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Journal of Risk and Uncertainty, 14:283–300 (1997)
© 1997 Kluwer Academic Publishers
Insensitivity to the Value of Human Life: A Study of
Psychophysical Numbing
DAVID FETHERSTONHAUGH
Department of Psychology, Stanford University, Stanford, California 94305-2130 (415) 725-5487; fax (415)
725-5699; email df@psych.stanford.edu
PAUL SLOVIC
University of Oregon and Decision Research, Eugene, Oregon
STEPHEN M. JOHNSON
Decision Research
JAMES FRIEDRICH
Willamette University
Abstract
A fundamental principle of psychophysics is that people’s ability to discriminate change in a physical stimulus
diminishes as the magnitude of the stimulus increases. We find that people also exhibit diminished sensitivity in
valuing lifesaving interventions against a background of increasing numbers of lives at risk. We call this
“psychophysical numbing.” Studies 1 and 2 found that an intervention saving a fixed number of lives was judged
significantly more beneficial when fewer lives were at risk overall. Study 3 found that respondents wanted the
minimum number of lives a medical treatment would have to save to merit a fixed amount of funding to be much
greater for a disease with a larger number of potential victims than for a disease with a smaller number. The need
to better understand the dynamics of psychophysical numbing and to determine its effects on decision making
is discussed.
Key words: decision making, life saving, value of life, risk-benefit analysis, psychophysical numbing
JEL Classification: J17
Nobel laureate Albert Szent-Gyorgi once observed, “I am deeply moved if I see one man
suffering and would risk my life for him. Then I talk impersonally about the possible
pulverization of our big cities, with a hundred million dead. I am unable to multiply one
man’s suffering by a hundred million.” Most people seem to at least tacitly appreciate the
kind of insensitivity toward loss of human life articulated in Szent-Gyorgi’s statement. We
recognize the need for creative attempts to drive home the severity of catastrophic losses.
One activist group lobbied Congress by placing 38,000 pairs of shoes, boots, and sneakers
around the Capitol building to sensitize representatives to the 38,000 gunshot fatalities
America experiences annually (“38,000 Shoes,” 1994). Another example is given by
Rummel (1995), who asked people to consider this century’s total democide (state sanc-
tioned killing, aside from warfare) of 170,000,000 by imagining a chain of bodies laid
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head to toe reaching from Honolulu, across the Pacific and the continental U.S., to
Washington D.C. and then back again more than 16 times. Losses of life framed in these
ways attempt to mitigate the insensitivity that seems to occur so naturally when we try to
comprehend past tragedies or think rationally about how to mitigate or prevent large
losses of life in the future.
What psychological principles lie behind this insensitivity? In the 19th century, E. H.
Weber and Gustav Fechner discovered a fundamental psychophysical principle that de-
scribes how we perceive and discriminate changes in our physical environment. They
found that people’s ability to detect changes in a physical stimulus rapidly decreases as
the magnitude of the stimulus increases (Weber, 1834; Fechner, 1860). What is known
today as “Weber’s law” states that in order for a change in a stimulus to become just
noticeable, a fixed percentage must be added. Thus perceived difference is a relative
matter. To a small stimulus, only a small amount must be added. To a large stimulus, a
large amount must be added to be equally noticeable. Fechner proposed a logarithmic law
to model this nonlinear growth of sensation. Numerous empirical studies by S. S. Stevens
(1975) have demonstrated that the growth of sensory magnitude (c) is best fit by a power
function of the stimulus magnitude f
c5kf
b
where the exponent bis typically less than one for measurements of phenomena such as
loudness, brightness, and even the value of money (Galanter, 1962).
1
For example, if the
exponent is 0.5 as it is in some studies of perceived brightness, a light that is four times
the intensity of another light will be judged only twice as bright.
Our cognitive and perceptual systems seem to be designed to sensitize us to small
changes in our environment, possibly at the expense of making us less able to detect and
respond to large changes. As the psychophysical research indicates, constant increases in
the magnitude of a stimulus typically evoke less and less of a change in response. Ap-
plying this principle to the valuing of human life suggests that a form of psychophysical
numbing may result from our inability to appreciate losses of life as they become more
catastrophic—a phenomenon that could impair our ability to make consistent, equitable,
and wise decisions.
2
Evidence of psychophysical numbing comes from a study by Summers, Slovic, Hine,
and Zuliani (in press), who hypothesized that people may exhibit a systematic distortion
in perception of death tolls from wars not unlike the systematic distortion found in many
traditional experiments in sensory psychophysics. They found that deaths from wars were
perceived according to a power function where b50.32. Thus, respondents in these
experiments perceived a war that claimed eight times more lives than a second war to be
only about two times greater in magnitude. The degree of psychophysical numbing in
these experiments changed as a function of how the losses were framed. Respondents’
insensitivity was reduced (b5.99) when the same total number of casualties was pre-
sented as “deaths per day” rather than “deaths per war.”
