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OCR for page 51
IV. INTERPRETATIONS OF THE DATA
The material which follows consists of two interpretations of
the data which were presented in the preceding section: First, the
specific hypotheses which were developed before collection of the data
were tested. In general, these hypotheses predict specific relation-
ships between demographic, social, and threat-related variables in
the population, and disaster behavior. Second, an application of a
game theoretic model was developed, and an attempt was made to fit
the data to the model.
Hypotheses
the river ant! 10W ground
A number of the variables under consideration in the analysis
of the data have been shown to be related to geographical proximity to
The responses of residents of low areas
differ from tho se of people who lived on high ground. In addition, re -
spondents who lived in the previously flooded areas estimate that they
were personally in cianger more often than do others. Using the entire
sample, city and saturation, we get the following tabulation:
TABLE 26
RELATIONSHIP BETWEEN AREA OF
RESIDENCE AND ESTIMATE OF DANGER
Area of Residence
Flooded
Non-flooded
Total
Certain
Estimate of Doubtful
Physical Danger None
Total
53
12
9
13
13
9
66
25
18
74
35
109
1 . . 1
fin order to determine whether or not we could legitimately combine
the city -floode d and s aturation s ample s fo r thi s table, we fir st had to
, . · .
compare them against one another on this variable -- "Estimates of
Physical Danger. ', The obtained Chi-square was 2. 15, which has a
probability of about . 40. It is, therefore, legitimate to combine them
as we have done above.
51
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This table yields a Chi-square~ of 12. 37, which is significant
beyond the . 01 level of confidence. Because of this finding and others
previously reported showing the critical relationship between geograph-
ical proximity to threat and threat-oriented behave ors, it seemed ap -
propriate to restrict ourselves to the city-flooded and saturation
samples in the testing of many of the hypotheses. The inclusion of the
city-non-flooded sample in such tests would} give rise to serious dis-
tortion because the major determinant of differential behavior is
geographical proximity to the river or low ground.
In order legitimately to add the saturation sample to the city-
flooded sample, however, it was neces sary to be confident that we could
as sume that the s e two we r e s ample s fr am the s ame population. T e st s
between them were concluctec3 for a number of the major variables
under consideration here, similar to the one referred to in the footnote
on page 51. The major comparisons were made on: Hearing the re-
port, believing the report, fleeing, and believing in physical danger
and danger to property. In each case, the statistical tests applied give
us no justification for rejecting the null hypothesis. This supports our
~ We wanted to determine whether or not the relationships discovered
in our data could have occurred with any great frequency by chance
alone, or whether we could have some degree of assurance that the re-
sults we obtained could have occurred only infrequently by chance. In
order to do this, we applier} the Chi-square test to the data. The value
of the obtained Chi-square is evaluates] by its size and the number of
cells in the table tested. Note that after each report of a Chi-square,
we indicate the level of confidence which we can place in the results.
Thus if we state that the Chi-square value reporter! is significant be-
yond the . 01 level of confidence, this means that the differences be-
tween the various cells would be exp ected to oc cur le s s than once out
of 100 times by chance alone. If this is the case, we are fairly confi-
dent that the relationship obtained is not a chance relationship, but
rather one that we would elect to find again and again in similar situ-
ations. If, on the other hand, we state that a Chi-square of a given
size has a significance level of . ZO, this means that we could elect to
find such a relationship 20 times out of 100 by chance alone. In this
case, we assume that no lawful relationship exists. We have adopted
the conventional practice of accepting as significant (non-chance) only
tho s e r elationship s which are stall stically significant beyond the . 0 5
level of confidence.
52
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c ontention that the s e two s ample s c an legitimately be combine ~ fo r
the purpo s e of te s tiny the hypothe s e s .
As previously indicated, residents of the flooded area were
generally of somewhat lower socio-economic status than residents of
the non-flooded area. It might be asked whether this difference would
help account for differences in flight behavior reported between the
two groups. However, as will be made clear in the following analysis,
there is no evidence that this variable is responsible for the differences.
1. Hypothesis: People who have roles of responsibility for
others are more likely to check for confirmation than those who do
. . .. . _
not have such roles.
. .
As noted above, te sts were re striated to the flooded areas
since both the necessity for seeking verification and possibly the time
available to do so varied with the geographical location of the respon-
dent.
