . American
Psychologist, 1959 , 14 , C~ 17.
g I
Janis , I.L. Victims of Groupthink. E~ ston :Houghton-Mifflin ,
1972.
Jervis, R. Perception and Misperce~ tion in International
Relations. Princeton : Princeton University Press , 1975.
Jones , E . E . , Kanouse , D . E . , Kelly, H . H . , Nisbett , R . E . , Valins , S.,
and Weiner , B. Attribution: Perceiving the Causes of Behavior.
Morristown : General Learning Press , 1972.
Kahneman , D., and Tversky , A. On the psychology of prediction .
$ Psychological Review , 1973, 80, 237—351.
Kahneman, D., and Tversky , A. Intuitive prediction : Biases and
corrective procedures. Management Science, 1978, in press.
I
4—1
_ _ _ _ - - -— - _—.-
- —~~~~
-- --—- --
I
Kuhn , T.S. The Structure of Scientific Revolutions. Chicago :
University of Chicago Press , 1962.
Michotte , A. The Perception of Causality. New York : Basic
Books , 1963.
Nisbett , R.E., and Borgida , E. Attribution and the psychology
of prediction . Journal of Personality and Social Psychology,
1975, 32, 932—943.
Nisbett , R.E. , Borgida , E., Crandall , R . , and Reed , H. Popular
induction : Information is not necessarily informative. In
J.S. Carroll and J.W. Payne (Eds.) Cognition and Social Behavior.
• Hillsdale: Lawrence Erlbaum Associates, 1976.
Ross , L. The intuitive psychologist and his shortcomings:
Distortions in the attribution process. In L. Berkowitz (Ed.)
Advances in Experimental Social Psychology. New York : Academic
• Press, 1977.
• Slovic , P., Fischhoff , B. and Lichtenstein , S. Behavioral
decision theory. Annual Review of Psychology, 1977.
Turoff , M . An alternative approach to cross-impact analysis.
Technological Forecasting and Social Change, 1972, 3, 309-339.
Tversky , A., and Kahneman , D. Judgment under uncertainty :
Heuristics and biases , Science, 1974, 185, 1124—1131.
I
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II. SUPPLEMENTARY NOTES
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IS. KEY WOR DS (Contgnu. on rev., ., aid. ii necessary aid identify by block number)
probability assessment
heuristics
causality
judgmental biases
20. ASSTR
~
CT (Con Sffiue on ,.s..r,. aid. if necessary aid Identify by block number)
In contrast to the normative theory of evidence , where the
.mpact of data is determined solely by their informativeness ,
levelopfr’the thesis that the impact of evidence on intuitive
~udgments of probabilities depends critically on whether it is
)erceived as causal , diagnostic or incidental. The first part of
if the paper shows that people assign greater impact to causal data
:han to uiagnostic data of equal informativeness. When the same
latuin has both causal and diagnostic implications, the former- rover)
DO ~~~~~~~
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0. (Continued )
dominate the latter. The ease with which people explain
unexpected
facts and the reluctance to revise old conceptions
in the light of new facts are related to the dominance of caus~ 1
over diagnostic reasoning. The second part of the paper
analyze~~ the use and neglect of base-rate data in terms of the
role of these data in causal schemata. It is shown that baserate
information wnich is given a causal interpretation affect~
judgments , wnile base-rate information which cannot be
interprete~ in this manner is given little or no weight.
To appear in: N. Fishbein (Ed.) Progress in Social Psychology.
Hillsdale : Lawrence Erlbaum Associa tes , 1977.
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