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Kahneman and Tversky (1979) have incorporated this psychophysical principle of
decreasing sensitivity into prospect theory, a descriptive theory of decision making under
uncertainty. A major element of prospect theory is the value function, which relates
subjective value to actual gains or losses.The function is concave for gains and convex for
losses. When applied to human lives, the value function implies that the subjective value
of saving a specified number of lives is greater for a smaller tragedy than for a larger one.
Such psychophysical numbing may have dramatic implications for the judgments and
decisions people make. For example, an intervention that reduces the number of deaths in
a tragedy from 2,000 to 1,000 may be judged substantially more valuable than one that
reduces deaths from 99,000 to 98,000. Even though both interventions save the same
number of lives, in the former people may decide to act while in the latter they may not,
perhaps under the impression that saving 1,000 lives out of 2,000 is a significant propor-
tion but saving 1,000 out of 99,000 is merely “a drop in the bucket.”
How should we value the saving of a life? We believe that, in most circumstances, “a
life is a life”—the value of saving a certain number of people from death should not be
affected by the number or proportion of others who remain unsaved. This perspective
presumes a linear relationship between the number of lives one can save in a given
situation and the value associated with saving them. Thus an effort saving 200 lives would
have twice the value of another that saves 100 lives. This would lead decision makers to
prefer the intervention that saves the greatest number of lives even if that number is
proportionally smallest when compared to the number at risk. Stated differently, we argue
that the value of lives saved should be based on the number an intervention can save, and
should therefore be independent of the size of the population from which the saved lives
originate.
Under a one-to-one correspondence between the number and value of saved lives, the
value of a life-saving effort should also be independent of when in the process those lives
are saved. For example, the value of saving the first 100 individuals in a tragedy should
not change if instead these individuals happened to be the last 100 saved. According to
prospect theory’s curved value function, however, the value of saving lives will in many
cases depend on when in the process those lives are saved. For example, the value of
reducing deaths by 100 early in an intervention would not likely be equivalent to that of
an identical reduction later in the process; a reduction in loss of life that brings the death
toll closer to zero might appear more valuable.
Except for the study by Summers, Slovic, Hine, and Zuliani (in press) and a demon-
stration by Tversky and Kahneman (1981) showing that the nonlinear value function does
seem to apply to gains and losses of life, little empirical work has been conducted that
investigates psychophysical numbing in the domain of life saving. The three studies
reported here explored how people value life-saving interventions. We hypothesized that
respondents’ judgments would exhibit psychophysical numbing by responding to life-
saving interventions in a manner consistent with prospect theory’s value function. Studies
1 and 2 examined how the perceived benefit of saving lives changes when interventions
saving the same number of people are implemented in tragedies that differ in magnitude.
We predicted that such life-saving interventions would be valued more highly when the
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number of lives at risk was small than when the number at risk was large. We also
predicted that saving lives later in an intervention, bringing the death toll closer to zero,
would be valued more highly. Study 3 examined how the total number of people at risk
influences people’s estimates of the number of lives an intervention must save to justify
afixed amount of funding. We predicted that, when the number at risk was larger, the
intervention would be required to save more lives.
1. Study 1
1.1. Method
Materials and Procedure. Undergraduate volunteers (n554) from two sections of an
economics statistics course were instructed in a short questionnaire to imagine themselves
as a government official of a small, developing country and were asked to evaluate four
government programs (Programs A, B, C, and D) being considered for funding. Each of
the programs “cost about the same” and addressed the following issues: the employment
problem in their country, the transportation problem in their country, and the life-
threatening refugee problem in Rwanda.
3
The transportation program proposed to remedy
poor road conditions, and the employment program proposed to decrease the jobless rate.
There were two Rwandan refugee programs, each proposing to provide enough clean
water to save the lives of 4,500 refugees suffering from cholera in neighboring Zaire. The
Rwandan programs differed only in the size of the refugee camps where the water would
be distributed; one program proposed to offer water to a camp of 250,000 refugees and the
other proposed to offer it to a camp of 11,000.
Respondents evaluated the programs in pairs, one pair per page. Because the two
Rwandan programs were never paired together, only five of the six possible pairings
appeared in the booklets. All respondents evaluated the same paired comparisons, pre-
sented in one of two randomized orders. Each page contained brief descriptions of two
programs being compared, followed by a response scale such as that shown below for
Programs A and B.
Program A Program B
6543210123456
Strong
preference
for A
Slight
preference
for A
No
pref
Slight
preference
for B
Strong
preference
for B
On the last page, participants responded to several questions designed to verify whether
they perceived that the same number of refugees would be saved by either of the Rwandan
programs. The final item requested respondents to briefly explain whether it was better to
save lives in the smaller or the larger refugee camp.
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1.2. Results and Discussion
The manipulation checks verified that most respondents correctly perceived that the two
Rwandan programs saved the same number of lives.
