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A collective model for the formation of public opinion: An application to nuclear public acceptance
Mathl. Comput. Modelling Vol. 19, No. 11, pp. 95-111,
1994 Copyright@1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 08957177194 $7.00 + 0.99
0895.7177(94)00077-8
A Collective Model for the Formation of Public Opinion: An Application to Nuclear Public Acceptance T. OHNISHI CRC Research Institute, Inc. Nakase l-3-D16, Chiba 261-01, Japan (Received June 1993; accepted July 1993)
Abstract-A collective model is proposed for the formation of public opinion and applied to the problem of public acceptance for nuclear energy in Japan. The selection of attitude for the people to a certain subject is assumed to be made depending on the sociopsychological pressure suffering from the surroundings, and on the quality and quantity of information on that subject released from the newsmedia. The reportorial stance of the newsmedia, on the other hand, is assumed to vary depending on, not only public opinion, but also the resultant of the mutual watch of the newsmedia to each other, concerning the state of information on the subject. Both an individual person and an individual medium are regarded as an interactive but structureless particle, and the interactions between the particles of the people and of media are described by introducing respective potentials of the type of molecular dynamics. Applying this model to the issue of electricity generation by nuclear energy, it was found to well reproduce the observed movement of public opinion in Japan. It also became clear that this sort of physical model is quite useful for understanding the status of socially collective phenomena in which nonlinearity and self-organization are strongly concerned.
1. INTRODUCTION Public opinion has been a subject of continuous interest in social sciences; many explanations have been proposed concerning not only the mechanism for the formation and growth of public opinion but also its interactive relation with and its influence on the various social organizations such as policy-making and administrative agencies [l-5]. According to recent theories of public opinion [6-lo], the newsmedia are pointed out to play an important role in swaying public opinion. It is also recognized that the reportorial stance of the newsmedia is varied depending on the movement of public opinion. In these models, the public and the newsmedia can be regarded as a synergetically evolving system where they interact and feed back their influences to each other. Prom a more microscopic viewpoint, where public opinion is a resultant reflex of the attitude of many individuals constituting the society [lO-121, the formation of public opinion can be interpreted as a collective process in which individuals interact with and affect each other, in both social and psychological senses, to result in the change of attitude under the influence of the newsmedia. Prom the same microscopic point of view, the newsmedia pay attention to each other regarding their information on various issues, feeding back it to the subsequent reports of their own. Also in the field of newsmedia, therefore, individual media are affected from many other media with which they are surrounded, psychologically interacting with each other. In the field of social sciences, a vast amount of descriptive discussions, together with some qualitative models, have been made for studying the relation and interaction between public opinion and the newsmedia [13]. To qualitatively investigate the formation, the growth and the
95
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extinction of public opinion, the author has recently constructed a cellular automaton model for public opinion [14]. In this model, seeds for public opinion concerning a certain subject, that is, opinion leaders, are first formed in the society, induced by information released by the newsmedia. Setting each cell in correspondence to an individual person, this model can simulate the state of diffusion and extinction of a certain sort of attitude arising in the society around from the opinion leaders. Example calculations for the secular variation of public opinion regarding the use of nuclear energy in Japan were found to well reproduce the observation. In that model, however, each cell is static in time, so that it can only affect and be affected by a limited number of cells surrounding itself throughout calculation. Moreover, the newsmedia were macroscopically treated and, therefore, the interaction among the newsmedia was not modelled. In this paper, more realistic and more dynamical modelling is made in simulating the interactions among the people, among the newsmedia, and between the people and the media by the introduction of a multiparticle model widely used in natural sciences [15-181, and it is investigated to what extent socially collective phenomena can be mimicked by this type of modelling. By the introduction of a qualitative model of this sort, public opinion whose behavior has been grasped only phenomenologically is intended to be treated as a forecastable quantity. In the next section, some facts obtained in social sciences on the socially collective phenomena, especially related to the formation of public opinion, are derived. In Section 3, the methodology of modelling is given, and in Section 4 an example for the application of this model to the movement of public opinion regarding the use of nuclear energy in Japan is described. Conclusions are given in the last section.
2. SOCIALLY
COLLECTIVE
PHENOMENA
In the following, representative knowledge on the socially collective phenomena accepted in the field of sociology and sociopsychology is given [8,10,13,19-241, which seems significant in modelling the formation of public opinion. (1) Each individual acts freely and independently according to both one’s own judgement and environmental conditions. Under a certain specific condition, however, the people interact with each other, their influence expanding in a wide range of space, to lead a directional and collective social movement which is called the socially collective phenomena. (2) In a social group, a certain force manifests which makes the thought, liking, and action of social members to be homogeneous. As a result of such a psychological force, the group becomes self-organizable. In so far as the various conditions are unchanged in a long time, however, each individual is re-attracted naturally to one’s own home style which is the most comfortable and the least risky for each. The extent of self-organization or group cohesiveness is, therefore, realized depending on the strengths of two types of force, the force acted on the individual to make him or her stay in the group, and the force to make him or her part from the group. (3) Prevalence is defined as a socially collective phenomenon which is born, dynamically changed, and extinguished in the society in a certain period of time for a large part of people in the society by freely selecting, adopting, and rejecting the style of things such as interests, likings, actions, and thoughts. According to this definition, the prevalence is, therefore, interpreted as an infectious process in a social scale. It can also be interpreted as a self-organization process occurring in the society; namely, a force acts on each member in the society that forces one to adapt to the society by adopting the prevalence as an appropriate standard of action. Prevalence, thus, has influence on the society through the sociopsychological pressure, which forces the people to follow the flow of prevalence once it grows and prevails in the society. (4) Opinion is formed of two components; the one is the latent opinion which is held rather continuously in time in the mind of the people, and the other is the actual opinion which
Formationof Public Opinion
97
appears intermittently in time, being activated by the social processes such as the contact with the newsmedia and with the surrounding people. The ups and downs of public opinion can be interpreted in terms of the prevalence process: the latent opinion already constructed in an individual’s mind preferentially adopts only the news which is most fittable to the psychological state of one’s mind at that time. This is the starting process of prevalence. The prevalence of opinion or attitude, thus, begins with information from the impersonal newsmedia, but the decision for each individual whether he or she accepts it or not is made under the influence of personal communication. Thus, the newsmedia activate a latent opinion to make it an actual one and, therefore, have a role to initiate the prevalence of opinion in the society. (5) Public opinion is stimulated by being informed of the movement of actual opinion via the newsmedia. Perceiving the psychological pressure from the society, the people have a trend to adopt the same opinion as their surroundings. Such a growing aspect of public opinion is further reported by the media. As a result of this cyclic process, an avalanche phenomenon appears in public opinion which rapidly changes from a randomly distributed state to a cohesive one. Thus, the newsmedia act as the promoter or the accelerator for prevalence besides as an initiator. The reportorial state of the newsmedia, however, becomes saturated, or in other words, the freshness of information becomes weakened when the amount of news reported up to that time reaches to a certain critical value. At that time, the media like to report some other subject quite different from the one prevailed hitherto to change the prevalent situation. The newsmedia, therefore, also act as a decelerator for prevalence. (6) Every newsmedium usually watches the state of information made by other media surrounding itself, and such mutual watch results in the definition of situation for each issue, according to which the reportorial stance and the amount of information subsequently released for the issue are determined. This process soon prevails all over the newsmedia as an avalanche to lead rapid fixation of the reportorial style of the issue for all media. Considering that the people are regarded as the consumers of mass communication, the state of the public, that is, public opinion at that time must be taken into account in forming the definition of situation. Mutual stimulation between the public and the newsmedia thus occurs in society, further promoting the avalanche for the formation of the sense of value for the issue common for both people and newsmedia.
3. MODELLING 3.1.
Prerequisites
for the Model
In what follows, public opinion is assumed to be determined through sociopsychological interactions arising only between the public and the newsmedia, and interactions participated with other elements than these two are considered unessential for the formation of public opinion. Two groups of multi-particle systems for the public and the newsmedia, both of which are constituted from interactive but structureless particles, are introduced, each particle representing an individual person in the society or a unit medium of the newsmedia. To mimic the actual situation, personality or characteristics are attributed to each particle by setting different values for constants and coefficients from each other, the gathering of these values being considered to obey a Gauss distribution. The particles are assumed to well communicate to each other so that the real space where they physically distribute is not modelled; they are assumed to cohere on one spatial position (this is the so-called one point approximation in physics) and the effect of time delay arising from the extent of space is not taken into consideration. Table 1 gives a correspondence between socially collective phenomena regarding the formation of public opinion and the respective interpretations in physics on the ground of the multi-particle model.
T. OHNISHI
98 Table
1. Correspondence
between social and physical images.
