A Simple Way to Elicit Subjective Ambiguity:
Application to Low-dose Radiation Exposure in
Fukushima
Fumihiro Yamane, Kyohei Matsushita,Toshio Fujimi, Hideaki Ohgaki
Kota Asano

April 2014
Discussion Paper No.1417

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANA Simple Way to Elicit Subjective Ambiguity:
Application to Low-dose Radiation Exposure in Fukushima

Fumihiro Yamane,1 Kyohei Matsushita,2 Toshio Fujimi,3 Hideaki Ohgaki,4 and Kota Asano5

1

Graduate School of Economics, Kobe University(address: 2-1 Rokkodai-machi, Nada word, Kobe city, Hyogo prefecture 657-8501, Japan)
2

Faculty of Economics, Shiga University

3

Depertment of Civil and Environmental Engineering, Kumamoto University

4

Institute of Advanced Energy, Kyoto University

5

Graduate School of Human and Environmental Studies, Kyoto University

Abstract: We develop a new and less burdensome methodology called the high-and-low choicemethod to elicit and analyse ambiguity in public risk perception. We apply this method to thecancer mortality risk due to low-dose radiation exposure around the Fukushima Daiichi nuclear
power plant, a real uncertain problem caused by the accident that is the second severest one
after the Chernobyl case. The empirical results shed new light on Slovic’s (1987) seminal work;
considering radiation as an unknown risk made public perceptions for the mortality rate more
ambiguous, and the dread image led people to perceive larger and more ambiguous risks. In
addition, those who accessed popular information media (television, newspaper, internet, social
network services, and conversations with neighbours) tended to have more negative andambiguous perceptions.

Keywords: subjective ambiguity, belief elicitation, structural analysis, mortality rate, radiation
exposure, Fukushima

1. INTRODUCTION
Revealing public risk perception as a cardinal measure poses an important challenge in orderto analyse the huge discrepancy between the subjective and objective scientific assessments1 or
the causality from perception to preference in a meaningful way. The key issue is how to elicit
true perception. However, this is not an easy task because, in many cases, people have neverponder about their own estimates of hazard occurrence probability, and stating such uncertain
values precisely becomes burdensome. Excessive burden would make the measurement error
extremely large, thus causing inefficiency and may lead to inconsistent parameter estimates ofthe structural model for risk perception. Therefore, researchers must always pay special
attention to reduce this kind of burden.
Another challenge is to elicit subjective ambiguity. While the majority of risk perception
studies implicitly assume that individuals can provide certain (or point) estimates, some studies
have tried analysing individuals who are uncertain, but alternatively have second-orderprobability

distributions,subjective

likelihood

distributions

over

the

domainofhazard-occurring probability (referred to as subjective distribution in this paper). Those whoare confronted with uncertainty conform to reality in many risk-related matters, and someapproaches have been developed to elicit their ambiguities.
Our first contribution is to develop a less burdensome belief revealing method for the generalpublic (hereafter the high and low choice method) and apply it to elicit Fukushima prefectural

1

See Sjӧberg (1999) as an example of comparisons between public and experts’ perceptions inqualitative measures such as a risk rating {0: none, 1: very small, …, 6: extremely large}.
However, strict interpersonal comparisons are not possible since such measures have only
ordinal meanings. See Viscusi and Hakes (2003) for more details about this problem.

residents’ subjective ambiguities regarding mortality risk due to low-dose radiation exposure.
As explained in subsection 3.1, reducing the burden is quite important in this case study.

Figure 1. Location of the Fukushima Daiichi Plant

The second contribution is to develop simple structural models of perceived uncertainty
without any assumption on the shape of subjective distribution (even the uniform shape). In
many uncertain cases, it is easy to imagine that each person has a different shape of his or her
distribution: discrete or continuous, symmetric or asymmetric, unimodal, bimodal or trimodal,
or some combination of them. The researchers cannot easily observe and distinguish this kindof cognitional diversity. To treat this problem, there would be at least two approaches. One is toadopt a more flexible shape assumption as the previous studies did – from the normal
distribution (Cameron, 2005) to the beta distribution (Viscusi and Magat, 1992; Riddel andShaw, 2006; Delavande, 2008) and the induced distribution (ID) (Hill et al., 2007; Riddel,
2009; Nguyen et al., 2010, Riddel, 2011). However, if adopting the beta distribution or the ID,
we cannot consider possible persons who have discrete, trimodal, uniform or the other shapes.
Therefore, even these flexible distributions are still restrictive to account completely fordecision-making under uncertainty. Another approach, the distributional assumption-freemodel developed here, does not suffer from such a difficulty.
In addition, a more serious difficulty in applying the ID model lies in misreading the meaningof a parameter denoted asin Riddel (2009, 2011). The above studies using the ID modelinterpreted it as indicating subjective ambiguity, but in fact, it indicates interpersonal variation(hetero-aspect) in estimating the median of the subjective distribution. This detail is explainedin subsection 3.2.