Ratings on the 13-point preference scale constituted the dependent measure. For the
four pairings containing a Rwandan program, participants’ responses were subsequently
recoded so that a preference for the Rwanda program in a pair was coded as a positive
number and a preference for the non-Rwandan program in a pair was coded as a negative
number. For example, in a pair containing the large-camp program and the transportation
program, if a participant circled a “2” to indicate a slight preference for the transportation
program, the rating would have been recoded as a “22.” Thus, participants’ recoded
responses ranged from 26to16. Because responses in the transportation vs. employment
program comparison were not of theoretical interest, they were excluded from the analy-
sis. An analysis of variance on respondents’ preferences revealed no effects due to re-
spondents’ gender or to the order in which the paired comparisons were presented. Data
were therefore combined without regard for these variables.
We predicted that preference ratings would be greater for the small-camp program than
the large-camp program. Because these programs were never paired together, however, we
compared respondents’ ratings for the two Rwandan programs in pairings that shared a
common non-Rwandan program. For example, we compared respondents’ ratings in the
transportation vs. the small-camp pairing with their ratings in the transportation vs. the
large-camp pairing. We expected that the recoded rating for the small-camp pairing would
be greater than the rating for the large-camp pairing.
This prediction was tested using a within-subjects, 2 32 analysis of variance on
preference ratings, varying comparison program type (transportation or employment) and
Rwanda camp size (large or small). As predicted, the results revealed a camp-size main
effect, F(1, 52) 58.24, p,.01 (see Figure 1). Even though most respondents realized
that the same number of refugees could be saved in either camp, they preferred the
small-camp program (M5.45) over the large-camp program (M52.20) when paired
with either the transportation or employment programs.
The same ANOVA was conducted on the preferences of 22 respondents who indicated
on the last page of the booklet that saving 4,500 lives in the large camp was neither better
nor worse than saving 4,500 lives in the small camp. Even these respondents, who indi-
cated no preference between one life-saving Rwandan program and the other when asked
directly, preferred the small-camp program (M5.93) over the large-camp program (M5
.41) when evaluations were masked by paired comparisons, F(1, 21) 53.92; p5.06.
One last question asked respondents whether it was better to save lives in the smaller
or the larger refugee camp, and to state why. About 44% of respondents reported that it
was better to save lives in the smaller camp. As perhaps the strongest evidence for the
psychophysical numbing hypothesis thus far, this result is quite remarkable, especially
considering that the life-saving potential of each Rwandan program was reinforced by the
preceding question in which nearly all respondents reported that the interventions would
save the same number of lives. Approximately 42% of respondents reported no preference
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between the two programs and 14% indicated that it was better to save lives in the larger
camp.
We suggest that the sizable proportion of respondents who preferred to save lives in the
smaller camp reflects people’s general tendency to become desensitized to the life-saving
potential of interventions applied to larger tragedies. However, what appears to be psy-
chophysical numbing might not be caused by insensitivity at all, but actually by respon-
dents’ sensitivity to preventing further casualties among refugees—an eminently reason-
able goal. Respondents might have preferred the small-camp program because of the
increased hazard of administering a limited supply of a scarce commodity to a large and
desperately needy group of people, as might likely be found in a large camp. Not only
might such an effort incur additional casualties through the riot it could spark, but people
could be at greater risk of infection or later reinfection due to the increased tendency for
water-borne diseases to spread in a larger compared to a smaller refugee camp. We have
labeled these explanations the riot and contagion hypotheses, respectively.
Evidence in the present study suggested that most respondents considered neither the
riot nor the contagion hypotheses. In fact, only one participant mentioned the riot hy-
pothesis as a rationale when responding to the final question (i.e., whether it was better to
save lives in the small or the large refugee camp, and why). Seven respondents, however,
did cite some form of the contagion hypothesis, though several used it to support their
preference for saving lives in the larger camp. The fact that even the 22 respondents who
stated that saving lives in the larger camp was neither better nor worse than saving lives
in the small camp exhibited psychophysical numbing also speaks against these hypoth-
eses. Unless a substantial portion of respondents used but failed to report one or both of
these hypotheses as part of their rationale, we believe it unlikely that either hypothesis
could be widely responsible for the effects found in the above analyses.
Figure 1. Main effects in Study 1 for Rwanda camp size (11,000 or 250,000) and program type (transportation
or employment) using preference ratings from paired comparisons. Ratings were coded on a 13-point scale (26
to 16). Positive numbers indicate preference for a Rwanda program over a non-Rwanda program.
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Furthermore, the next study reports data that not only replicates the present study, but
provides evidence that essentially rules out both the riot and the contagion hypotheses as
alternative explanations for psychophysical numbing.
2. Study 2
Study 2 retained much of the content and structure of the previous study. Participants first
read a cover story about the Rwandan refugee crisis and then evaluated one small coun-
try’s life-saving intervention proposed for several refugee camps. For each camp, all
respondents answered two questions: (1) how beneficial would sending the aid be? and (2)
should aid be sent or not? Study 2, however, differed from the previous study in several
respects. In Study 2, comparisons between the Rwandan scenarios were easier, which
would presumably lessen psychophysical numbing among respondents. Whereas Study 1
paired each Rwandan scenario with a “dummy” scenario, making direct comparisons
between Rwandan scenarios more difficult, Study 2 omitted dummy scenarios and had
respondents evaluate Rwandan scenarios individually.