Social Images Individual
person or
individual
newsmedium
Physical Single particle
Society
Multi-particle
Individuality
Different
Sociopsychological
Distance pressure
Repulsive
system
values of constants
for particles Social distance
Images
from each other
between particles or attractive
force
or cohesive force Interactive
process between particles
For the ith particle of the public, a variable xi, representing the state of opinion or attitude and two-dimensional coordinates (yi, zi), denoting a sociopsychological position of the particle relative to other particles are introduced. In this case, public opinion is given by averaging the quantity zi over all particles. With regard to information released by the newsmedia, two types of components are considered; the one is the information from simply reporting issues which take place every day in the society (this is called the reportorial component, and its amount of information is denoted by QR hereafter), and the other is the prevalent component with the amount of information Qp, for which the tone and the amount of information strongly correlate to the movement of public opinion. Corresponding also to these components, variables XF and XF representing the state of reportorial attitude are, respectively, introduced for the jth particle of the newsmedia, together with the sociopsychological coordinates (Yj , Z,), corresponding only to the prevalent component. Although the value of XT is assumed to vary with time, the Xp is considered to be unchanged, reflecting that the fundamental stance for the information of the reportorial component is unchanged with time for every newsmedium. Averaging XJF and XF with weights QF and Qp, the quantity Xj just corresponding to zi for the public is defined as Xj = (Xj”Qj” + X; Q,‘)/(Q,” + 9;). Th e variable Xj represents the attitude or the reportorial stance of the jth medium and is used for quantifying the quality of information. The variable ranges of the quantities xi, XF, and XT are all limited within [-1, l], their signs being set positive when the attitude with regard to a considering issue is affirmative, whereas negative when it is contradictory. The attitude becomes stronger with increasing the absolute value of the variable. Sociopsychological positions (yi, zi) and (Yj, Zj), which are defined within the rectangular regions 0 5 yi, .zi 5 1 and 0 < Yi, Zj 5 1, are both varied with time depending on the psychologically repulsive and attractive forces arising from the interaction among the people and among the newsmedia, respectively. Distributions of particles on the (y, z) and (Y, Z) planes represent the state of social distance between constituents, and are useful to form a judgement by what extent the individual person or the individual medium is independent or similar to each other in the sense of sociopsychology. The opinion {zi} for the people is changed not only by the qualitative things such as the sociopsychological pressure or the reportorial stance of the newsmedia, but also by the quantitative amount of information provided by the media. Here the expression {xi} denotes the set of the quantity xi. Hence, the extent to which the individual attitude quantitatively fits the state of information of the newsmedia is one of the major factors for determining the change of zi. It is the reportorial component of information which plays a role to induce the prevalence of certain
Formation
of Public Opinion
99
opinion, that is, to induce the change of {xi} toward a certain direction, when the component well fits the attitude of the people at that time. The amount of prevalent component becomes large only after the prevalence of the opinion grows in the society and a definitive public opinion appears as a result of socially collective phenomenon. Since the media change their own attitude Xj perceiving the attitude change of the people, both attitudes of the people and the media axe closely connected with each other, giving feedback to each other, Figure 1 conceptually depicts the relation between the public and the newsmedia, where the arrows are directed to the direction of forces and actions. According to this, formulation is made in what follows.
____ ___ ____ ________________~ Extemt of L Event, Frequency of Event 1
--__________
Amount of lnrormetlon
--..----____----~
fteportorisl Component Prevalent Component 11
1
t
MuwalSlance dlha
Rbk. AwIude
Nmsmadda
I t
I
t
Figure 1. Conceptual diagram of the relation between the public and the newsmedia.
3.2.
Formulation
The time variation of opinion xi for the ith public-particle is given by 1 dx;
+
y.
d_ *
’
(7
-
]Xi
-Xij’
xi)
(1)
where ai, pi, and yi are constants, d is the average attitude of the newsmedia, and x8 the initial value of xi. The first term on the right hand side represents the change of public attitude which is drawn toward the direction of average stance of information of the media. The quantity gi gives the extent for the public attitude to be resonant with information released by the newsmedia, and is given by F(t; X) 6(X - xi) dX.
(2)
Here F(t; X) dX represents the amount of information released at a time t with reportorial attitude within the range [X - 9, X + %$I, and a(z) is the Kronecker’s delta. The second term on the right hand side of (1) is to mimic the recovery of the people to home style when the sociological pressure is not perceived from the environment; with increasing pi, the particle becomes more and more traditional and conservative in characteristic traits. The third term of (1) is to give the effect of the change of individual attitude toward the average opinion or the general trend of surrounding people. This term gives the extent of trend for the submission to sociopsychological pressure and for the adaptation with the surroundings when yi is positive, and for the resistance to environmental atmosphere when yi is negative. Such trends become strong with increasing the absolute value of ri. The quantity di is the sociopsychological pressure suffered from the surroundings, whereas the quantity ii is the average attitude of surrounding
100
T.
OHNISHI
people, which is perceived by the particle i. The latter two quantities are, respectively, given by
(4 where &e is the sociopsychological potential acting on the particles i and C, and rig is a vector for the social distance between i and e; rie = re - ri, re E (ye, .ze), and r-i E (yi, zi). In the actual society, individuals are subject to a psychological force regarding the adaptation of a certain prevalence to result in the approach or the separation with each other in a sense of sociopsychology. To simulate such a situation, every particle is assumed to fluctuate on the sociopsychological (y, z) plane, being subject to the sociopsychological forces from all particles by which it is surrounded. Assuming such sociopsychological fluctuation to be analogous to the physical Brownian motion, the time variation of the position of particle i, ri, can be described by the following equation of motion and a Langevin-type equation: gi=pi dt
dpi dt
=
and
mi’ -Ei
pz +
Xi
Cxepcpk e ze
drie
e
’
(6)
where rni is the mass of particle (this is set in what follows as mi = 1, for simplicity), pi is the quantity corresponding to momentum, and &i and
El
lrieIpnl
+ 12 Iriel-
m
,
where [i, Es, ni, and ns are constants, whose values are the measures for indicating to what extent and with what strength the psychological interaction prevails in the society. The first term on the right hand side of (6) is for the deceleration of motion, which is originated from the inelastic scattering between particles in the multi-particle model. The coefficient Ei represents the extent of psychological resistance against the change of sociopsychological situation. The resistance becomes strong with increasing Ei. Both the second and the third terms, on the other hand, are to give fluctuation. The second one gives the force for the particle i to approach the particle with the same opinion as itself but to part from the particle with a different opinion. This force is assumed to be given by the product of the strength of sociopsychological force-field perceived by the particle i from its environment, C xe d&/drie, and the extent of attitude of the particle, xi. When the force is given by this form, the quantitative variable xi can be interpreted as a scalar with the same characteristics as the mass or the charge, which is intrinsic for each particle. With this second term, the sociopsychologically cohesive and dispersive phenomenon can be simulated. The third term, on the other hand, is to show the manifestation of individuality without adapting him or her to the surroundings, for instance, with the intention that the value of oneself be higher than any others surrounding him or her. The strength of this mentality is not dependent on the attitudinal state of the particle but on the strength of the sociopsychological force-field. The greater the value is for the coefficient
(Xj’” - Xj’) +r.D.
IXjpoI
’ ’
(Tj -X,p) IXj - Xpjl'
(8)
Formation of Public Opinion
101
where Aj, Bj, and I’j are constants, 3 is the average attitude of the public, namely public opinion, and X3?” the initial value of XT. The first term on the right hand side of (8) is to give the effect for the newsmedium to change its reportorial stance according to the varying state of public opinion. The change of the stance is assumed to follow the change of public minds without any time delay. The second term has the same meaning as of the second one of the public attitude of (1). The third term, on the other hand, is to give the effect for the medium to change voluntarily its reportorial stance, being based on the definition of situation of the issue which is shaped up among the newsmedia. Its time variation is proportional to the strength of psychological force-field Dj. The quantities Dj and Xj are given by similar formulae as equations (3) and (4):
where @je is the inter-particle potential for the media particles and Rje is the vector representing the social distance between particles. The former is defined as @je = Zi IRjeleN1 + Zz IRjel-N2 ,
(11)
where El, Ez, Ni, and Ns are constants. Also for the time variation of the sociopsychological position Rj, the similar expressions as for the public case are introduced: dRj _ Pj --Mj’ dt dPj _ -Ej dt-
and
(12)
Pj + Xj Dj - Hj C 2, e
(13)
where Ej and Hj are constants, and Mj is set unity hereafter. The distribution of the amount of information released by the newsmedia, F(t; X), is related to the public attitude via the quantity gi given by (2). When the amount of reports released by the individual medium at a given time t, Qj (t), 1s ’ g’iven, the quantity F(t; X) is obtained by
F(t; X) dX = C’
Qj(t),
where the summation C’ is to be performed only for the Qj(t) whose reportorial stance is fallen within the range [X - y, X + y]. The quantity &j(t) is given by definition as &j(t) = e amount of prevalent component Qy seems to increase with increasing the Th Q?(t) + Q:(t). absolute value of g,
and hence is assumed here to be proportional to some power of 1% I:
(15) where Cj and 4 (> 0) are constants. The rough estimation of the exponent q can be made with the following arguments. (1) The public and the newsmedia are considered to form a global system feeding back information to each other. In this case, the more significant the issue is for the society, the more it is repeatedly reported in this social system. As a consequence, the total amount of
102
T. OHNISHI
information released by the media during a certain period of power of the amount of input to the system, that is, the initial ponent for the issue [25]. Since the output from the system is component, when the issue is important and a large-scale one,
&j(t) = Q;(t) m (Q,“(t))’
time grows with the second amount of reportorial comdominated by the prevalent the following relation holds:
(16)
e
The general rightness of the above relation between Qr and QT was also pointed out, regardless of the scale of issues [25]. (2) Generally speaking, the time derivative of the public opinion 1g 1 seems to be approximately proportional to the amount of information given at that time, as does the case of the diffusion of innovations [26]. When the prevalence weakly takes place, it holds that QJt)
21
Q:(t)
cc
I2 I.
(17)
From these considerations, the value q = 2 is adopted in the following, which seems to be appropriate at least in the case of weak prevalence of public opinion. 3.3.