The hypothesis was tested in two ways: A comparison was
made between people who had official and semi-official disaster jobs
in the community and those who die] not. Second, a comparison was
made betweenthose who had familiar responsibilities andthose who
did not. (Another interesting comparison would have been between
roles of responsibility and sources checked. However, there were
so few respondents who sought confirmation from unofficial sources
that such a comparison was not possible.
TABLE 27
RELATIONSHIP BET WEEN RESPONSIBILIT INS
AND CONFIRMATION AT TEMP TS
Community Responsibility
. _ .. .
Disaster Job
No Disaster Job
Total
Attempted Ye s
Confirmation No
Total
10
7
15
37
.. .
25
44
17
52
69
. . ,
53
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As can be seen in Table 27, individuals with disaster jobs re-
ported seeking confirmation more often than those without such jobs.
However, the Chi-square~ is 3. 77, and is only significant between
the . 05 and . 10 levels of confidence.
The comparison based on familial responsibilities yielded
chance results.
2. Hypothesis: Persons in disaster-struck areas tend to
show more solidarity Han those in non disaster-struck areas.
There was no relationship found between living in a disaster-
struck area and attempts to assist community members either in flee-
ing, preparing for disaster, spreading the rumor, or calming others,
nor for all of these combined.
However, indivicluals who did not live in previously flooded
areas communicated the denial message to others significantly more
often (see Table 28~.
TABLE 28
RELATIONSHIP BETWEEN AREA OF RESIDENCE
AND DENIAL COMMUNICATIONS
Area of Re sidenc e
Floodec] Non-Floode d T otal
12 13 25
61 23 84
. _ . 1
73 36 1 09
Denial Ye s
Communication No
Total
.
This table yields a Chi-square of 4. 22 which is significant be-
tween the . 02 and . 05 levels of confidence. More than one interpreta-
tion of this relationship is possible. Many of the people who lived on
Tithe Yates' correction for continuity was applied for computing these
Chi-squares as well as for all He others.
54
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low ground had fled to a nearby hill. The denial was broadcast gener-
ally over car radio s in that locale, and there may have seemed little
reason to repeat this message. By the time these people reached
home, agitation in the community had somewhat subsided, and the
need to communicate the message at that time may have been small.
On the other hand, people who had fled may have felt shame-faced, or
may have wanted to avoid the responsibility for sending others back
. . . ~
into the danger areas. It is impossible to tell which, if any, of these
factors was responsible for the relationship found.
3. Hypothesis: People are more likely to believe and act on
-
reports communicated by official sources than those communicated by
unofficial sour c e s .
An attempt was made to te st belief in the thr eat me s s age
against its source, but there were too few people who dud not believe
the thre at to make such a te st po s sible . It would appe ar that re sidents
had been so sensitized to the possibility of the catastrophe that the
source of the message was relatively unimportant, and any alarm was
sufficient to produce belief.
The difference in credibility of sources was checked against
further attempts at confirmation made by the recipients of messages.
This test yielded non- significant results ~ People who received threat
messages from unofficial sources were no more likely to seek addi-
tional verification than were individuals who heard the threat message
from officials. Respondents' estimates of danger, en c] their speed of
flight, were also found to be unrelated to the source of the Great mes-
sage.
In summary, stall stical te sts of the data give no basi s to the
contention that people are more likely to believe and act upon threaten-
ing reports if they come from official sources.
The case of the denial message is quite different. It was not
possible to apply the usual statistical test to the credibility of various
sources of clenial, because of the small number of people who received
the message from an unofficial source. An examination of Table 29,
however, leads one to the conclusion that official sources of denial were
in fact more cr edible than were unofficial sourc e s .
\
55
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TABLE 29
CREDIBILITY OF DENIAL SOURCES
Sour c e of the Fir st Denial Me s s age
Official Unofficial Total
- - -1
Denial Source Official
Leading to
Belief
Unofficial
Total
7
G
9
45
47
Previous studies (17) have indicated that if the source of alarm
is official, threat-oriented behavior is more likely. We find that this
is not true for the Port Jervis threat message, while it is true for the
denial. The possible cost of failing to believe any threat message is
quite high; it results in a delay of action which is dangerous in case the
threat materializes. On the other hand, there is little cost to display-
ing caution in the acceptance of denial messages. Further, unofficial
sources accounted for most of the threat messages which were later
being denied. Now that the unreliability of unofficial sources was being
displayed, individuals may have chosen to rely only on sources which
they conside red to be official.