Though easier in this regard, Study 2 was generally more complex because it contained
a more detailed cover story and incorporated two additional independent variables. Be-
sides the camp-size manipulation found in the previous study, Study 2 manipulated when
in the life-saving process the humanitarian aid was distributed. We predicted that saving
a portion of lives near the end of a crisis would be valued more highly than saving an
equal portion near the beginning of a crisis because the former solves virtually all the
problem whereas the latter does not. Study 2 also manipulated the reliability of the
equipment used to administer the aid (i.e., purified water). We included this variable to
discourage respondents from rating the intervention as maximally beneficial in every
scenario.
2.1. Method
Overview of Design. The present study manipulated three within-subjects variables: size
of refugee camp (11,000 or 250,000), amount of pure-water aid a camp was receiving
before a water-purification plane was sent (low or high), and reliability of the plane (60%
or 100%). This yielded the eight different scenarios participants read and it allowed us to
analyze their responses in a 2 3232 repeated-measures factorial design. All respon-
dents evaluated the same eight scenarios. Half received the block of four 100%-reliable
plane scenarios first and the block of four 60%-reliable scenarios second, and half re-
ceived the blocks of four in the reverse order. Within each block of four scenarios, the
“camp-size” and “prior-aid” variables were mixed according to a latin-square design.
There were two dependent variables: (1) the rated benefit of sending a plane, and (2) a
yes/no decision on whether or not to send a plane.
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Materials and Procedure. University of Oregon students (n5162) were paid $4 to
complete an 11-page questionnaire about the Rwandan refugee crisis. The cover story of
the questionnaire informed respondents that the U.N. High Commissioner for Refugees
was coordinating a massive humanitarian aid campaign by requesting that able countries
send assistance to the Rwandan refugees in Zaire. Many refugees had a water-borne
disease and would die if purified water did not soon become available. One small country
was considering sending one of two Dash-8 water-purification planes to Zaire. Although
each water system was capable of producing only a small fraction of the water needed,
each could keep about 1500 disease victims alive each day. The purification system in one
plane was 100% reliable, and the system in the other plane was only 60% reliable—
reliable in the sense that there was only a “60% chance that the system would work once
it got to Zaire.” Once a plane was operating in a camp, respondents were informed that,
“aid-workers will distribute the clean water to designated disease victims, which usually
saves the victims’ lives.” The cost to this small country of delivering and operating these
purification systems was significant in light of its economy.
The following pages contained eight scenarios about the four refugee camps (see Table
1 for a summary of information given in the eight scenarios). Each scenario was identi-
cally structured. For example, on one page respondents read the following scenario (Sce-
nario 1):
“The city of Moga in Zaire now has about 11,000 Rwandan refugees. Few water
purification systems from other countries are now in place. 5% of the clean water
needed for disease victims in this camp is currently being met. If the 100%-reliable
Dash-8 water purification plane is sent to Moga, 50% of this camp’s water need for
disease victims would be met.”
For scenarios using the 60%-reliable plane, the following phrase was added: “…,
provided the purification system works.”
Tab le 1 . Summary of information in the eight scenarios given to all respondents in study 2
Scenario
number
Zairian
refugee camp Camp size
Water system
reliability Prior aid Post aid
1 Moga 1 11,000 100% 5% 50%
2 Moga 2 11,000 60% 5% 50%
3 Fizi 1 11,000 100% 50% 95%
4 Fizi 2 11,000 60% 50% 95%
5 Uvira 1 250,000 100% 5% 7%
6 Uvira 2 250,000 60% 5% 7%
7 Kalehe 1 250,000 100% 93% 95%
8 Kalehe 2 250,000 60% 93% 95%
Note. The prior-aid variable indicates the amount of pure water need being met for disease victims in a camp
before the aid was delivered. Post aid indicates the water need that would be met for disease victims after the aid
was provided. Within each level of plane reliability, the intervention in each camp was capable of keeping the
same number of disease victims (1,500) alive each day (which usually saves the victims’ lives).
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In the other small-camp scenarios (Fizi 1 and Fizi 2—see Table 1), 50% of the clean
water need was currently being met, so the aid increased this to 95%, provided the system
worked.
In the two scenarios involving the Uvira camp (250,000 refugees), the prior aid met 5%
of the water need and the additional aid would bring this to 7%. In the scenarios involving
the Kalehe camp (scenarios 7 and 8), 93% of the water need was being met and the
additional aid would bring this to 95%. Thus, the intervention proposed to save 2% of
disease victims in a given large camp and 45% of disease victims in a given small camp.
Recall, however, that the same absolute number of lives (1,500) would be saved in each
case, regardless of camp size.
Each scenario was followed by two questions. First, “What would be the benefit of
sending this Dash-8 plane to this camp?” Respondents answered this question on a nine-
point Likert scale, titled “Benefit,” anchored at the ends by: 0 (“extremely low benefit”)
and 8 (“extremely high benefit”). Second, they were asked, “Given the benefit indicated on
the scale above, would it be worth sending the plane to this camp?” Respondents circled
either “Yes” or “No.” On each page, participants were reminded that responses to each
scenario should be independent of their responses to the other scenarios.