On the other hand, as mentioned in subsection 5.3, our approach gives us only limited
information about subjective ambiguity – a tradeoff of avoiding any assumptions on
distributional shape. In the same subsection, we discuss when and how we can use this limited
information to analyse decision-making under uncertainty.
Despite of this limitation, our empirical results shed new light on the seminal work of Slovic(1987); considering radiation as an unknown risk made the respondents’ risk perceptions more
ambiguous, and the dread image led them to perceive larger and more ambiguous risks. In
addition, those who accessed popular information media (television, newspaper, internet, social
network services (SNS), and conversations with neighbours) in order to learn the health effectsof radiation, tended to have more negative and ambiguous perceptions.

2. UNCERTAINTY FOR LOCAL RESIDENTS AFTER THE NUCLEAR POWER
PLANT ACCIDENTThe Fukushima Daiichi nuclear power plant accident caused radioactive contamination overa wide area and cast dark shadows over the residents living there: evacuation, unemployment,
reduced sales, property value losses, invidious discrimination, and so on. Among these, thehealth effects of radiation exposure continue to be the main common issue for most people. To
reduce public exposure, citizens are prohibited to live in evacuation areas, where the annual
dose is calculated to exceed 20 mSv. Based on the Act on Special Measures concerning theHandling of Radioactive Pollution (enacted August 2011), the national and local governmentscommenced full-scale decontamination projects January 2012 onwards (see Figures 3 and 6 formore details). Nevertheless, the residents’ unease may continue unabated as they tend to havenegative and ambiguous perceptions for this particular risk (described in section 4).

Such perceptive gaps could be caused by several reasons. First, most people are unfamiliar
with radiation in spite of the fact that we are always exposed to background radiation; irrelevantto the accident, the national average exposure dose from the natural environment and in medical
settings is 2.1 mSv/year and 3.9 mSv/year, respectively (Nuclear Safety Research Association,2011). Most of the scientific knowledge about the health effects of radiation has not beenshared with the public although Japan is the only nation to have suffered the aftermath of
atomic bombings. Of course, this could be attributed to the highly technical nature of thisknowledge.
Another reason making the problem complex is the fact that the health effects of low-dose
exposure is not clear. Previous epidemiological surveys suggests that the carcinogenic rate
significantly rises in proportion to exposure doses exceeding 100 mSv, but still have not proved
for less than 100 mSv (e.g. Preston et al. (2003)). That is, we are actually facing the problem of
uncertainty defined by Knight (1921). On the other hand, several theories have been proposed
for low-dose radiation effects: the linear non-threshold model (Gofman, 1981), the bystander
effect (Nagasawa and Little, 1999), the hormesis effect (Luckey, 1980), and so on. Different
theories result in differing risk assessments, and this conflicting information might make public
perception more ambiguous.2
The above situations are likely to impose additional welfare losses on the residents. As
numerous experiments have detected, human beings tend to reveal some kind of preferences forrisk and uncertainty, known as risk/ambiguity aversion or loving. Especially, we often observe
ambiguity aversion in cases of low mean probability losses (see reviews by Camerer and Weber(1992) or Viscusi and Chesson (1999)) like the situation of our case study. Of course, it must be
2

Unfortunately, some false rumours without scientific basis have also been spread throughhearsay via the internet and SNS.

noted that the residents’ welfare losses would strongly relate to their own risk perceptions,rather than to scientific assessments.