Finally, it might be worthwhile to comment here on the rela-
tive credibility among various official sources. Although no statistical
test could be applied to the data of Table 30, they are suggestive of
hypotheses which can be tested definitively in other field studies.
Obviously the total number of cases is too small to apply any
tests. We can, however, make a few informal comments. Note that,
with the exception of the entry "official on the street, " the largest entry
in the columns is along the diagonals. This suggests that for at least
the first three categories, denial from any of these sources was quite
effective. In addition, all of those who heard the radio as a first denial
source eventually accepted that source. Using this same reasoning, we
can rank the relative effectiveness of the various official sources:
Radio, Central Official (Official at a communication center), Loud-
speaker (on Police and Fire vehicles) and Official on the street (removed
56
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two to
soondent might
frolic a communication center).
the first ~~
On intuitive ground s, we expe ctec}
be more effective, if only for the reason that the re
O assume that communication centers would have the
latest and most accurate information. It would appear that future
studies might be able to verify the hypotheses clerived from these data.
TABLE 3 0
RELATIVE CREDIBILITY OF OFFICIAL SOURCES OF DENIAL
Loudspeaker
Denial Radio
Source
Leading Central
to Offici al
B elief
Official on
the Street
Source of the First Denial Message
....
LoucI- Central
sp e eke r Radio Offi ci al
. .. _
~O O
4 ~1
1 0 7
O O O
. . .
Official on
the Street
.
o
5
o
4
Total
.
8
18
8
4
_
Hypothe sis: The probability of s eeking and accepting in
~ormat~on trom authorities increases with education and with ace.
A1~'ost all respondents who attern~ted confirm;~tinn :~t :~11
turned to official sources.
~. ~.
No relationship was found between education
and age with either the source of attempted confirmation, or the likeli-
hood of seeking confirmation of the threat message.
5. Hypothesis: Those who heard previous rumors concerning
_ .. . .. . _ . . .
a dam-break during the tingle which immediately preceded this false
report are more likely to accept and act on it tbDt nth~r~
, . .
One major factor contaminated these data. Although only
relatively few people heard actual rumors concerning a dam-break
57
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prior to the rumor under consideration, over 90 per cent had been ex-
posed to speculation concerning the po s sibility and the consequence s
of such a br eak. It would s e e m that such sp e culation would have the
same affect as actual rumor that the event had taken place. If this is
true, of course, almost all respondents will fall into the same cate-
gory (those who heard prior threatening statements about a dam-break)
so that tests of the effects of this prior exposure are impossible.
Since coders were carefully instructed to distinguish between
respondents who heard that the dam had broken, and those who heard
that it might break, we attempted to compare these two groups. In
light of the previous statement of contamination, we did not really ex-
pect to find any significant relationship. A Chi-square test revealed
no correlation between exposure to rumor and flight. Further there is
~ _ ~ ~___ ~ ~_ 1 ~_ _ _ . ~ ~
no tendency Ior people exposer to previous rumor to listen to more
denials or denial sources before accepting the truth of the denial.
6 . Hypothe si s: P eople who think that the thr eat i s immediate
to them or to their families are less likely to seek confirmation than
_
those who feel that there is adequate time to escape.
This was a difficult hypothesis to test because many respon-
ctents were unable to estimate the time they thought it would take for
the water to reach them. This is not surprising, since respondents
could not know how long the dam "had been broken" before they heard
about it. In many cases these people merely indicates} that they thought
they had just time enough to get away safely. These respondents were
grouped with those who estimated inundation in less than forty-five
minutes -- a reasonably safe estimate of the amount of time it would
take any person in the city to prepare and evacuate. A comparison
was then made between individuals who estimated less than an hour till
inundation, andthosewho estimatedthattheyhacimorethanan hour.
The data in Table 31 yield a Chi-square of 1. 34 which is not
statistically significant. If respondents' reports of their estimated
time to escape were accurate, it would seem that either (1) these est~-
mates do not affect the likelihood of confirmation, or (2)
felt Mat the short delay caused by attempting to confirm
cantly affect their chance of e s cape .