After completing this task, participants responded to a question designed to assess
whether they correctly perceived that the same number of lives would be saved by an
intervention, regardless of the size of camp where it was implemented.
2.2. Results and discussion
A check on subjects’ understanding of the problem revealed that 60% of respondents
correctly perceived that the water systems would save about the same number of lives
regardless of refugee camp size, 23% believed that substantially more lives would be
saved in the larger camp, and 17% believed that substantially more lives would be saved
in the smaller camp. The analyses reported below omitted this last group of respondents
because their belief could have quite reasonably lead them to prefer implementing the
intervention in the small camps, not because of psychophysical numbing but simply
because it could have saved more lives.
A23232 within-subjects ANOVA on respondents’ benefit ratings provided strong
support for the psychophysical numbing hypothesis (see Figure 2). A significant main
effect for camp size, F(1, 132) 5160.5, p,.001, indicated that respondents believed
sending the planes to small camps was more beneficial (M56.46) than sending them to
large camps (M54.54). A main effect for the prior-aid variable, F(1, 132) 515.35, p
,.001, indicated that respondents believed sending the planes to camps that were already
satisfying a substantial portion of their clean-water need was more beneficial (M55.73)
than sending them to camps that were only satisfying a small portion of their water need
(M55.27). And, not surprisingly, the results revealed a main effect for plane reliability,
F(1, 132) 512.01, p,.001, indicating that respondents believed the 100%-reliable
plane (M55.67) was more beneficial than the 60%-reliable plane (M55.33). No other
effects were significant.
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As predicted, respondents appeared to favor interventions more when implemented in
the later stages of the life-saving process. For example, respondents thought it was more
beneficial to save 2% of those at risk in the large camps when the threat of a tragedy was
nearly contained than when it was just beginning to take its toll. As the absence of
interaction effects indicated, this was as true for small camps as it was for large.
A23232 ANOVA on respondents’ dichotomous decisions about whether or not to
send the planes to the camps also revealed a significant main effect for camp size, F(1,
130) 5105.4, p,.001, indicating that respondents decided to send the planes to small
camps more often (93%) than to large camps (59%). A main effect for plane reliability, F
(1, 130) 54.61, p,.05, indicated that respondents decided to send the reliable plane to
the camps slightly more often (78%) than the unreliable plane (74%). Interestingly, the
main effect for prior aid was not significant, F(1, 130) 5.47, p5.50. Respondents
decided to send the planes 75% of the time to camps receiving little prior aid, and 77% of
the time to camps receiving substantial prior aid. No other effects were significant.
The above analyses show that respondents’ judgments and decisions about sending aid
to refugee camps differed greatly depending on camp size. It is possible that such re-
sponses could be justified if they were based on some rationale such as the riot hypothesis
or the contagion hypothesis. However, in addition to the evidence against the riot and
contagion hypotheses from Study 1, data from the present study provided strong evidence
that neither of these alternative hypotheses were widely considered. If respondents had
considered such explanations, one would have expected them to substantially devalue the
interventions for those scenarios in which the risk of rioting or reinfection was the
greatest, namely, large camps in the early stages of the life-saving process. In these
scenarios, respondents were faced with implementing an intervention whose supply of aid
was particularly inadequate for the demand (see Table 1, Uvira 1 and Uvira 2). The data,
Figure 2. Main effects in Study 2 for the three within-subjects variables: camp size (11,000 or 250,000), prior
aid (low or high), and plane reliability (60% or 100%). Benefit rating was scored on a scale from 0 (low) to 8
(high).
Plane reliability
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however, did not reflect this interaction pattern. Rather, respondents devalued interven-
tions to the same degree both in large camps needing little additional aid and large camps
needing massive additional aid.
3. Study 3
In the previous studies, we asked respondents to make evaluations about one type of
intervention (saving a fixed number of lives) applied to several tragic circumstances
varying in magnitude. In Study 3 we asked respondents to estimate the minimum number
of lives each of several interventions must save to merit a fixed amount of money. If
people tend to view an amount of assistance in a large tragedy as less valuable than an
equivalent amount in a small tragedy, as was shown in the previous studies, then they
should require more life-saving assistance to be “added” to the large tragedy to make the
assistance in each of equal value. In the present study, therefore, we predicted that re-
spondents’ estimates of the minimum number of lives each intervention would have to
save would be greater for the larger than the smaller tragedies.
3.1. Method
Materials and Procedure. University of Oregon students (n5165) were paid $4 to
complete a questionnaire asking them to imagine that they were the chairperson on the
board of “Science For Life,” a charitable foundation in charge of distributing large sums
of money to research institutions that develop treatments for serious diseases. Each re-
spondent was asked to determine which medical institutions Science For Life should fund
with its limited resources. The three medical institutions (X,Y, and Z) that were requesting
support each proposed to implement a new treatment that would significantly reduce the
annual number of deaths caused by a particular disease. Respondents were also instructed
to assume that: (1) the treatments will induce a cure for some people and thus “save their
lives,” and (2) the people who are not cured will experience no other beneficial effect; that
is, the treatment will not improve their “quality of life.”