Constants
and Parameters
Distributions for the initial momenta and initial attitudes of particles and the sets of various constants related to particles are all assumed to obey a Gauss distribution or an overlapped Gauss distribution in m-fold, such that Q(x) =
_(x - Piv c _A&m &5G$exp { 2(a&)2
> ’
m I 3,
where C, aFf, = 1, and the superfix x denotes the constants relating to the quantity x. Those initial quantities and constants are all randomly determined using the distribution (18). For the particles both of the public and the newsmedia, their initial positions on the sociopsychological y.~- and YZ-planes are also set randomly. Completely reflective conditions are imposed on the boundaries so that the subsequent movement of particles is limited on those respective planes within a unit length in each direction. In order to avoid the piling of particles on one point after interactive movement on the plane, the distance of the closest approach for an arbitrary pair of particles or the diameter of a hard core particle r-0 is introduced, along with its related parameter X such as -l/2 rosT=P x
(19)
A’
where F is the mean distance between particles, and p is the mean surface density of particles. A potential of the form of (7) gives the inter-particle distance rm, where the maximum force is realized between two particles as l/h-%) Tm=
--
=
kTo
=
;P-‘/~.
(20)
Here k is a constant, its value being estimated from its definition to be in the range 1 N 10. On the other hand, the strength of field for the psychological force, which appears on the right hand side of (6), is given by
Formation
of Public Opinion
103
where b is a constant, whose value is estimated to be of the order 0.1 N 10 when 0((i) using relations (19) N (21), the coefficients
[ 12 =
Also for the potential
p(‘++“‘)X%
p(‘+++,na
of newsmedia
(
b
>I’
1 _ $/&a-nr)
(
b
1 _ !.$k(m-n2)
particles,
= 1. By by X, k,
and
>I
(23)
.
the coefficients
(22)
81 and S2 can be replaced
by
constants A, K, and B, which are similarly defined as X, k, and b above. All of the constants and parameters discussed above must be determined so that the secular variation of public opinion obtained by the model just corresponds to its behavior observed in the past. Figure 2 shows the flow diagram for the numerical calculation. In this model, the amount of information for the reportorial component released at a time t, Q?(t), is required as an input quantity. This is the only one exogenous variable, which acts as a driving force for activating the public-media system. Outputs are the distributions of public opinion and of the reportorial stance of the newsmedia at the time t, together with the information on the value of the prevalent component, and the cohesive state of two types of particles on each sociopsychological plane. In what follows, the integration of differential equations is performed with a time step At = & yea.rs.
mlountdhfommbnd
wcanpocrml
-no ml dPubkatnudomd
(or)
t
vmlaa ( 2,) -
(x,1 IYA and 1
tom. pauc I
Amomldhfamaond
mt-pwnt
v-
t
ix,), (Y, 1 and
(Z,) co~btho
(STOP) Figure 2. Flow diagram for the numerical calculation. At the two SRS on the left hand side, the subroutine shown on the right hand side is called.
4.
A CASE STUDY: PUBLIC OPINION REGARDING NUCLEAR ENERGY IN JAPAN
4.1. Determination
of Constants and Parameters
Information on the quantity Q:(t) together with the actual data on the movement of public opinion as reference data for fixing the values of constants are first discussed. Since 1970 or so, the prevalent component of the news concerning nuclear energy in Japan, that is, the information in which the public were highly interested, and on which the media
104
T. OHNISHI
continued to report during a certain period of time, has been almost limited to the negative phase of nuclear issues, such as impediments and accidents at nuclear power stations, the risk and danger of electricity generation by nuclear power, the failure of the research and development of nuclear energy, and the anti-nuclear movement in the public. It seems quite difficult, however, to clearly discriminate on what portion of the negative reports corresponds to the prevalent component and what portion to the reportorial component. In this paper, the articles reported by the newspapers distributed on a nation-wide scale in Japan are all treated as the reportorial component, daringly assuming that the fraction of prevalent component in the newspapers is sufficiently low as compared to the fraction reported by other media such as television, radio, magazines, and books,
QjR(t) = wj I(t),
(24)
where wj is a constant parameter; I(t) is the sum of the area of negative articles regarding nuclear energy, including headlines and photos on three newspapers, The Asahi, The Mainichi, and The Yomiuri during one month, counted in units of column x cm in the small-scale editions of these newspapers. Since about two decades ago, many surveys on the public opinion regarding nuclear energy have widely been done in Japan by various agencies. Of these opinion polls, the results of the one which has three selection branches concerning the use of nuclear energy in electricity generation, such as: (1) approve it (this fraction in the poll being denoted as fP), (2) oppose it (fa), and (3) undecided, are adopted here. With these fractions, the public opinion in our meaning at a given time t, O(t), is given by 0(t)
=
01 f,
+ 02 fa
=
01(t)
J-p(t) + 02(t)
fact),
(25)
where 01 and 02 are both the values within the range [-1, 11,which are the averages of variable {xi} corresponding, respectively, to the pro- and anti-nuclear sympathizers. Average attitudes both of the pro and anti-nuclear sympathizers have not probably been constant from the early days of the nuclear era, but must have been varied gradually with time in accordance with the gradual change of life style or the sense of value, and also with the gradual alteration of generation [27,28]. Those coefficients 01 and 02 are, therefore, functions of time, and the following formulae are assumed as the simplest expression for their time dependency: O,(t)
= 7),(t - 1973.0) + V,,
m = P, a,
(26)
where t is in years. Constants qrn and u, are to be determined so that the public opinion given by (25) fits well the model opinion, f E xi xi/n. The final values of various constants along with these rlrn and yrn must be searched iteratively, so that the above fitting is realized most satisfactorily. In the following calculations, 500 particles each are considered for both the public and the newsmedia, statistical accuracy being of the order (5OO)-1/2 2~ 5%. An extremely affirmative attitude to nuclear energy is assumed to correspond to zi = 1 and Xj = 1, whereas an extremely negative one is zi = -1 and Xj = -1. The attitudinal variables zi and Xj are distributed within these two strongest extremes so that xi = 0 and Xj = 0 both correspond to a neutral attitude to nuclear energy. The following are standard values for representative constants: pLa= 1.5 x 10m4 and ga = 0.5p&, for the statistical constants of the coefficient ai in equation (1); CL* = 1.0 and g* = 0.5/_~*, for the Aj in equation (8); nr = Ni = 1, 712 = N2 = 2, X = A = (20)‘i2, k = K = 3, b = B = 5, for the constants of the interactive potentials; and pc = 500, uc = 0.5pc, 0.3817, c? = 0.5@‘, for the amount of information released by the newsmedia. and/P= Of those constants, the first cited, @, is a measure to show the extent of influence of the newsmedia to the public, that is, a sort of coupling constant between the public and the newsmedia. Therefore, pa is to be noted as a significant parameter to see what difference may appear in the
Formation of Public Opinion
105
public opinion in cases when the extent of infiltration of the newsmedia into the society differs. The last one, /.P, on the other hand, is the quantity to give relative significance of the reportorial component to the resultant prevalent component; it is another important parameter to see what difference may occur in the public opinion in societies where the amount of reportorial component regarding a certain issue differs from each other, being due to, for instance, a difference of the form of political organization. In what follows, the cases are also investigated when the values of pa and pw are varied around the standard values. 4.2.
Numerical
Figure resultant
Results
and
3 shows the monthly prevalent component,
Discussions variation of the amount of input reportorial component averaged over all newsmedia. The amount of reportorial
and the compo-
nent has peaks with about an order of magnitude higher then the background only when large scale nuclear accidents (shown by keywords) happen. Although the amount of prevalent component grows almost as large as the reportorial one in t 2 1980, it cannot exceed the latter under the standard values of the constants. In t 2 1980, the prevalent component grows also in the case of accidents but only up to an order of magnitude lower than the reportorial one; it becomes negligible as compared with the latter calm period. Although with a fixed value of CL” to 1.5 x 10P4 and with a variable pLwin the region ~1w 5 4.0, the relative intensity of the prevalent component to the reportorial one never exceeds unity, even at the time of accidents, its value during a calm period gradually grows with ~1”. This indicates that the prevalence regarding antinuclear thought becomes easier to occur not only during the accident, but also in a calm period in the case when the @’ is increased, that is, when the amount of reportorial component released every day becomes large. Such situation seems in no contradiction with the real society [29].
Figure 3. The behavior of the amount of information averaged over all newsmedia for the input (thick line) and the output (thin and dashed lines), corresponding, respectively, to the reportorial and prevalent components of information. The output for the case of pcl = 6.0 x low4 is drawn only in the region of t 2 1984 for the sake of clarity. The keyword attached to the leftmost peak of the input data, Mutsu, indicates the accident of the nuclear powered ship Mutsu, whereas the other keywords correspond to accidents at the respective nuclear power stations for electricity generation.
Figure 4 shows the time variation of the first terms on the right hand side of both equations (1) and (8) averaged over all particles, i xi aigi ]zi] (It - zi)/]X - zi( and & Cj Aj IXjl $$/Iz), which represent, respectively, the extent of influence of the reportorial stance of the media on the public attitude, and that of the public attitude on the stance of the media. Although in a calm period the newsmedia have only negligible influence on the public attitude, it impulsively
106
T. OHNISHI
and strongly affects the public opinion during an accident so that the public attitude to nuclear energy comes to be aggregated toward a negative direction. Although the attitude change of the public influences the reportorial stance of the media by about one-tenth the influential degree in the reverse direction, its effect clearly appears in the case of nuclear accident; the public affects the media during the first half period of attitude change, such that they draw the stance of the media in the same direction as the public’s one, but conversely to this, the media move in the reverse direction to the public opinion and recover their own original positions in the second half period. The value of one-tenth of this relative intensity is not so sensitive to the values of @ and pA.
-:
fromNawamedia to Public
----
I
: tram Public to Newsmedia
/f=l.5xlo-~
r'=0.3017
Figure 4. Time behavior of the strength of coupling terms between the public and the newsmedia.