58
few people
. . · ·, .
WOU1Ct SlgnlI1
-
OCR for page 59
TABLE 3 1
RELATIONSHIP BETWEEN IMMEDIACY OF
THREAT AND CONFIRMATION AT TEMP TS
E s timate d Time Until Inundation
~ . . _ . _
Minimal Time
Attempte d Y e s
Confirmation
No
Total
One Hour or More
Total
20
6
21
14
41
20
26
35
. _ _
71
Hypothesis: Among those who accept the report as true,
. ~. ~
tho.~e wits Ire Hn,~htf',1 ;'hn,7t the - blent; :~1 ~ - rYm' fm their ~, =~
more likely to seek confirmed_ m~ ~ ~= _ I_ -God · · · It
.
dange r .
confirmation.
Ambiguity in a situation is expected to increase the need for
The simple indication of the existence of a specific threat
is insufficient information for some respondents. These individuals are
unable to determine whether or not the disaster will affect them, en c!
we would expect suchpeople to be galore likely than others to seek con-
firmation.
In te s tiny thi s hypothe si s, we us ed all individual s who believed
the false report, regardless of their geographical location, since dis-
tance from the threat Is clearly incorporated in the hypothesis.
The Chi-square for Table 32 is 11. 53, which is significant
well beyond the . 01 level of confidence. It is clear, then, that amb~g-
uity about the range of destruction increases the probability of the use
of confirmation channels. Another implication of ambiguity becomes
apparent when one considers that speed of flight and attempts to con-
firm are highly, and negatively, correlated; time taken to seek confirm-
ation delays flight. Although in section 7 above we indicated that people
did not seem to attach too much significance to delay for confirmation,
we must point out that there are in fact cases in which such delay might
59
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result in loss of life. As could be elected, certainty of danger ant]
speed of flight are also highly correlated:
TAB LE 3 2
RELATIONSHIP BE T WEEN DANGER ES TIMATES
AND CONFIRMATION AT TEMP TS
E stimate s of Danger to Property ~
,,
Certain of Damage
Doubtful of Damage
Total
Yes
Attempted
Confir mation No
Total
18
49
16
34
56
67
23
So
TABLE 3 3
RELATIONSHIP BETWEEN DANGER ESTIMATES
AND FLIGHT BEHAVIOR
Estimates of Danger to Property
.
Certain of Damage
Fled immediately afte r
fir st me s sage:
Fled later, or was stop
ped in preparation
Believed, but did not
flee
Total:
35
28
4
67
Doubtful of Damage
Total
37
8
14
24
36
18
91
1 _
The Chi-square is 32. 60, which is well beyond the . 001 level
of significance. The two sets of results clearly imply that doubts
60
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about the extent of danger to the re spondent and hi s property have two
effects which in many instances could be deleterious: (~) The jamming
of c ommuni c ation channel s, and ( 2) the delay of flight and p o s s ible
loss of lives as a function of such delay.
S. Hypothesis: People who are integrated into the community
, .. . . . . .
are more likely to seek confirmation through their own personal
. . . . . .
s our c e s of c o mmuni c all on than th r ough off i c ~ al s our c e s .
. . . . _
We hac3 hoped to be able to develop a measure of degree of in-
tegration into the community. Because of the time limitation during
the data-collection phase of the study, it was impossible to do so. The
only measure available which might be related to the variable under
consideration is the respondent's length of residence in Port Jervis.
However, the possibility that the correlation between integration and
length of residence might be low led us to abandon attempts to test this
hypothesis.
as, _ _
. . ~. · . .
. .
9e Hypothesis: People who get the report while they are part
Of an intimate group are more likely to behave in a group-oriented
. .
manner than are those who are not part of an intimate group.
. .
Hypothesis: People who are separated from family mem
bers at the time of the report are more likely to act with relation to
· _ . . . . . . _ . .
the absent family member than with relation to the community, and in
general are more likely to manifest greater agitation than others.
. . . . . . .
These hypotheses were impossible to test because most re-
spondents were at home with their families at the time the rumor was
cir culated.
10. Characteristics of residents who flecl: One of the objec-
tives of the study was to determine whether we could define any differ-
ences between residents who fled and those who did not. Experiences,
attitudes, and information sources of the re~r~ondent.~ ware ~ Amine
in various ways.