Respondents completed two tasks: an estimation task and a ranking task. The first task
required them to estimate for each disease “How large a reduction in yearly deaths makes
[the] institution worthy of funding?”
Each respondent made estimates for all three medical institutions. Each page of the
questionnaire presented information about one medical institution, X, Y, or Z, and infor-
mation about the number of deaths caused in the previous year by the disease for which
the institution proposed treatment, Disease A, B, or C, respectively (see “Task 1 Infor-
mation” in Table 2). Thus, on each page respondents read the following:
“Medical Institution (X) [Y] {Z} has developed a treatment for Disease (A) [B] {C}
and now requests $10 million from Science For Life. Last year, people with Disease (A)
[B] {C} did not have access to this treatment, and (15,000) [160,000] {290,000} died
from the disease. Given Science For Life’s shrinking budget, what is the minimum num-
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ber of lives this treatment would have to save next year in order for Medical Institution (X)
[Y] {Z} to merit funding?”
Respondents recorded their estimates on a blank line provided on each page. Six
versions of the questionnaire were distributed, reflecting all possible orderings of the three
stimulus scenarios.
The second task asked the same respondents to imagine that they must now choose
which proposal among the three submitted should receive the $10 million. They were told
that partial funding was not possible and they must rank order the three medical institu-
tions. Before giving their preference order, respondents were told that: (a) Institution X
would reduce deaths from Disease A from approximately 15,000 per year to about 5,000
per year, (b) Institution Y would reduce deaths from Disease B from approximately
160,000 per year to about 145,000 per year, and (c) Institution Z would reduce deaths
from Disease C from approximately 290,000 per year to about 270,000 per year (see
“Task 2 Information” in Table 2).
Thus, there was an inverse relationship between “number of lives saved” and “propor-
tion of lives saved”: Disease C deaths were to be reduced by the greatest number (20,000)
but by the smallest percentage (7%), whereas Disease A deaths were to be reduced by the
smallest number (10,000) but by the greatest percentage (67%). Respondents were asked
to rank the three proposals from most worthy to least worthy to receive the $10 million
funding.
Results and Discussion. The results from Task 1 indicated that a majority of respondents
exhibited psychophysical numbing (see Table 3). When estimating the minimum number
of lives an institution’s treatment must save to merit a $10 million award, 65% of par-
ticipants gave estimates that increased as the size of the population at risk increased.
Approximately 28% required that the same number be saved, regardless of size, and 7%
gave either varied or decreasing estimates. We also calculated the medians and geometric
means, which are less affected by extreme values. Table 3 shows that the arithmetic
means, medians, and geometric means all reflect a substantial effect consistent with
psychophysical numbing. For those who responded in accord with the numbing hypoth-
esis, the median number of lives Institution Y’s treatment was required to save (mdn. 5
Tab le 2 . Information given to respondents in Task 1 and Task 2 of Study 3
Number of deaths per year
Task 1 Task 2
Medical institution Disease treated Last year This year Next year
X A 15,000 15,000 5,000
Y B 160,000 160,000 145,000
Z C 290,000 290,000 270,000
Note. In Task 1, respondents were asked to indicate the minimum number of lives the treatment would have to
save to merit $10 million in funding. In Task 2, respondents were asked to rank order the three programs with
regard to priority for receiving $10 million in support.
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60,000) was more than six times greater than that of X’s treatment (mdn. 59,000),
whereas the median estimate for Z’s treatment (mdn. 5100,000) was more than 11 times
greater than the estimate for X’s treatment. Interestingly, for the 28% of respondents
whose estimates did not vary with disease size, the median estimate was only 100, far less
than that of the psychophysical numbing respondents’ estimates for even the small-scale
disease (mdn. 59,000).
Figure 3 shows the proportion of lives that respondents required each disease treatment
to save. Three clearly defined groups emerged from the analysis: 16 respondents (10%)
made estimates such that the proportion of lives saved remained constant across disease
size; 91 respondents (55%) made estimates such that, as disease size increased, the
Tab le 3 . Estimated minimum number of lives each institution would be required to save in Task 1 of Study 3
Psychophysical numbing
respondents
n5107 (65%)
Consistent respondents
n547 (28%)
Instituition Instituition
XY ZXYZ
Arithmetic mean 7,746 63,780 111,625 3,047 3,047 3,047
Geometric mean 4,701 32,678 56,707 100 100 100
Median 9,000 60,000 100,000 100 100 100
Lower quartile 3,000 16,000 29,000 1 1 1
Upper quartile 10,000 100,000 200,000 5,000 5,000 5,000
Note: Institutions X, Y, and Z each proposed treatment for a disease that caused 15,000, 160,000, and 290,000
annual deaths, respectively.
Figure 3. Respondents’ estimates in terms of proportion of lives that each institution should save (Study 3).