Figure 5 shows the time variation of public opinion together with the results of public opinion polls. The coefficients appearing in (26) with which the calculated opinion curve best fits the actual values are rlP = -1.9 x 10w3, vP = 0.7, 71, = 7.6 x 10e3, and V, = -1.5. These values and signs indicate that, for decreasing time, the averages of the public attitudes to both pro- and anti-nuclear energy, especially the latter one, become weaker and approach a neutral position. This means that in the 197Os, a major fraction of anti-nuclear sympathizers were the people who strongly opposed nuclear energy, but that gradually changed with time to be the people who only weakly arrest to nuclear energy, showing a gradual change of the sense of value. In general, public opinion is calculated to get worse with every large-scale nuclear accident. After an accident it recovers but never to the former value, so that the global trend for the opinion gradually become negative with time. Such a trend of the public opinion was also found in the previous cellular automaton model [14]. It seems common also for countries other than Japan [30,31]. In the case when large scale accidents do not take place during a long time, and when the amount of negative information released by the newsmedia continues decreasing, however, the public attitude to nuclear energy is naturally ameliorated. When the calculation is extended to the future with the input amount of information after March 1992, I set equal to the same value as that in February 1992, 10, a society with 0.084 for the value of public opinion O(t) is realized at t = January 2000. When the conditions I = 0.1 IO and I = 3.0 IO are adopted, on the other hand, public opinion becomes 0.114 and 0.039, respectively, in January 2000. Figure 6 shows the distribution of attitude for the public particles. The public is assumed, at the beginning, to be an aggregate composed of: few people strongly arresting to nuclear energy (this being called the component a), many people weakly arresting to or weakly supporting it
Formation _____ 0.4
:a”=o.3817
. . . . . .. . . . . . .. : jp=,
of Public Opinion o : Actual
107
Value
FJx 10-3
Public Attitude -0.2 Figure 5. Time behavior of the calculated public opinion to nuclear energy.
attitude
of the public and actually surveyed
(component n), and a moderate number of people positively supporting it (component p). Whenever a large accident occurs (as for the case at 1974.50), a peak corresponding to the component p disappears and it seems to be changed to another component n, shifting toward x < 0. Since a major part of people originally belonging to n also moves toward a negative direction, the fraction of people with negative attitude rapidly becomes increased. The component p can barely recover its fraction within a finite time after the accident, as is seen in the distributions at 1988.50 and 1992.0. At these times, a peak corresponding to p is re-formed at its original position and the attitudinal distribution is recovered to a form with three local maxima. Roughly speaking, the public attitude oscillates between two distributional patterns corresponding to the accident and calm times.
Figure times.
6.
Distributions
of attitude
{zi}
for 500 public
particles
at four different
108
T. OHNISHI
Figure 7 shows the spatial distribution of model particles on the sociopsychological plane. The size of each symbol was set to be proportional to the strength of attitude, ]zi] or ]Xj(. In the case of the public, although the particles have a tendency to cohere around the particle with the same sign and with stronger attitude, the particles of passive attitude with smaller ]zi] distribute almost uniformly on the plane to form a background. This situation seems to mimic the actual society, at least qualitatively, in that parts of the public with strong wills of pro- and anti-nuclear energy approaches each other to form groups for enhancing or discarding nuclear facilities more actively, and in that many people with no definitive opinions exist independently of each other and distantly from those active groups, in the sense of sociopsychology. Such a cohesive phenomenon appearing in the society is a manifestation of self-organization in a nonlinear system [32]. Similar cohesive patterns like these can be realized also in the previous model of public acceptance
[14]. The media particle,
contrarily
to this, does not show any trend of
cohesion, indicating the psychological isolation of the media from each other.
(a) 1979.0 P. 3 ,
..I
.. .
(b) 1983.0
* .,
.*
. ..;.
(c) 1987.0 (d) 1991.0 Figure 7. Distribution on sociopsychological planes of the articles for the public (a)-(e) and for the newsmedia (f). The case (e) is an extended calculation by setting input data after March 1992 to be of the same value as that in February 1992. Asterisks and polygons are the particles with negative and nonnegative values of attitude, respectively.
Formation
of Public Opinion
199
(f) 1991.0 (e) 1995.0 Figure 7. (continued). Distribution on sociopsychological planes of the articles for the public (a)-(e) and for the newsmedia (f). The case (e) is an extended calculation by setting input data after March 1992 to be of the same value as that in February 1992. Asterisks and polygons are the particles with negative and nonnegative values of attitude, respectively.
C(“=1.5X10~
P’10.3317
Figure 8. Time behavior of the cohesive factor s.
As a measure of cohesiveness of particles on the sociopsychological plane, the cohesive factor s, a weighted average of reciprocal distance between particles, is defined as (27) The larger the value of s, the higher becomes the degree of cohesion around particles with large absolute values of attitude. Figure 8 shows the time behavior of cohesion factor both for the public and media particles. In t 2 1975, the media particle does not show any tendency for cohesion, Although also for the public particle, cohesion does not take place in t 5 1979, an abrupt change of attitude occurs on breaking out the accident at Three Mile Island (TMI), and the fraction of people with an anti-nuclear mind rapidly increases within 1 N 2 months after that. Although after the next one or two months, a major fraction of backsliding people recover their attitudes, the people with stronger attitudes increase the degree of cohesion to sustain its cohesive state long after that. At the time of the Chernobyl accident, many more people rapidly change their attitudes to a side against nuclear energy so that the maximum of s exceeds 100. After the recovery of public attitude, the rate of increase of the cohesive factor gradually grows
110
T. OHNISH~
with time, oscillating synchronously with the amount of information released by the newsmedia. The degree of psychological cohesion of the public becomes especially high in t 2 1989, when the standard values of constants are used, but it differs from model to model depending on the adopted values of those constants. For example, in the case of pa = 6 x 10s4 and @ = 0.03817, a psychologically cohesive state appears at the time of the TM1 accident, but the Chernobyl accident does not play any significant role for cohesion. In any case, it is clear that major nuclear accidents can become a trigger for the psychological cohesion of the public. 5. A collective model can regarded as an interactive collective phenomena are tem of multi-particles. In
CONCLUSIONS
be constructed to mimic the real society, with an individual person particle and with the society as a gathering of such particles. Socially considered here to be a resultant of the interaction among the systhis paper, public opinion was considered to be a product of socially
collective phenomena, and its formation is assumed to be realized under the influence not only of the sociopsychological force arising from the people themselves, but also of the psychological interaction between the public and the newsmedia. The input quantity is the amount of information of the reportorial component released by the newsmedia, and the output is the quantities corresponding to the attitude of individual particles and the spatial distribution of particles on the sociopsychological plane. By selecting appropriately the values of constants and parameters, this model w&s found to rightly reproduce the movement of public opinion concerning nuclear energy in Japan. In such a collective model, the extent of the influence of a variable on a certain quantity is difficult to precisely estimate because of the strong nonlinearity of the interaction between particles. It is, however, such nonlinearity that acts as a source for driving the complex movement of public opinion and for inducing the psychologically cohesive state of the public. Success or failure of the sociological model can almost be said to depend on its ability to reproduce properly the self-organization appearing in the society, which originates from the nonlinearity of the social system itself. From this viewpoint, this sort of collective model seems to be quite a successful one and useful for understanding quantitatively, or at least qualitatively, the states of sociopsychological forces prevailing in the society. It should also be useful for forecasting the future state of public opinion, or more generally speaking, of the socially collective phenomena under specified external conditions.
REFERENCES 1. D. Katz and F. Stotland, A preliminary statement of a theory of attitude structure and change, In Psychology: Study of a Science, Vol. 3, (Edited by S. Koch), pp. 423-475, McGraw-Hill, New York, (1959). 2. R.E. Lane and D.O. Sears, Public Opinion, Prentice-Hall, New York, (1964). 3. V.C. Troldahl and R. Van Dam, Face-to-face communication about major topics in the news, Pub. Opinion Quarterly 29, 626-634 (1965). 4. E. Noelle-Neumann, The Spiral of Silence: Public Opinion: Our Social Skin, University of Chicago Press, Chicago, (1984). 5. C.J. Glynn and J.M. McLeod, Implications of the Spiral of Silence: Theory for Communication and Public Communication Yearbook 1984, pp. 43-65, Southern Illinois University Press, Carbondale, IL, (1985). 6. M.M. McCombs and D.L. Shaw, The agendssetting function of msss media, Publ. Opinion Quarterly 36, 176-187 (1972). 7. L. Erbring, E.N. Goldenberg and A.H. Miller, Front-page news and realworld cues: A new look at agendesetting by the media, Am. J. Political Sci. 24, 16-49 (1980). 8. D.F. Roberts and C.M. Bschen, Mass communication effects, Ann. Rev. Psychology 32, 307-356 (1981). 9. D.F. Roberts and N. Maccoby, Effect of mass communication, The handbook of Social Psychology, Vol. 2, 3rd Edition, (Edited by G. Lindzey and E. Aronson), pp. 539-598, Random House, New York, (1985). 10. D. Zillmann and J. Bryant, Editors, Selective Exposure to Communication, L. Erlbaum Assocs., Hillsdale, NJ, (1985). 11. D. McQuail and S. Windahl, Communiuation Models: For the Study of Mass Communication, Longmann, White Plains, NY, (1981).
Formation of Public Opinion 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
30. 31. 32.