The reader will recall that almost 90 per cent of those who
fled lived in the previously flooded area. Using the entire sample
(flooded anti nonfloodeci), the previous evacuation experience of the
respondent and his place of residence are the only variables related
. . .
61
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application of this model to the Port Jervis situation comes as a post
hoc statement. An examination of the data led to the suggestion that
this kind of mode} might fit, and that such a formulation might provide
hypothe s e s fo r te sting in futur e s tudi e s .
We will assume that there exist disasters which differ in at
least the following functional ways:
1. There Is a difference in the amount of forewarning.
2. There is a difference in ambiguity; i. e., there is more
doubt in some instances than in others about the extent and range of
destruction which mill ensue, if the disaster strikes.
3. There is a difference in the amount and accuracy of prior
information which is available concerning measures for dealing with
the disaster, if it strikes.
These differences will be assumed to be powerful factors in
the determination of differential population reactions to the disaster
when it strikes. The differences in reaction which we will examine
will be (1) the degree of rationality, which will be defined as the de-
gree of conformity to a minimax strategy in a properly weighted game
theoretic matrix, and (2) the degree of homogeneity, which will be de-
fined as the degree to which behaviors summered over individuals
reflect individual behaviors; i. e., when the game played by the group
is the same as that of one player. Neither of these conditions predicts
uniform behavior for individuals in the population, as will be shown
later in this development.
We hypothesize that if the forewarning is long, the ambiguity
minimal, and the prior information maximal, the population will react
in (l) a rational, and (2) a fairly homogeneous fashion.
The individual, or "player, '' who is faced win a threatening
situation, first defines it and Men makes a decision as to the cost to
hills of various responses. When the definition is made and the alter-
nate responses stated, we saythat the game is fixed; the definition of
the situation fixes the alternatives, or " strategic s, " which the individ-
ual believes are open to the opponent. The responses the individual
66
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perceives as open to himself are his strategies. By making a shrewd
estimate of which strategy to employ, the individual will minimize his
loss in playing the game. The player will ask the following questions:
1. What will the opponent do?
2. What alternatives are open to him as the player?
3. How much do different outcomes appeal to him?
4. Which player strategy will result in the more appealing
outcomes, provicied that We choice of the opponent is not completely
determinable? In other words, for any outcome, when will he least
r egrets the strategy he cho se ?
L`et us take as an example a case in which the opponent of the
player is "nature. '' We will assume that nature floes not care whether
it "wins" or "loses" the game; the play is against an indifferent, rather
than a malignant, opponent. The player assumes, in this example,
that the opponent has four choices: A, B. C anti D. He sees for him-
self four alternatives: a, b, c, and d. The player then decides what
his regret will be about the strategy he chooses, given one of the
choices of the opponent. For instance, if the player is killed, his re-
gret for having chosen a strategy which yielded that result will be
great; if he escapes without loss of life or property, his regret will be
less. Let us assume that he fixes regrets with weights of 0, 1, 2, 3
and 4 for particular outcomes on this kind of continuum. The galore
for the player is now fixed. He has only to decide which strategy he
will (afterwards) regret least having played:
it In the usual theory of finite two-person games, the entries in the
matrix of the game are actual costs, i. e., in the ith column and jth
row i s entered the co st to the fir st player if he choo se s the ith strategy
available to him and his opponent chooses the jth opposing strategy.
It is fount] on the basis of empirical evidence that a human placed in a
situation of uncertain outcome similar to that of a finite two-person
game actually makes his choices on the basis of a mini~'ax principal
whe re the entrie s in the game matrix ar e regrets . If the human is con-
sidered as the first player, and nature, or some other opposing force
the second, then the human plays as though the minimum entry in
every column is zero. The minimum cost in that column has been
assigned regret zero; i. e., there is nothing to regret if, for this
strategy, the opponent's choice results in minimal cost to him. All
entries in a given column are correspondingly reduced by an amount
equal to the minimum.
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MAN
a
b
c
d
A
N _
A B
T
U C
R
E D
FIGURE 1
O
4
3
1
.
1
o
4
2
..