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proportion saved decreased, but at a rate where the number required to be saved was
greater for larger diseases; and 47 respondents (28%) made estimates such that, as the
disease size increased, the proportion saved decreased at a rate such that the number of
lives saved remained constant. The remaining 11 individuals (7%) exhibited no consistent
pattern, and were therefore not included in any of the three groups mentioned.
These results suggest that respondents evaluated the interventions using two evaluation
strategies. Some respondents appeared to employ a proportion rule; some, an absolute
number rule; and still others seemed to employ some combination of the two. That is,
some respondents believed a given institution to be “worthy” of funding only if the ratio
of number of lives saved to total number of lives at risk reached some proportion threshold
(proportion rule). Those who followed the number rule also held a threshold, but one that
was based on an absolute number of lives saved rather than a proportion saved. The
majority of respondents, however, fell into a third group that made estimates in a manner
consistent with an anchoring and adjustment process. In such a process, for example, one
might choose a reasonable proportion threshold for the smallest disease treatment, say
“must save at least 50% of those at risk”, and then adjust this threshold downward for the
treatments of larger diseases, say “save 47%” for the medium disease and “save 45%” for
the largest disease. In fact, many of the 55% of respondents who appeared in this category
imposed proportion thresholds that were within 5% across the three disease treatments.
In Task 2, we gave information about the annual expected reduction in deaths for each
of the three disease treatments (see “Task 2 information” in Table 2). Respondents then
rank ordered the treatments from “Most worthy” to “Least worthy” to receive funding.
The results were quite different from those of Task 1 (see Table 4). More than 60% of
respondents preferred to fund disease treatments that maximized the number of lives
saved, preferring Institution Z (20,000 saved) over Institution Y (15,000 saved) over
Institution X (10,000 saved). Approximately 16% preferred treatments that maximized the
proportion of lives saved, choosing the preference order XYZ. The remaining 23% of
respondents fell somewhere in between the above two groups, choosing preference orders
that maximized neither the number of lives saved nor the proportion of lives saved.
The three groups that emerged in Task 2 roughly corresponded to those that emerged in
Task 1, though the proportion of respondents in each did not. In Task 2, a majority of
respondents seemed to employ the absolute number rule by consistently preferring to save
Tab le 4 . Task 2 in Study 3: frequency and percentage of respondents’ preference orders (N5164)
Maximize number
of lives saved
Maximize propor-
tion of lives saved Other
Preference order: ZYX XYZ XZY YXZ YZX ZXY
Frequency 99 26 15 9 7 8
Percentage 60% 16% 9% 5% 4% 5%
Note: Institution X proposed a treatment that would reduce annual deaths by 10,000 (67% of those at risk);
Institution Y proposed a treatment that would reduce annual deaths by 15,000 (9%); Institution Z proposed a
treatment that would reduce annual deaths by 20,000 (7%).
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a greater number of lives; others seemed to employ a proportion rule by consistently
preferring to save a greater proportion of lives, and about one quarter seemed to attempt
some combination of the two strategies.
The results of Task 2 underscore two important points. First, the task format can
significantly influence the degree of psychophysical numbing. Second, even in the rather
simple and transparent format studied here, psychophysical numbing does not disappear.
4. General discussion
Evidence from the present studies shows that people often judge the value of life-saving
efforts in much the same way they judge the intensity of stimuli in traditional psycho-
physical experiments. Just as a fixed decrease in brightness seems greater when the
original intensity is small than when it is large, an intervention saving a fixed number of
lives seems more valuable when fewer lives are at risk to begin with—when the savings
is a larger proportion of the number at risk. When such psychophysical numbing occurs,
the value of a life-saving intervention is inversely proportional to the magnitude of the
threat rather than being determined by the absolute number of lives the intervention can
save.
A significant portion of the respondents in each of the present studies exhibited psy-
chophysical numbing. Many respondents in the first two studies judged interventions
serving larger refugee camps to be considerably less valuable than ones serving smaller
camps, even though the interventions could save the same number of lives. Furthermore,
when respondents in Task 1 of Study 3 estimated the number of lives several proposed
disease treatments would have to save to be equally worthy of a fixed amount of funding,
median estimates were more than 11 times greater for the intervention that treated the
disease killing 290,000 annually than the one killing 15,000 annually.
Although psychophysical numbing was present in each study, its prevalence varied.
This is important because it shows that the incidence of the phenomenon is mutable. For
example, over 67% of participants responded psychophysically in Task 1 of Study 3,
whereas only 16% responded psychophysically in Task 2. In addition, Study 3 suggested
that those most likely to see the value of an intervention as independent of a problem’s
size were also the ones who attached the greatest value to saving lives generally. For
example, psychophysical respondents in Study 3 required over 1,000 times as many lives
to be saved (median estimate) in the largest disease category than respondents who gave
consistent responses (see Table 3)!