111
J. Bryant and D. Zilhnann, Editors, Perspectives on Media Effects, L. Erlbaum Assocs., Hillsdale, NJ, (1986). M.L. De Fleur and S. Ball-Rokeach, Theories of Mass Communication, 5th Edition, Longmann, White Plains, NY, (1989). T. Oh&hi, A cellular automaton model for the change of public attitude regarding nuclear energy, Prog. Nucl. Energy 26, 163-205 (1991). D. Fincham and D.M. Heyes, Recent advances in molecular dynamics computer simulation, Adu. Chem. Phys. 63, 493-575 (1985). M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids, Oxford Univ. Press, London, (1987). D. Greenspan, Particle simulation of biological sorting on a supercomputer, Computers Math. Applic. 18 (9),823-834 (1989). D. Greenspan, Supercomputer simulation of colliding microdrops of water, Computers Math. Applic. 19 (7), 91-97 (1990). H.G. Blumer, Fashion, In International Encyclopedia of the Social Science, Vol. 5, (Edited by D.L. Shills), Macmillan & Free Press, New York, 341-345, (1968). D. Cartwright and A. Zander (Editors), Group Dynamics: Research and Theory, 3rd Edition, Harper & Row, Scranton, PA, (1968). D. McQuail, Mass Communication Theory: An Introduction, Sage, Newbury Park, CA, (1983). L. Berkowitz, Some effects of thoughts on anti- and pro-social influences of media events: A cognitive neoassociative analysis, Psycho. Bull. 95, 410-427 (1984). J.H. Davis, Group Perfownance, Addison-Wesley, Reading, MA, (1969). N.J. Smelser, Theory of Collective Behavior, Free Press, New York, (1963). T. Ohnishi, Selective amplification of the amount of nuclear information released by the newsmedia, Ann. Nucl. Energy 20, 525-532 (1993). E.M. Rogers, Difision of Innovations, 3 rd Edition, Free Press, Glencoe, IL, (1983). D. Kazama and T. Akiyama, Japanese value orientations: Perspective and change (II), Stud. Broadcast. 16, 5-26 (1980). FL Inglehart, Changing values in Japan and the west, Comparat. Polit. Stud. 14, 445-479 (1982). A. Mazur, Media influences on public attitudes toward nuclear power, In Public Reaction to Nuclear Power: Are There Critical Masses?, (Edited by W.R. Freudenburg and E.A. Rosa), pp. 97-114, Westview Press, Boulder, CO, (1984). W.R. Freudenburg and R.K. Baxter, Host community attitude toward nuclear power plants: A reassessment, Sot. Sci. Quarterly 65, 11291136 (1984). C. Hohenemser and 0. Renn, Chernobyl’s other legacy, Environment 39, 4-11 and 40-45 (1988). G. Nicolis and I. Prigogine, Self-Organization in Non-Equilibrium System, Wiley Interscience Publ., New York, (1977).
1994 Copyright@1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 08957177194 $7.00 + 0.99
0895.7177(94)00077-8
A Collective Model for the Formation of Public Opinion: An Application to Nuclear Public Acceptance T. OHNISHI CRC Research Institute, Inc. Nakase l-3-D16, Chiba 261-01, Japan (Received June 1993; accepted July 1993)
Abstract-A collective model is proposed for the formation of public opinion and applied to the problem of public acceptance for nuclear energy in Japan. The selection of attitude for the people to a certain subject is assumed to be made depending on the sociopsychological pressure suffering from the surroundings, and on the quality and quantity of information on that subject released from the newsmedia. The reportorial stance of the newsmedia, on the other hand, is assumed to vary depending on, not only public opinion, but also the resultant of the mutual watch of the newsmedia to each other, concerning the state of information on the subject. Both an individual person and an individual medium are regarded as an interactive but structureless particle, and the interactions between the particles of the people and of media are described by introducing respective potentials of the type of molecular dynamics. Applying this model to the issue of electricity generation by nuclear energy, it was found to well reproduce the observed movement of public opinion in Japan. It also became clear that this sort of physical model is quite useful for understanding the status of socially collective phenomena in which nonlinearity and self-organization are strongly concerned.
1. INTRODUCTION Public opinion has been a subject of continuous interest in social sciences; many explanations have been proposed concerning not only the mechanism for the formation and growth of public opinion but also its interactive relation with and its influence on the various social organizations such as policy-making and administrative agencies [l-5]. According to recent theories of public opinion [6-lo], the newsmedia are pointed out to play an important role in swaying public opinion. It is also recognized that the reportorial stance of the newsmedia is varied depending on the movement of public opinion. In these models, the public and the newsmedia can be regarded as a synergetically evolving system where they interact and feed back their influences to each other. Prom a more microscopic viewpoint, where public opinion is a resultant reflex of the attitude of many individuals constituting the society [lO-121, the formation of public opinion can be interpreted as a collective process in which individuals interact with and affect each other, in both social and psychological senses, to result in the change of attitude under the influence of the newsmedia. Prom the same microscopic point of view, the newsmedia pay attention to each other regarding their information on various issues, feeding back it to the subsequent reports of their own. Also in the field of newsmedia, therefore, individual media are affected from many other media with which they are surrounded, psychologically interacting with each other. In the field of social sciences, a vast amount of descriptive discussions, together with some qualitative models, have been made for studying the relation and interaction between public opinion and the newsmedia [13]. To qualitatively investigate the formation, the growth and the
95
T.
96
OHNISHI
extinction of public opinion, the author has recently constructed a cellular automaton model for public opinion [14]. In this model, seeds for public opinion concerning a certain subject, that is, opinion leaders, are first formed in the society, induced by information released by the newsmedia. Setting each cell in correspondence to an individual person, this model can simulate the state of diffusion and extinction of a certain sort of attitude arising in the society around from the opinion leaders. Example calculations for the secular variation of public opinion regarding the use of nuclear energy in Japan were found to well reproduce the observation. In that model, however, each cell is static in time, so that it can only affect and be affected by a limited number of cells surrounding itself throughout calculation. Moreover, the newsmedia were macroscopically treated and, therefore, the interaction among the newsmedia was not modelled. In this paper, more realistic and more dynamical modelling is made in simulating the interactions among the people, among the newsmedia, and between the people and the media by the introduction of a multiparticle model widely used in natural sciences [15-181, and it is investigated to what extent socially collective phenomena can be mimicked by this type of modelling. By the introduction of a qualitative model of this sort, public opinion whose behavior has been grasped only phenomenologically is intended to be treated as a forecastable quantity. In the next section, some facts obtained in social sciences on the socially collective phenomena, especially related to the formation of public opinion, are derived. In Section 3, the methodology of modelling is given, and in Section 4 an example for the application of this model to the movement of public opinion regarding the use of nuclear energy in Japan is described. Conclusions are given in the last section.
2. SOCIALLY
COLLECTIVE
PHENOMENA
In the following, representative knowledge on the socially collective phenomena accepted in the field of sociology and sociopsychology is given [8,10,13,19-241, which seems significant in modelling the formation of public opinion. (1) Each individual acts freely and independently according to both one’s own judgement and environmental conditions. Under a certain specific condition, however, the people interact with each other, their influence expanding in a wide range of space, to lead a directional and collective social movement which is called the socially collective phenomena. (2) In a social group, a certain force manifests which makes the thought, liking, and action of social members to be homogeneous. As a result of such a psychological force, the group becomes self-organizable. In so far as the various conditions are unchanged in a long time, however, each individual is re-attracted naturally to one’s own home style which is the most comfortable and the least risky for each. The extent of self-organization or group cohesiveness is, therefore, realized depending on the strengths of two types of force, the force acted on the individual to make him or her stay in the group, and the force to make him or her part from the group. (3) Prevalence is defined as a socially collective phenomenon which is born, dynamically changed, and extinguished in the society in a certain period of time for a large part of people in the society by freely selecting, adopting, and rejecting the style of things such as interests, likings, actions, and thoughts. According to this definition, the prevalence is, therefore, interpreted as an infectious process in a social scale. It can also be interpreted as a self-organization process occurring in the society; namely, a force acts on each member in the society that forces one to adapt to the society by adopting the prevalence as an appropriate standard of action. Prevalence, thus, has influence on the society through the sociopsychological pressure, which forces the people to follow the flow of prevalence once it grows and prevails in the society. (4) Opinion is formed of two components; the one is the latent opinion which is held rather continuously in time in the mind of the people, and the other is the actual opinion which
Formationof Public Opinion
97
appears intermittently in time, being activated by the social processes such as the contact with the newsmedia and with the surrounding people. The ups and downs of public opinion can be interpreted in terms of the prevalence process: the latent opinion already constructed in an individual’s mind preferentially adopts only the news which is most fittable to the psychological state of one’s mind at that time. This is the starting process of prevalence. The prevalence of opinion or attitude, thus, begins with information from the impersonal newsmedia, but the decision for each individual whether he or she accepts it or not is made under the influence of personal communication. Thus, the newsmedia activate a latent opinion to make it an actual one and, therefore, have a role to initiate the prevalence of opinion in the society. (5) Public opinion is stimulated by being informed of the movement of actual opinion via the newsmedia. Perceiving the psychological pressure from the society, the people have a trend to adopt the same opinion as their surroundings. Such a growing aspect of public opinion is further reported by the media. As a result of this cyclic process, an avalanche phenomenon appears in public opinion which rapidly changes from a randomly distributed state to a cohesive one. Thus, the newsmedia act as the promoter or the accelerator for prevalence besides as an initiator. The reportorial state of the newsmedia, however, becomes saturated, or in other words, the freshness of information becomes weakened when the amount of news reported up to that time reaches to a certain critical value. At that time, the media like to report some other subject quite different from the one prevailed hitherto to change the prevalent situation. The newsmedia, therefore, also act as a decelerator for prevalence. (6) Every newsmedium usually watches the state of information made by other media surrounding itself, and such mutual watch results in the definition of situation for each issue, according to which the reportorial stance and the amount of information subsequently released for the issue are determined. This process soon prevails all over the newsmedia as an avalanche to lead rapid fixation of the reportorial style of the issue for all media. Considering that the people are regarded as the consumers of mass communication, the state of the public, that is, public opinion at that time must be taken into account in forming the definition of situation. Mutual stimulation between the public and the newsmedia thus occurs in society, further promoting the avalanche for the formation of the sense of value for the issue common for both people and newsmedia.