2
4
4
3
4
. .
o
If the player cannot p redetermine natur e ' s choice, and as signs
an equal probability to all four alternatives (note that the probability
as signed by the playe r i s subj e ctive, and may not be the s ame as the
objective probability of the occurrence of the event), he will choose
strategy (a) because his total regrets in this column are minimal. al-
though it is the case that if nature in fact chooses (B), he would have
been better off choosing strategy (b). If the individual assigned high
probability to (C) as the choice which will be made bv nature. he
might be better off choosing strategy (c). However, if there is a fin-
ite probability of (B) being selected by nature, the individual has
placed himself in a Position where he may experience the regret. he
_,
, ~, _
~, _ _z ~ a, _ ~ · ~
has weighted (4~. When (41 represents, saY. the regret of death. he
~ , , cat - --
_ ~ ~ r ton ~ ~ ; 1 ~1 _ ~ ~ ~ 1 ~ _ ~ ~ ~ _ ~ _ _ ~ ~ · .
Moldy L,= unwllllug lo employ any strategy wnlcn Includes this regret as
a possibility. The regret assigned in such cases
.. v should actually be
weighted infinitely; any strategy which included it would be maximal
and would never be se. lected.
When the individual assigns subjective probabilities to the choices of
the opponent and chooses his own strategies on a probability basis,
we say that he is using a "mixed strategy. " In the disaster case, of
course, the behavior will always seem fixed, because the individual
choo s e s only once, but the behavior summed ove r individual s may
look like a mixed strategy.
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When a sudden and unexpected disaster strikes, the individual
has not yet developed such a aviatrix. He may 30 so on the spot, within
some limits, but the range of alternatives he derives may be seriously
narrowed by the lack of time. On the other hand, he may not develop
a game at all, but may act in some random, or at least non-rational,
way. We can elect that the definition of the disaster and of alterna-
tive strategies made quickly and suddenly will diner considerably
from those made by another individual under the same circumstances;
the games will be different. While the model for each of these players
may fit a game theoretic model, there is absolutely no reason to ex-
pect that the behaviors summed over inclividuals will resemble a
game theoretic matrix. The summed behaviors will not reflect the
structure of the individual behaviors. Perceptions of the situation
are different, the alternatives different, the activities relatively un-
related. An analysis of the group's behavior would yield a statistical
statement, but not a game theoretic statement.
On the other hand, when a disaster is (1) elected, (2) clear-
cut in terms of its range of penetration en cl extent of destructive power,
and (3) prior information has been provided as to the best methods for
handling such a disaster, we can expect that individuals will, in large,
play the same game. They believe they know, in this case, the
choices available to the opponent, and the relative regret they will
feel for specific outcomes; the game is fixed. This floes not in any
way imply that individuals will perform one given activity. The strat-
egy chosen may be a function of some variable (say, time or location)
rather than a simple activity; in actual situations of risk, strategies
will ordinarily be such functions, so that individuals' activities will
differ as they choose the least-regret solution to the game.
The descriptive account of the Port~Jervis situation yields
one striking intuition: The predefinition of the consequences of a
break in the Wallenpaupack Dam affecter} the behavior of city residents.
Protocol data indicate that discussion of the consequences of this ca-
tastrophe had taken place in the city during the days before the spread
of the false report. We will assume that this discussion narrowed
the perception of residents concerning what might be the cause of any
sudden disturbance in the community. Evidence for this assumption
is ample: respondent data indicate that if traffic was heavy, people
noisy, sirens blowing, or the word "dam'' mentioned, this was likely
69
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to be interpreted as meaning that the Wallenpaupack had given way.
In short, the differences in content and source of threat messages had
no measurable effect on people who heard them. The data supply this
fact: Advice to flee (against no such advice) in the Port Jervis situa-
tion is completely uncorrelated With flight, both within and between
the floodecI and non-flooded areas of the city. Mes sage s from official
sources carried no more weight, behaviorally, than messages from
other sources.
Port Pelvis represents a situation in which people were
aware long enough in advance of a preci sely defined threat, and had
discussed it so thoroughly that advice on which activity to perform
became irrelevant. We hypothesize that people had, at some level,
predetermined what the extent of penetration of the water would be,
and what their rule for action would be, if the Wallenpaupack broke.
we would elect then, according to the previous formulation, that the
action which followed receipt of the false report would be both rational
and homogeneous.