3. PREVIOUS METHODS
3.1. Belief Elicitation
So far, roughly two approaches have been proposed to elicit subjective ambiguity: direct andindirect approaches. An example of an indirect approach is the exchangeability method(Baillon, 2008; Abdellaoui et al., 2011). This method enables us to observe some points of each
respondent’s cumulative distribution function without imposing any assumption for the
distributional shape. The drawback is that the iterative questions are sometimes quite
burdensome for the respondents. Even if this is not so, these questions would become
imprudent in cases of health- or mortality-related matters, since the questions treat such risks astargets of a gamble. For example, consider a case study where respondents are queried, ‘which
event do you want to bet 50 dollars on?: (i) less than 30% of people will catch a cold this winteror (ii) 30% or more will’.
In the direct approach, each respondent is simply asked to state his or her estimate. For
instance, Riddel et al. (2003) asked respondents to state precise values of their point or theirlowest and highest estimates of mortality rate caused by radioactive waste transportation(similar to the open-ended contingent valuation method (CVM)). In order to determine theprobability for contracting nerve disease or lymphoma caused by environmental pollution,
Viscusi and Magat (1992) asked a point estimate equivalent to ambiguous information of [x%,y%]. Delavande (2008) elicited some points of subjective cumulative function for the
probability of getting pregnant. However, stating precise values of unknown matters would be
difficult (like willingness-to-pay in the Exxon-Valdez case), which we believe must also be thecase for this study for the reasons mentioned previously. On the other hand, concerning
mortality rate due to arsenic contamination of tap water, Jakus et al. (2009) asked the
respondents to choose values closest to their point or lowest and highest estimates from a list of
probabilities (as with the payment card CVM). However, this method inevitably causes
measurement errors. This could be why Nguyen et al. (2010), who used the same data as Jakuset al. (2009), could not obtain efficient and interpretable-signed estimates for some parametersin their structural analysis.
Alternatively, we could ask respondents to select an interval including their estimates of therise in the cancer mortality rate due to additional radiation exposure, and thus, they would notneed to state precise values. This interval-choice method stems from the double-boundeddichotomous choice CVM, but does not suffer from several problems specific to this type of
CVM, such as yea-saying (Kanninen, 1995), nay-saying (Whitehead, 2002), and starting-point
biases (Herriges and Shogren, 1996). Those problems are said to be caused by sequential
questioning in order to observe one or two bounds of an interval including the true
willingness-to-pay (i.e. exhibiting the starting bid and after that the follow-up bid). In contrast,
our approach makes it possible to observe bounds of the interval simultaneously.
In addition, we presume that all respondents are fundamentally uncertain and therefore, havesome kinds of subjective distribution (such people were called as uncertain respondents in
Riddel et al. (2003)). Therefore, we asked each respondent to select two intervals: one
including the lowest estimate, and the other, the highest. In contrast, Riddel et al. (2003) called
those who could state their point estimates as certain respondents and assumed that somepeople could be classified as such in their case study. However, such people can be treated as
specific cases in our presumption (i.e. their subjective distributions degenerate), and it would be
preferable to think of them as rare cases in today’s Fukushima.

3.2. Structural Model
For empirical analyses on subjective ambiguity, in order to consider the possibility that the
subjective distribution may have a skewed or bathtub shape, assuming the beta distribution ismore appropriate than the normal distribution. However, according to Riddel (2009), there are
two drawbacks: (i) the difficulty in identifying the global maxima of the likelihood function andeven more seriously, (ii) the fixed relationship between the mean (central tendency of the
distribution) and the variance (variability).
The ID model of Heckman and Willis (1977) is irrelevant to these problems. However, there
is a technical issue. Here, we briefly review the Riddel’s (2009) derivation to clarify matters.
The ID modeling starts by specifying the following latent variable model.
𝐼=𝜇+− 𝜀 where 𝜀~𝑁(0,1), ~𝑁(0, 𝜎𝜔2 ), and 𝜀 ⊥Hill et al. (2007) interpreted 𝜇 and.

(1)

as the median and ambiguity parameters respectively(Riddel (2009) and Nguyen et al. (2010) did the same). We will reconsider this point later.
Based on equation (1), the respondent’s estimate of hazard occurrence probability (𝜋) and its
cumulative function are derived as follows.
𝜋 = Pr(𝐼 > 0) = Φ(𝜇 + ).
𝐻(𝜋′)= Pr(𝜋 < 𝜋′)Φ−1 (𝜋 ′ ) − 𝜇
= Φ(
).
𝜎𝜔

(2)
(3)

On the basis of the Heckman and Willis’s labor force participation model (1977), which
provided the foundation for the ID modeling, equation (2) is interpreted as an extended versionof binary response models (logit and probit); in the ID model, the index function is replacedwith a probability function. Parameterize 𝜇 and 𝜎𝜔 as linear functions of observed factors (𝑋and 𝑍) respectively.

