477
In light of the findings discussed in the preceding section, it is useful to
consider situations in which people will not neglect extension completely.
Extension effects are expected, in the present model, if the individual (i) has
information about the extension of the relevant set; (ii) is reminded of the
relevance of extension; and (iii) is able to detect that her intuitive judgments
neglect extension. These conditions are least likely to hold – and complete
neglect most likely to be observed – when the judge evaluates a single object
and when the extension of the set is not explicitly mentioned. At the other ex-
treme, the conditions for a positive effect of extension are all satisfied in psy-
chologists’ favorite research design: the within-subject factorial experiment,
in which values of extension are crossed with the values of other variables in
the design. As noted earlier, this design provides an obvious cue that the ex-
perimenter considers every manipulated variable relevant, and it enables par-
ticipants to ensure that their judgments exhibit sensitivity to all these vari-
ables. The factorial design is therefore especially inappropriate for testing
hypotheses about biases of neglect (Kahneman & Frederick, 2002).
In spite of these objections, within-subject factorial designs have been used
in several experimental studies of extension neglect. Figure 10 illustrates the
remarkably consistent additive extension effect that has emerged in these exper-
iments (Schreiber & Kahneman, 2000). In each of the experiments, the ex-
tension variable has a slight but significant effect, and combines additively
with other information. The additivity is noteworthy, because it is normative-
ly inappropriate. For each panel of Figure 10, a compelling normative argu-
ment can be made for a quasi-multiplicative rule in which the lines should
fan out.
4
The observed pattern is compatible with a process of anchoring and
adjustment: the intuitive judgment provides an anchor, and small adjust-
ments from that anchor are made to accommodate the role of extension.
Patient A
0
1
2
3
4
5
6
7
8
0
10
20
Time (m inutes)
Pa
in
In
te
n
s
it
y
Patient B
0
1
2
3
4
5
6
7
8
0
10
20
Time (minutes)
Pa
in Int
e
n
s
it
y
Figure 9. Pain intensity reported by two colonoscopy patients.
4
Anderson (1996, p. 253) has described several other situations in which variables that should be
combined multiplicatively are combined additively.
478
Tests of monotonicity
Extensional variables, like sums, obey monotonicity. The sum of a set of posi-
tive values is at least as high as the maximum of its subsets. In contrast, the
average of a subset can be higher than the average of a set that includes it.
Violations of monotonicity are therefore bound to occur when an extension-
al attribute is judged by a prototype attribute: it must be possible to find
cases in which adding elements to a set causes the judgment of the target vari-
able to decrease. This test of prototype heuristics is less demanding than the
hypothesis of extension neglect, and violations of monotonicity are compatib-
le with some degree of sensitivity to extension (Ariely & Loewenstein, 2000).
Nevertheless, violations of monotonicity in important tasks of judgment and
choice are the strongest source of support for the hypothesis that prototype
attributes are substituted for extensional attributes in these tasks.
• Conjunction errors, which violate monotonicity, have been demonstrated
in the Linda problem and in other problems of the same type. There are
no documented exceptions to the predicted pattern when the judgments
are obtained in a between-subjects design, or when the two critical out-
Figure 10. (a) Willingness to pay to restore damage to species that differ in popularity as a
function of the damage they have suffered (from Kahneman, Ritov, & Schkade, 1999); (b)
Global evaluations of aversive sounds of different loudness as a function of duration for
subjects selected for their high sensitivity to duration (from Schreiber & Kahneman, 2000);
(c) Ratings of probability for predictions that differ in representativeness as a function of
base-rate frequency (from Novemsky & Kronzon, 1999); (d) Global evaluations of episodes
of painful pressure that differ in temporal profile as a function of duration (Ariely, 1998).
Ariely Data
30
35
40
45
50
55
60
65
70
75
80
0
10
20
30
40
50
Duration in Seconds
A
ver
si
ven
ess
Down
Down&Up
Up
Up&Down
Schreiber & Kahneman Data
0
1
2
3
4
5
6
7
8
9
10
0
5
10
15
20
25
30
Duration in Seconds
A
ver
siven
ess
71 dB
75 dB
78 dB
80 dB
Nov emsky & Kronzon Data
0
10
20
30
40
50
60
70
80
90
0
20
40
60
80
100
Base-rate (%)
Po
st
er
ior
P
roba
bilit
y
(
%
)
Programmer
Surgeon
Accountant
Engineer
`
Kahneman, Ritov, & Schkade Data
0
5
10
15
20
25
30
35
0
20
40
60
80
Percentage Population Decline
M
ean
c
ontr
ibuti
on i
n
$
Low
Medium
High