The threat situation was defined as follows: The Wallenpau-
pack Dam may break. If it does, a large volume of water will deluge
at least certain areas of the town. ~ ~ ~ ~ ~"
the situation was as follows:
The activity defined f or handling
Do not be in a low area when the water
strikes. Flight, then, became a function of a time variable: move-
ment away from a given area should vary as a [unction of the time at
which the water will strike that area. (Note that this time can increase
indefinitely; i. e., the report is false and the water will strike at time =
infinity. ~
At thi s point, of cour s e, individual s could choo s e to play on
the basis of maximum utility, minimum cost, or minimum regret,
and might weight their activities somewhat differently. In this formula-
tion, minimum regret will be assigned to the activity which turner] out
to be most appropriate, given a specific outcome (strategy chosen by
nature ~ .
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The game laid out for the player is approximately as follows:
MAN
(must leave area at time ~ ~
Minimum 30 minutes 1 hour 2 hours ,[ Infinity
N
A (water will
T strike at
U time =
R
E
Minimum
45 minutes
.
1-1/2 hours
.
3 hours
Infinity
. ...
FIGURE 2
Since players cannot be positive of the time at which the
water will strike, their summer] behaviors will look like a mixed
strategy. We will have to determine the position of the player when
he receives the message to determine the time at which he perceives
the water will strike; if he is in the valley, he will expect it to strike
sooner than if he is on a hill. In fact, if he is on the hill, he may feel
that it will not reach him, so that his estimate of time is infinity.
Where we have chosen some element from the set of locations, we can
define the rule giving us the (probable) element from the set of times
to evacuate, assuming a minimum regret weighting.
The difficulty in the formulation lies in the choice of weights
for outcomes. Although we attempt here to fit a minimum regret
weighting, on an intuitive basis, there is little reason to assume that
it will provide the best fit with this kind of data. The use of the mocle!
does depend, however, on the question of whether individual weight-
ings will fall into similar ranges. Even if individuals rank regret
similarly, we must date amine whether the de gr ee of pref er enc e, i . e .
the decrease in regret from each alternative to the next, is fairly
homogeneous over individuals.
A number of laboratory experiments in decision theory (4,
19) have been done to determine the kinds of choices which people will
make under risk when the alternatives are well defined. The decision
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is taken to be dependent both upon the relative preference for possi-
ble outcome s, and the subj e at' s probability e stimate s for the occur -
rences of these outcomes. Methods for simultaneous and independent
prediction of utility and subj ective probability are being te sled exten -
sively. * Many experiments have used the gain and loss of small
sums of money as outcomes. The extent to which the results can be
generalized to situations of risk outside the laboratory remains
que stionable .
A mathematician** who did not participate in the collection
or analysis of the dicta was asker} to fix the weights in the matrix of
Figure 2 according to his own intuition, on a principle of regret, and
to choose strategies accordingly. A sketch of the weighting proced-
ure he used follows.
Greatest regret is assigned to the least appropriate activi-
ties for specific outcomes, in which a great deal might have been
gained by deciding on a different strategy. The regret for death is
presumed tc, be infinitely large, so that no strategy involving it as a
serious rislt will be employed. Other regrets are weighted from ()
(no regret -- avoidance of flight or flight at the last possible safe
moment) to 5 (the delay of flight to We point where considerable risk
of physical danger is taken, or immediate flight in case the Great
never materializes. ~ It is assumed that regret increases if the indi-
~ndual acts with greater haste than necessary, for delay enables the
player (~) to collect possessions which otherwise he would have to
abandon, and (2) to hear possible later messages which may obviate
Me neec} for flight. Behavior on the hill will be (Lifferent from that in
* Although Mere is stridence that the utility and probability statements
which wall be made in simple risk situations rrmy be predictable, this
cannot be construed as meaning that the se statements will be uniform
for aU individuals, or for one individual over time.
** Dr. Murray Gerstenhaber suggested the use of this model after
determining from a general description of respondent behaviors that
people acted in what he felt, intuitively, to be a reasonable fashion.
We cannot, therefore, say that his weighting of relative regret was
entirely independent of his knowledge of actual behaviors.
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the valley, because the valley (river) position is inherently danger -
ous, and because the water will strike there sooner. The following
matrix results:
MAN
(must leave area before time = ~
N
Minimum
A
T3/4 hr.