There are several other features in the present studies that may have affected the degree
to which psychophysical numbing occurred. First, the way information about life-saving
interventions was framed changed the degree of numbing. In Study 3, for example,
numbing was frequent when information about the interventions highlighted the magni-
tude of each tragedy (Task 1), but far less frequent when the information emphasized the
magnitude of each intervention’s life-saving potential (Task 2). Thus, descriptions of
events that focus on the outcomes of the intervention rather than the tragedy it serves
appear to reduce the degree of psychophysical numbing.
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Second, the ease of comparison between different interventions may have also contrib-
uted to the degree of numbing respondents exhibited. In Task 2 of Study 3, where the
numbing incidence was low, information on each intervention and tragedy was presented
side-by-side, whereas in Task 1, information about each tragedy was presented on separate
pages. Study 1 also showed that ease of comparison may have been a factor. Those who,
when asked directly, reported no preference between two interventions that saved the same
number of lives, nevertheless preferred the intervention serving the smaller tragedy in the
previous task where direct comparisons were more difficult.
Despite this variability, however, the present studies suggest that psychophysical numb-
ing is a robust phenomenon—ingrained in the workings of our cognitive and perceptual
systems, which seem geared to sensitize us to small changes in our environment, perhaps
at the cost of making us less able to appreciate and respond adequately to large changes.
When we contemplate nuclear war, for example, and its immense capability for death and
destruction, it may be difficult to escape psychophysical numbing as we attempt to grasp
the significance of the difference between 10,000, 100,000, or a million or more deaths.
Where we lack perceptual sensitivity, we might also expect to find that our language is
also inadequate to discriminate among degrees of harm or destructiveness. Thus John
Hersey’s elegant chronicle of the aftermath of the Hiroshima bombing (which killed about
140,000 people) simply refers to the scene as havoc (Hersey, 1946, p. 5) and terrible (p.
86). Lifton (1967) refers to Hiroshima as a disaster, a term commonly applied to events
that are far less severe. Holocaust,catastrophe,calamity,tragedy … the vocabulary of
disaster seems sparse indeed. Can the potential deaths of large numbers of people really
be comprehended without an adequate vocabulary of destructiveness?
Some who have worried about the incomprehension of mass destruction are pessimis-
tic. Humphrey (1981), for example, writes of our ability to be moved greatly by the plight
of single human beings at the expense of insensitivity to “giant dangers.” He says:
“In a week when 3,000 people are killed by an earthquake in Iran, a lone boy falls
down a well shaft in Italy—and the whole world grieves. Six million Jews are put to
death in Hitler’s Germany, and it is Anne Frank trembling in her garret that remains
stamped in our memory.”
We must live with this … It will not change. I do not expect my dog to learn to read
The Times, and I do not expect myself or any other human being to learn the meaning
of nuclear war or to speak rationally about megadeaths …” (pp. 21–22).
Yet writers such as Hersey, Lifton, Jonathan Schell (1982), and many others do have the
power to move us emotionally with their eloquent descriptions of individual and societal
tragedies despite the lack of adequate one-word descriptors. Is that a sign that we can,
indeed, comprehend these tragedies in a way that will help us to make good decisions
about preventing them or managing their risks?
Modern technology has great power to cause, prevent, and alleviate mass human suf-
fering. Yet the psychophysical numbing we have observed in our studies is strong enough
and pervasive enough to raise some disturbing questions about our ability to make rational
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decisions when many lives are at stake. Further research is clearly needed to illuminate the
dynamics of psychophysical numbing and determine its effects on decision making.
Acknowledgment
We acknowledge with thanks support from the National Science Foundation under Grant
Number SBR-9422754 to Decision Research and a Graduate Research Fellowship granted
to the first author. Any opinions, findings, conclusions, or recommendations expressed in
this paper are those of the authors and do not necessarily reflect the views of the National
Science Foundation. We also thank Sarah Lichtenstein for her comments on the manu-
script and Leisha Mullican for her technical assistance in the preparation of the report.
Notes
1. A striking example of psychophysical insensitivity to money was Ronald Reagan’s assertion that a $4.6
billion job program “would add virtually nothing to the federal budget” (Eugene Register-Guard, March 25,
1983).
2. Lifton (1967) used the term “psychic numbing” to refer to the accommodation and reduced sensitivity to
shocking and emotionally overwhelming threats and experiences, such as those created by nuclear war.
Hiroshima survivors, for example, said that they very quickly “ceased to feel.” We use the term “psycho-
physical numbing” to reflect a cognitive or perceptual form of insensitivity, different from the emotional
quality of psychic numbing. Whereas psychic numbing is adaptive, enabling survivors and rescue workers
to cope with trauma, psychophysical numbing may degrade our ability to appreciate the consequences of
our actions.
3. In the summer of 1994, when these data were collected, ethnic warfare in Rwanda had resulted in over a
million refugees fleeing into neighboring Zaire. The brutal nature of the civil war, as well as the problems
of disease and hunger that plagued the refugees, had made the Rwandan conflict the topic of considerable
print, radio, and television news attention (Cooper, 1994; Purvis, 1994; World News Tonight, 1994a,
1994b). Participants’ likely familiarity with the Rwanda crisis should have helped to make the potential loss
of life addressed in the judgment task particularly salient and realistic.
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