𝜇 = 𝛽 ′ 𝑋 + 𝜈𝜇 .

(4)ln𝜎𝜔 = 𝛾 ′ 𝑍 + 𝜈𝜔 .

(5)

𝜈𝜇 and 𝜈𝜔 are stochastic terms. Then, the conditional cumulative function is𝐻(𝜋 ′ |𝑋, 𝑍) = Φ (Φ−1 (𝜋 ′ ) − (𝛽 ′ 𝑋 + 𝜈𝜇 )).
exp(𝛾 ′ 𝑍 + 𝜈𝜔 )(6)

If we assume that the stochastic terms are bivariate normally distributed and put the restrictionthat ln𝜎𝜔 ≤ 0 in order to exclude bimodal distributions, then the likelihood function for an
uncertain respondent whose lowest and highest estimates are 𝜋 𝐿 and 𝜋 𝐻 respectively, isderived as follows.
−𝛾′ 𝑍 𝑅 𝐿

𝐿= ∫
−∞

(7)

∫ 𝜙2 (𝜈𝜇 , 𝜈𝜔 )𝑑𝜈𝜇 𝑑𝜈𝜔 ,𝑅𝐻where 𝑅 𝐿 = Φ−1 (𝜋 𝐿 ) − 𝛽 ′ 𝑋 , 𝑅 𝐻 = Φ−1 (𝜋 𝐻 ) − 𝛽 ′ 𝑋 , and 𝜙2 (∙) is the bivariate normal
density function.
This double integral form looking complex at a glance is caused by including the stochastic
terms in equations (4) and (5), but excluding them makes another serious problem clear.
Nguyen et al. (2010) did so and derived the following function.
Φ−1 (𝜋 ′ ) − 𝛽 ′ 𝑋
𝐻(𝜋 |𝑋, 𝑍) = Φ ().
exp⁡(𝛾 ′ 𝑍)′(8)

It must be noted that this cumulative function is also derived by considering heteroskedasticity.
Now, reconsider the latent variable model of equation (1).

− 𝜀 is the composite error term.

As the variance of 𝜀 is common for all respondents, it is a homoskedastic error. On the other
hand, this is not so for the variance of

because of the specification in equation (5). In fact, if

the heteroskedasticity is specified as|𝑍~𝑁(0, exp⁡(2𝛾 ′ 𝑍)), as with the heteroskedastic probit

model in Wooldridge (2010, p. 601), then equation (8) is immediately derived. Therefore, in anatural interpretation,is only a heteroskedastic error, which does not represent the subjective

ambiguity.3 Our interpretations would also be supported form Heckman and Willis (1977)
mentioned above, since they included these two errors to consider individual homogeneity andheterogeneity in estimating the sample mean functions for sequential labor force participation,
respectively.
In summary, the previous studies using the ID approach estimated hetero-aspect (sample orinterpersonal variability) in estimating 𝜇 = 𝛽 ′ 𝑋 , instead of ambiguity (intrapersonalvariability) – is it possible to interpret the interpersonal variability as ambiguity of therepresentative person in sample although such a person is not of our interest? Moreover, Φ(𝜇)does not necessarily have a clear meaning as the median of subjective distribution, and it isinterpreted just as something included in [𝜋 𝐿 , 𝜋 𝐻 ].
In contrast, our modelling in section 5 has two advantages. First, it does not put any
assumption on the shape of the subjective distribution. In other words, any shapes (evenuniform, bimodal, trimodal or non-continuous) are allowed. Second, we constructed twomodels explicitly having the meanings of the median and range of the distribution respectively.

3

To understand the problem, consider the following two simple cases, where there are only two
persons, and they are identical in 𝑋 and 𝑍. In the first case, they state the same [𝜋 𝐿 , 𝜋 𝐻 ], and𝜋 𝐻 − 𝜋 𝐿 is large. Then, 𝜎𝜔 is estimated to be small while their ambiguities are large. In thesecond case, the first person’s range (𝜋1𝐻 − 𝜋1𝐿 ) and the second person’s (𝜋2𝐻 − 𝜋2𝐿 ) wereequally small, but 𝜋1𝐿 − 𝜋2𝐻 > 0 is large (the first person’s estimate was even higher than theother’s). Conversely, 𝜎𝜔 is estimated to be large in contrast to their small ambiguities.