3. MODELLING 3.1.
Prerequisites
for the Model
In what follows, public opinion is assumed to be determined through sociopsychological interactions arising only between the public and the newsmedia, and interactions participated with other elements than these two are considered unessential for the formation of public opinion. Two groups of multi-particle systems for the public and the newsmedia, both of which are constituted from interactive but structureless particles, are introduced, each particle representing an individual person in the society or a unit medium of the newsmedia. To mimic the actual situation, personality or characteristics are attributed to each particle by setting different values for constants and coefficients from each other, the gathering of these values being considered to obey a Gauss distribution. The particles are assumed to well communicate to each other so that the real space where they physically distribute is not modelled; they are assumed to cohere on one spatial position (this is the so-called one point approximation in physics) and the effect of time delay arising from the extent of space is not taken into consideration. Table 1 gives a correspondence between socially collective phenomena regarding the formation of public opinion and the respective interpretations in physics on the ground of the multi-particle model.
T. OHNISHI
98 Table
1. Correspondence
between social and physical images.
Social Images Individual
person or
individual
newsmedium
Physical Single particle
Society
Multi-particle
Individuality
Different
Sociopsychological
Distance pressure
Repulsive
system
values of constants
for particles Social distance
Images
from each other
between particles or attractive
force
or cohesive force Interactive
process between particles
For the ith particle of the public, a variable xi, representing the state of opinion or attitude and two-dimensional coordinates (yi, zi), denoting a sociopsychological position of the particle relative to other particles are introduced. In this case, public opinion is given by averaging the quantity zi over all particles. With regard to information released by the newsmedia, two types of components are considered; the one is the information from simply reporting issues which take place every day in the society (this is called the reportorial component, and its amount of information is denoted by QR hereafter), and the other is the prevalent component with the amount of information Qp, for which the tone and the amount of information strongly correlate to the movement of public opinion. Corresponding also to these components, variables XF and XF representing the state of reportorial attitude are, respectively, introduced for the jth particle of the newsmedia, together with the sociopsychological coordinates (Yj , Z,), corresponding only to the prevalent component. Although the value of XT is assumed to vary with time, the Xp is considered to be unchanged, reflecting that the fundamental stance for the information of the reportorial component is unchanged with time for every newsmedium. Averaging XJF and XF with weights QF and Qp, the quantity Xj just corresponding to zi for the public is defined as Xj = (Xj”Qj” + X; Q,‘)/(Q,” + 9;). Th e variable Xj represents the attitude or the reportorial stance of the jth medium and is used for quantifying the quality of information. The variable ranges of the quantities xi, XF, and XT are all limited within [-1, l], their signs being set positive when the attitude with regard to a considering issue is affirmative, whereas negative when it is contradictory. The attitude becomes stronger with increasing the absolute value of the variable. Sociopsychological positions (yi, zi) and (Yj, Zj), which are defined within the rectangular regions 0 5 yi, .zi 5 1 and 0 < Yi, Zj 5 1, are both varied with time depending on the psychologically repulsive and attractive forces arising from the interaction among the people and among the newsmedia, respectively. Distributions of particles on the (y, z) and (Y, Z) planes represent the state of social distance between constituents, and are useful to form a judgement by what extent the individual person or the individual medium is independent or similar to each other in the sense of sociopsychology. The opinion {zi} for the people is changed not only by the qualitative things such as the sociopsychological pressure or the reportorial stance of the newsmedia, but also by the quantitative amount of information provided by the media. Here the expression {xi} denotes the set of the quantity xi. Hence, the extent to which the individual attitude quantitatively fits the state of information of the newsmedia is one of the major factors for determining the change of zi. It is the reportorial component of information which plays a role to induce the prevalence of certain
Formation
of Public Opinion
99
opinion, that is, to induce the change of {xi} toward a certain direction, when the component well fits the attitude of the people at that time. The amount of prevalent component becomes large only after the prevalence of the opinion grows in the society and a definitive public opinion appears as a result of socially collective phenomenon. Since the media change their own attitude Xj perceiving the attitude change of the people, both attitudes of the people and the media axe closely connected with each other, giving feedback to each other, Figure 1 conceptually depicts the relation between the public and the newsmedia, where the arrows are directed to the direction of forces and actions. According to this, formulation is made in what follows.
____ ___ ____ ________________~ Extemt of L Event, Frequency of Event 1
--__________
Amount of lnrormetlon
--..----____----~
fteportorisl Component Prevalent Component 11
1
t
MuwalSlance dlha
Rbk. AwIude
Nmsmadda
I t
I
t
Figure 1. Conceptual diagram of the relation between the public and the newsmedia.
3.2.
Formulation
The time variation of opinion xi for the ith public-particle is given by 1 dx;
+
y.
d_ *
’
(7
-
]Xi
-Xij’
xi)
(1)
where ai, pi, and yi are constants, d is the average attitude of the newsmedia, and x8 the initial value of xi. The first term on the right hand side represents the change of public attitude which is drawn toward the direction of average stance of information of the media. The quantity gi gives the extent for the public attitude to be resonant with information released by the newsmedia, and is given by F(t; X) 6(X - xi) dX.
(2)
Here F(t; X) dX represents the amount of information released at a time t with reportorial attitude within the range [X - 9, X + %$I, and a(z) is the Kronecker’s delta. The second term on the right hand side of (1) is to mimic the recovery of the people to home style when the sociological pressure is not perceived from the environment; with increasing pi, the particle becomes more and more traditional and conservative in characteristic traits. The third term of (1) is to give the effect of the change of individual attitude toward the average opinion or the general trend of surrounding people. This term gives the extent of trend for the submission to sociopsychological pressure and for the adaptation with the surroundings when yi is positive, and for the resistance to environmental atmosphere when yi is negative. Such trends become strong with increasing the absolute value of ri. The quantity di is the sociopsychological pressure suffered from the surroundings, whereas the quantity ii is the average attitude of surrounding
100
T.
OHNISHI
people, which is perceived by the particle i. The latter two quantities are, respectively, given by
(4 where &e is the sociopsychological potential acting on the particles i and C, and rig is a vector for the social distance between i and e; rie = re - ri, re E (ye, .ze), and r-i E (yi, zi). In the actual society, individuals are subject to a psychological force regarding the adaptation of a certain prevalence to result in the approach or the separation with each other in a sense of sociopsychology. To simulate such a situation, every particle is assumed to fluctuate on the sociopsychological (y, z) plane, being subject to the sociopsychological forces from all particles by which it is surrounded. Assuming such sociopsychological fluctuation to be analogous to the physical Brownian motion, the time variation of the position of particle i, ri, can be described by the following equation of motion and a Langevin-type equation: gi=pi dt
dpi dt
=
and
mi’ -Ei
pz +
Xi
Cxepcpk e ze
drie
e
’
(6)
where rni is the mass of particle (this is set in what follows as mi = 1, for simplicity), pi is the quantity corresponding to momentum, and &i and
El
lrieIpnl
+ 12 Iriel-
m
,
where [i, Es, ni, and ns are constants, whose values are the measures for indicating to what extent and with what strength the psychological interaction prevails in the society. The first term on the right hand side of (6) is for the deceleration of motion, which is originated from the inelastic scattering between particles in the multi-particle model. The coefficient Ei represents the extent of psychological resistance against the change of sociopsychological situation. The resistance becomes strong with increasing Ei. Both the second and the third terms, on the other hand, are to give fluctuation. The second one gives the force for the particle i to approach the particle with the same opinion as itself but to part from the particle with a different opinion. This force is assumed to be given by the product of the strength of sociopsychological force-field perceived by the particle i from its environment, C xe d&/drie, and the extent of attitude of the particle, xi. When the force is given by this form, the quantitative variable xi can be interpreted as a scalar with the same characteristics as the mass or the charge, which is intrinsic for each particle. With this second term, the sociopsychologically cohesive and dispersive phenomenon can be simulated. The third term, on the other hand, is to show the manifestation of individuality without adapting him or her to the surroundings, for instance, with the intention that the value of oneself be higher than any others surrounding him or her. The strength of this mentality is not dependent on the attitudinal state of the particle but on the strength of the sociopsychological force-field. The greater the value is for the coefficient
(Xj’” - Xj’) +r.D.