U
R
EI-1/2 hr.
(Water
we
strike
at time
= )
Summed regret:
3 hr. ~
Infinity
Summed regret:
(time ~ minimum
has probability ~ 0)
O 1/2 hr. 1 hre 2 hr. Infinity
.
~ ~ W~
-
\10
14 \
\10
14\
~ . .
\= \m
13 \ 11 \
. 8 \6\
FIGURE 3
\ a)
10\
-\7^
5 \
\ ~
9 \
\8
4 \
An analysis of this matrix reveals the following choices an
individuM will make if he wishes to minimize regret:
A. On low ground
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1. If a finite probability is assigned to inundation in
minimum time (row 1), the individual will flee immediately (column
1~.
2. If the individual assigns minimum time (row 1) a
zero probability, he will delay flight for approximately 1/2 hour (dur-
ing which time he gathers his possessions and waits for possible dis-
confirmation. ~ (column 2. ~
B On high ground: He doe s not flee (column 5) .
The conditions which were initially stated for rational and
homogeneous behavior, as those terms were defined, are fulfilled in
the Port Jervis situation: (1) the possibility of the occurrence of this
catastrophe had been suggested widely days in advance, (2) there was
very little ambiguity about the nature of the disaster; people had cle-
cided (whether correctly or incorrectly is of no concern) what the
destructive range of the water would be, and (3) recent exposure to
flood conditions had given people a good deal of information about
topological and temporal variables they would have to consider in case
of the occurrence of this disaster.
The choices indicated in the matrix seem close to those made
by Port Jervis residents, under the given conditions. Those who lived
on high ground (in the previously non-flooded areas) almost never flec3.
The valley residents who estimated short time until inundation fled.
The valley people who estimated a longer time until inundation delayed
flight (members of this group often received disconfirmation in time
to avoid] flight completely). If this is indeed the case, we will say
that individuals behaved as though conforming to a game theoretic
model. Under ambiguous conditions, where the threat occurred suc3-
denly, and its consequences were undefined, we would have expected
(1) flight on the part of the hill people, because they would not know
how far the water would penetrate, and (2) time of flight relatively un-
related to geographical position. We would elect, in other words,
that a rational weighing of alternatives would not have taken place. An
attempt to fit the data to the model more precisely was not undertaken
for three reasons:
1. The hypothesis was developed after the interviews
and analysis of the data were completed; regrets can be juggled to fit
the data.
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2. The que stions asked in the interview se s signs, and
the data as codecl, are not in the proper form for precise testing of
this hypothesis; e. g., the time the respondent delayed flight is known
only in the most general terms.
3. There is some question as to the method of weighting
regrets or costs. In the future, a more precise way of accomplishing
this weighting _ priori may be possible (by inference from laboratory
experimentation). On the other hand, it may be feasible to have ex-
perimenters make such weightings before data collection in the field
study, to compare these weightings and establish a range within which
the hypothesis would be verified.
At this juncture, we wish only to point to the apparent fit to
the model, and the theory behind it. If the nature of the disaster and
of the alternative responses to it are widely known in advance of the
occurrence, it may be possible to predict group behaviors by develop-
ing this kind of matrix. Catastrophe in certain areas (of flood, tornado,
quake) and at certain times (during war, famine, or epidemic) are
often of this sort.
We would strongly suggest that future research be directed
first to a determination of the fit of this kind of model*. Second, the
problems of how to channel the perception of threat (to make the per-
c eption of it s c ons equenc e s unifo r m ove r individual s ~ should be ex -
amined. Third, an attempt should be made to determine a method
for fixing, in the minds of populations, the consequences of different
outcomes. If the threat is similarly perceived, and the relative pre-
ferences define c} for the populace, the behavior may be predictable
far enough in advance so that defensive and rehabilitative measures
appropriate to the situation can be taken. Of c our se, when the disaster
is inherently sudden and unexpected in onset, and when the community
is unaware of the nature of such a disaster in advance, we can elect
no conformity to this model.
*Other applications of game theoretic models to defense against disas-
ter have been attempted (14~. Matrices have previously been devel-
oped defining the relative utilities of certain community defenses
against disaster.
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Representative terms from entire chapter:
threat message