IXjpoI
’ ’
(Tj -X,p) IXj - Xpjl'
(8)
Formation of Public Opinion
101
where Aj, Bj, and I’j are constants, 3 is the average attitude of the public, namely public opinion, and X3?” the initial value of XT. The first term on the right hand side of (8) is to give the effect for the newsmedium to change its reportorial stance according to the varying state of public opinion. The change of the stance is assumed to follow the change of public minds without any time delay. The second term has the same meaning as of the second one of the public attitude of (1). The third term, on the other hand, is to give the effect for the medium to change voluntarily its reportorial stance, being based on the definition of situation of the issue which is shaped up among the newsmedia. Its time variation is proportional to the strength of psychological force-field Dj. The quantities Dj and Xj are given by similar formulae as equations (3) and (4):
where @je is the inter-particle potential for the media particles and Rje is the vector representing the social distance between particles. The former is defined as @je = Zi IRjeleN1 + Zz IRjel-N2 ,
(11)
where El, Ez, Ni, and Ns are constants. Also for the time variation of the sociopsychological position Rj, the similar expressions as for the public case are introduced: dRj _ Pj --Mj’ dt dPj _ -Ej dt-
and
(12)
Pj + Xj Dj - Hj C 2, e
(13)
where Ej and Hj are constants, and Mj is set unity hereafter. The distribution of the amount of information released by the newsmedia, F(t; X), is related to the public attitude via the quantity gi given by (2). When the amount of reports released by the individual medium at a given time t, Qj (t), 1s ’ g’iven, the quantity F(t; X) is obtained by
F(t; X) dX = C’
Qj(t),
where the summation C’ is to be performed only for the Qj(t) whose reportorial stance is fallen within the range [X - y, X + y]. The quantity &j(t) is given by definition as &j(t) = e amount of prevalent component Qy seems to increase with increasing the Th Q?(t) + Q:(t). absolute value of g,
and hence is assumed here to be proportional to some power of 1% I:
(15) where Cj and 4 (> 0) are constants. The rough estimation of the exponent q can be made with the following arguments. (1) The public and the newsmedia are considered to form a global system feeding back information to each other. In this case, the more significant the issue is for the society, the more it is repeatedly reported in this social system. As a consequence, the total amount of
102
T. OHNISHI
information released by the media during a certain period of power of the amount of input to the system, that is, the initial ponent for the issue [25]. Since the output from the system is component, when the issue is important and a large-scale one,
&j(t) = Q;(t) m (Q,“(t))’
time grows with the second amount of reportorial comdominated by the prevalent the following relation holds:
(16)
e
The general rightness of the above relation between Qr and QT was also pointed out, regardless of the scale of issues [25]. (2) Generally speaking, the time derivative of the public opinion 1g 1 seems to be approximately proportional to the amount of information given at that time, as does the case of the diffusion of innovations [26]. When the prevalence weakly takes place, it holds that QJt)
21
Q:(t)
cc
I2 I.
(17)
From these considerations, the value q = 2 is adopted in the following, which seems to be appropriate at least in the case of weak prevalence of public opinion. 3.3.
Constants
and Parameters
Distributions for the initial momenta and initial attitudes of particles and the sets of various constants related to particles are all assumed to obey a Gauss distribution or an overlapped Gauss distribution in m-fold, such that Q(x) =
_(x - Piv c _A&m &5G$exp { 2(a&)2
> ’
m I 3,
where C, aFf, = 1, and the superfix x denotes the constants relating to the quantity x. Those initial quantities and constants are all randomly determined using the distribution (18). For the particles both of the public and the newsmedia, their initial positions on the sociopsychological y.~- and YZ-planes are also set randomly. Completely reflective conditions are imposed on the boundaries so that the subsequent movement of particles is limited on those respective planes within a unit length in each direction. In order to avoid the piling of particles on one point after interactive movement on the plane, the distance of the closest approach for an arbitrary pair of particles or the diameter of a hard core particle r-0 is introduced, along with its related parameter X such as -l/2 rosT=P x
(19)
A’
where F is the mean distance between particles, and p is the mean surface density of particles. A potential of the form of (7) gives the inter-particle distance rm, where the maximum force is realized between two particles as l/h-%) Tm=
--
=
kTo
=
;P-‘/~.
(20)
Here k is a constant, its value being estimated from its definition to be in the range 1 N 10. On the other hand, the strength of field for the psychological force, which appears on the right hand side of (6), is given by
Formation
of Public Opinion
103
where b is a constant, whose value is estimated to be of the order 0.1 N 10 when 0((i) using relations (19) N (21), the coefficients
[ 12 =
Also for the potential
p(‘++“‘)X%
p(‘+++,na
of newsmedia
(
b
>I’
1 _ $/&a-nr)
(
b
1 _ !.$k(m-n2)
particles,
= 1. By by X, k,
and
>I
(23)
.
the coefficients
(22)
81 and S2 can be replaced
by
constants A, K, and B, which are similarly defined as X, k, and b above. All of the constants and parameters discussed above must be determined so that the secular variation of public opinion obtained by the model just corresponds to its behavior observed in the past. Figure 2 shows the flow diagram for the numerical calculation. In this model, the amount of information for the reportorial component released at a time t, Q?(t), is required as an input quantity. This is the only one exogenous variable, which acts as a driving force for activating the public-media system. Outputs are the distributions of public opinion and of the reportorial stance of the newsmedia at the time t, together with the information on the value of the prevalent component, and the cohesive state of two types of particles on each sociopsychological plane. In what follows, the integration of differential equations is performed with a time step At = & yea.rs.
mlountdhfommbnd
wcanpocrml
-no ml dPubkatnudomd
(or)
t
vmlaa ( 2,) -
(x,1 IYA and 1
tom. pauc I
Amomldhfamaond
mt-pwnt
v-
t
ix,), (Y, 1 and
(Z,) co~btho
(STOP) Figure 2. Flow diagram for the numerical calculation. At the two SRS on the left hand side, the subroutine shown on the right hand side is called.
4.
A CASE STUDY: PUBLIC OPINION REGARDING NUCLEAR ENERGY IN JAPAN
4.1. Determination
of Constants and Parameters
Information on the quantity Q:(t) together with the actual data on the movement of public opinion as reference data for fixing the values of constants are first discussed. Since 1970 or so, the prevalent component of the news concerning nuclear energy in Japan, that is, the information in which the public were highly interested, and on which the media
104
T. OHNISHI
continued to report during a certain period of time, has been almost limited to the negative phase of nuclear issues, such as impediments and accidents at nuclear power stations, the risk and danger of electricity generation by nuclear power, the failure of the research and development of nuclear energy, and the anti-nuclear movement in the public. It seems quite difficult, however, to clearly discriminate on what portion of the negative reports corresponds to the prevalent component and what portion to the reportorial component. In this paper, the articles reported by the newspapers distributed on a nation-wide scale in Japan are all treated as the reportorial component, daringly assuming that the fraction of prevalent component in the newspapers is sufficiently low as compared to the fraction reported by other media such as television, radio, magazines, and books,
QjR(t) = wj I(t),
(24)
where wj is a constant parameter; I(t) is the sum of the area of negative articles regarding nuclear energy, including headlines and photos on three newspapers, The Asahi, The Mainichi, and The Yomiuri during one month, counted in units of column x cm in the small-scale editions of these newspapers. Since about two decades ago, many surveys on the public opinion regarding nuclear energy have widely been done in Japan by various agencies. Of these opinion polls, the results of the one which has three selection branches concerning the use of nuclear energy in electricity generation, such as: (1) approve it (this fraction in the poll being denoted as fP), (2) oppose it (fa), and (3) undecided, are adopted here. With these fractions, the public opinion in our meaning at a given time t, O(t), is given by 0(t)
=
01 f,
+ 02 fa
=
01(t)
J-p(t) + 02(t)
fact),
(25)
where 01 and 02 are both the values within the range [-1, 11,which are the averages of variable {xi} corresponding, respectively, to the pro- and anti-nuclear sympathizers. Average attitudes both of the pro and anti-nuclear sympathizers have not probably been constant from the early days of the nuclear era, but must have been varied gradually with time in accordance with the gradual change of life style or the sense of value, and also with the gradual alteration of generation [27,28]. Those coefficients 01 and 02 are, therefore, functions of time, and the following formulae are assumed as the simplest expression for their time dependency: O,(t)
= 7),(t - 1973.0) + V,,
m = P, a,
(26)
where t is in years. Constants qrn and u, are to be determined so that the public opinion given by (25) fits well the model opinion, f E xi xi/n. The final values of various constants along with these rlrn and yrn must be searched iteratively, so that the above fitting is realized most satisfactorily. In the following calculations, 500 particles each are considered for both the public and the newsmedia, statistical accuracy being of the order (5OO)-1/2 2~ 5%. An extremely affirmative attitude to nuclear energy is assumed to correspond to zi = 1 and Xj = 1, whereas an extremely negative one is zi = -1 and Xj = -1. The attitudinal variables zi and Xj are distributed within these two strongest extremes so that xi = 0 and Xj = 0 both correspond to a neutral attitude to nuclear energy. The following are standard values for representative constants: pLa= 1.5 x 10m4 and ga = 0.5p&, for the statistical constants of the coefficient ai in equation (1); CL* = 1.0 and g* = 0.5/_~*, for the Aj in equation (8); nr = Ni = 1, 712 = N2 = 2, X = A = (20)‘i2, k = K = 3, b = B = 5, for the constants of the interactive potentials; and pc = 500, uc = 0.5pc, 0.3817, c? = 0.5@‘, for the amount of information released by the newsmedia. and/P= Of those constants, the first cited, @, is a measure to show the extent of influence of the newsmedia to the public, that is, a sort of coupling constant between the public and the newsmedia. Therefore, pa is to be noted as a significant parameter to see what difference may appear in the
Formation of Public Opinion
105
public opinion in cases when the extent of infiltration of the newsmedia into the society differs. The last one, /.P, on the other hand, is the quantity to give relative significance of the reportorial component to the resultant prevalent component; it is another important parameter to see what difference may occur in the public opinion in societies where the amount of reportorial component regarding a certain issue differs from each other, being due to, for instance, a difference of the form of political organization. In what follows, the cases are also investigated when the values of pa and pw are varied around the standard values. 4.2.
Numerical
Figure resultant
Results
and
3 shows the monthly prevalent component,
Discussions variation of the amount of input reportorial component averaged over all newsmedia. The amount of reportorial
and the compo-
nent has peaks with about an order of magnitude higher then the background only when large scale nuclear accidents (shown by keywords) happen. Although the amount of prevalent component grows almost as large as the reportorial one in t 2 1980, it cannot exceed the latter under the standard values of the constants. In t 2 1980, the prevalent component grows also in the case of accidents but only up to an order of magnitude lower than the reportorial one; it becomes negligible as compared with the latter calm period. Although with a fixed value of CL” to 1.5 x 10P4 and with a variable pLwin the region ~1w 5 4.0, the relative intensity of the prevalent component to the reportorial one never exceeds unity, even at the time of accidents, its value during a calm period gradually grows with ~1”. This indicates that the prevalence regarding antinuclear thought becomes easier to occur not only during the accident, but also in a calm period in the case when the @’ is increased, that is, when the amount of reportorial component released every day becomes large. Such situation seems in no contradiction with the real society [29].
Figure 3. The behavior of the amount of information averaged over all newsmedia for the input (thick line) and the output (thin and dashed lines), corresponding, respectively, to the reportorial and prevalent components of information. The output for the case of pcl = 6.0 x low4 is drawn only in the region of t 2 1984 for the sake of clarity. The keyword attached to the leftmost peak of the input data, Mutsu, indicates the accident of the nuclear powered ship Mutsu, whereas the other keywords correspond to accidents at the respective nuclear power stations for electricity generation.
Figure 4 shows the time variation of the first terms on the right hand side of both equations (1) and (8) averaged over all particles, i xi aigi ]zi] (It - zi)/]X - zi( and & Cj Aj IXjl $$/Iz), which represent, respectively, the extent of influence of the reportorial stance of the media on the public attitude, and that of the public attitude on the stance of the media. Although in a calm period the newsmedia have only negligible influence on the public attitude, it impulsively
106
T. OHNISHI
and strongly affects the public opinion during an accident so that the public attitude to nuclear energy comes to be aggregated toward a negative direction. Although the attitude change of the public influences the reportorial stance of the media by about one-tenth the influential degree in the reverse direction, its effect clearly appears in the case of nuclear accident; the public affects the media during the first half period of attitude change, such that they draw the stance of the media in the same direction as the public’s one, but conversely to this, the media move in the reverse direction to the public opinion and recover their own original positions in the second half period. The value of one-tenth of this relative intensity is not so sensitive to the values of @ and pA.
-:
fromNawamedia to Public
----
I
: tram Public to Newsmedia
/f=l.5xlo-~
r'=0.3017
Figure 4. Time behavior of the strength of coupling terms between the public and the newsmedia.
Figure 5 shows the time variation of public opinion together with the results of public opinion polls. The coefficients appearing in (26) with which the calculated opinion curve best fits the actual values are rlP = -1.9 x 10w3, vP = 0.7, 71, = 7.6 x 10e3, and V, = -1.5. These values and signs indicate that, for decreasing time, the averages of the public attitudes to both pro- and anti-nuclear energy, especially the latter one, become weaker and approach a neutral position. This means that in the 197Os, a major fraction of anti-nuclear sympathizers were the people who strongly opposed nuclear energy, but that gradually changed with time to be the people who only weakly arrest to nuclear energy, showing a gradual change of the sense of value. In general, public opinion is calculated to get worse with every large-scale nuclear accident. After an accident it recovers but never to the former value, so that the global trend for the opinion gradually become negative with time. Such a trend of the public opinion was also found in the previous cellular automaton model [14]. It seems common also for countries other than Japan [30,31]. In the case when large scale accidents do not take place during a long time, and when the amount of negative information released by the newsmedia continues decreasing, however, the public attitude to nuclear energy is naturally ameliorated. When the calculation is extended to the future with the input amount of information after March 1992, I set equal to the same value as that in February 1992, 10, a society with 0.084 for the value of public opinion O(t) is realized at t = January 2000. When the conditions I = 0.1 IO and I = 3.0 IO are adopted, on the other hand, public opinion becomes 0.114 and 0.039, respectively, in January 2000. Figure 6 shows the distribution of attitude for the public particles. The public is assumed, at the beginning, to be an aggregate composed of: few people strongly arresting to nuclear energy (this being called the component a), many people weakly arresting to or weakly supporting it
Formation _____ 0.4
:a”=o.3817
. . . . . .. . . . . . .. : jp=,
of Public Opinion o : Actual
107
Value
FJx 10-3
Public Attitude -0.2 Figure 5. Time behavior of the calculated public opinion to nuclear energy.
attitude
of the public and actually surveyed
(component n), and a moderate number of people positively supporting it (component p). Whenever a large accident occurs (as for the case at 1974.50), a peak corresponding to the component p disappears and it seems to be changed to another component n, shifting toward x < 0. Since a major part of people originally belonging to n also moves toward a negative direction, the fraction of people with negative attitude rapidly becomes increased. The component p can barely recover its fraction within a finite time after the accident, as is seen in the distributions at 1988.50 and 1992.0. At these times, a peak corresponding to p is re-formed at its original position and the attitudinal distribution is recovered to a form with three local maxima. Roughly speaking, the public attitude oscillates between two distributional patterns corresponding to the accident and calm times.
Figure times.
6.
Distributions
of attitude
{zi}
for 500 public
particles
at four different
108
T. OHNISHI
Figure 7 shows the spatial distribution of model particles on the sociopsychological plane. The size of each symbol was set to be proportional to the strength of attitude, ]zi] or ]Xj(. In the case of the public, although the particles have a tendency to cohere around the particle with the same sign and with stronger attitude, the particles of passive attitude with smaller ]zi] distribute almost uniformly on the plane to form a background. This situation seems to mimic the actual society, at least qualitatively, in that parts of the public with strong wills of pro- and anti-nuclear energy approaches each other to form groups for enhancing or discarding nuclear facilities more actively, and in that many people with no definitive opinions exist independently of each other and distantly from those active groups, in the sense of sociopsychology. Such a cohesive phenomenon appearing in the society is a manifestation of self-organization in a nonlinear system [32]. Similar cohesive patterns like these can be realized also in the previous model of public acceptance
[14]. The media particle,
contrarily
to this, does not show any trend of
cohesion, indicating the psychological isolation of the media from each other.
(a) 1979.0 P. 3 ,
..I
.. .
(b) 1983.0
* .,
.*
. ..;.
(c) 1987.0 (d) 1991.0 Figure 7. Distribution on sociopsychological planes of the articles for the public (a)-(e) and for the newsmedia (f). The case (e) is an extended calculation by setting input data after March 1992 to be of the same value as that in February 1992. Asterisks and polygons are the particles with negative and nonnegative values of attitude, respectively.
Formation
of Public Opinion
199
(f) 1991.0 (e) 1995.0 Figure 7. (continued). Distribution on sociopsychological planes of the articles for the public (a)-(e) and for the newsmedia (f). The case (e) is an extended calculation by setting input data after March 1992 to be of the same value as that in February 1992. Asterisks and polygons are the particles with negative and nonnegative values of attitude, respectively.
C(“=1.5X10~
P’10.3317
Figure 8. Time behavior of the cohesive factor s.
As a measure of cohesiveness of particles on the sociopsychological plane, the cohesive factor s, a weighted average of reciprocal distance between particles, is defined as (27) The larger the value of s, the higher becomes the degree of cohesion around particles with large absolute values of attitude. Figure 8 shows the time behavior of cohesion factor both for the public and media particles. In t 2 1975, the media particle does not show any tendency for cohesion, Although also for the public particle, cohesion does not take place in t 5 1979, an abrupt change of attitude occurs on breaking out the accident at Three Mile Island (TMI), and the fraction of people with an anti-nuclear mind rapidly increases within 1 N 2 months after that. Although after the next one or two months, a major fraction of backsliding people recover their attitudes, the people with stronger attitudes increase the degree of cohesion to sustain its cohesive state long after that. At the time of the Chernobyl accident, many more people rapidly change their attitudes to a side against nuclear energy so that the maximum of s exceeds 100. After the recovery of public attitude, the rate of increase of the cohesive factor gradually grows
110
T. OHNISH~
with time, oscillating synchronously with the amount of information released by the newsmedia. The degree of psychological cohesion of the public becomes especially high in t 2 1989, when the standard values of constants are used, but it differs from model to model depending on the adopted values of those constants. For example, in the case of pa = 6 x 10s4 and @ = 0.03817, a psychologically cohesive state appears at the time of the TM1 accident, but the Chernobyl accident does not play any significant role for cohesion. In any case, it is clear that major nuclear accidents can become a trigger for the psychological cohesion of the public. 5. A collective model can regarded as an interactive collective phenomena are tem of multi-particles. In
CONCLUSIONS
be constructed to mimic the real society, with an individual person particle and with the society as a gathering of such particles. Socially considered here to be a resultant of the interaction among the systhis paper, public opinion was considered to be a product of socially
collective phenomena, and its formation is assumed to be realized under the influence not only of the sociopsychological force arising from the people themselves, but also of the psychological interaction between the public and the newsmedia. The input quantity is the amount of information of the reportorial component released by the newsmedia, and the output is the quantities corresponding to the attitude of individual particles and the spatial distribution of particles on the sociopsychological plane. By selecting appropriately the values of constants and parameters, this model w&s found to rightly reproduce the movement of public opinion concerning nuclear energy in Japan. In such a collective model, the extent of the influence of a variable on a certain quantity is difficult to precisely estimate because of the strong nonlinearity of the interaction between particles. It is, however, such nonlinearity that acts as a source for driving the complex movement of public opinion and for inducing the psychologically cohesive state of the public. Success or failure of the sociological model can almost be said to depend on its ability to reproduce properly the self-organization appearing in the society, which originates from the nonlinearity of the social system itself. From this viewpoint, this sort of collective model seems to be quite a successful one and useful for understanding quantitatively, or at least qualitatively, the states of sociopsychological forces prevailing in the society. It should also be useful for forecasting the future state of public opinion, or more generally speaking, of the socially collective phenomena under specified external conditions.
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