4. SURVEY DESIGN AND DATA
In order to observe the public risk perception for low-dose radiation exposure and its relevant
factors, an internet questionnaire survey4 was conducted from 17 to 21 January 2013. The
researching subjects were residents over 15 years of age living in Fukushima Prefecture except
the evacuation area (Figure 2), and 4,527 monitors were randomly selected. We began by
explaining the purpose of the survey to them and described the content of the questions. In
particular, they were informed that they would be asked to estimate the rise in cancer mortality
rate due to additional exposure. Before answering, they were also requested to read an 8-pagebooklet explaining the meanings of fundamental terminologies (radiation, radioactivity, sievert,
becquerel, etc.), half-lives of the main pollutants (iodine-131, cesium-134, and cesium-137),
the kinds of the health effects (deterministic and stochastic effects), the scientific view thatradiation exposure might cause cancers even for doses less than 100 mSv and that thispossibility would be higher for young children, and the fact that the average Japanese citizen
4

The internet has become the preferred medium for social surveys for several reasons: (i) the
return rates are expected to be higher than mail surveys, because the subjects are sampled froma pool of people who contract with web research companies and embrace survey offers, (ii) in
contrast to phone or interview surveys, the data quality does not depend on the interviewers’
abilities, (iii) we can customize the questionnaire sheets to have the respondents answer allquestions in correct manners (no one can omit answering any question, the lowest estimate ofmortality rate cannot be higher than the highest, and so on), and (iv) we can measure the total
time each respondent spent on answering the survey and then exclude those who spentextremely short times. Although the respondents were sampled from internet users only, thisdisadvantage has become less relevant over the years with the increasingly widespread use of
the internet.

has been exposed to annual background exposure irrelevant to the accident (1.5 mSv/year fromthe natural environment and 2.3 mSv/year due to medical reasons 5 ). The questionnaire
consisted of twenty-seven questions regarding social, economic, and mental impacts of theaccident, risk perception, needs for decontamination projects, and socioeconomic
characteristics.

Figure 2. Objective Area and Radiation Dose Distribution (Air Dose Rate (μSv/hour))

In total, 1,973 (43.6%) subjects responded. However, we excluded 301 people who denied
answering about their family income, and therefore, the final sample size was 1,672. This
somewhat low return rate can be attributed to the fact that as our sample includes people who
actually live in a contaminated environment, the questions regarding cancer mortality ratewould have been stressful for them. Therefore, it is necessary to examine the representativenessof the sample. Table 1 shows a comparison with the official statistics for the socioeconomic
characteristics of Fukushima residents. The high rate of male in our sample can be attributed toseveral reasons: more males might have answered as the representatives of their families
because of the relic of patriarchal system, or females might have avoided answering because
they are thought to be more risk-avoiding than males and, if so, they would have experienced
higher stress levels for this survey. Many respondents were aged 30 to 50 years, which is a
general tendency in internet surveys as these age groups use the internet more frequently forrecreation and business. Our sample is also alike in terms of the low rate of single-personhouseholds, given that such households rarely participate in non-official surveys. The high rate
5

These values differ from those in section 2, because we referred to an earlier report of the
Nuclear Safety Research Association (2004) while preparing the booklet.

of respondents with family income less than 2 million yen could be attributed to the fact that thecorresponding official statistical survey excluded single-person households from its research. It
is important to interpret the analytical results while keeping these differences in mind.

Table I. Comparison with Official Statistics for the Socioeconomic Characteristics ofFukushima Residents

The procedure of risk perception elicitation was as follows. First, we presented two
documents (Figure 3) in order to share common information concerning the changes in thenational standards for the exposure dose for the general public and for the decontamination
projects. Next, we emphasized concrete values, 1 and 20 mSv, which are the legal standards forradiation protection and also our target values for the elicitation.

Figure 3. Explanations before the Risk Perception Question

Then, almost half the respondents were asked to predict the rise in the cancer mortality rate
due to an additional exposure of 1 mSv, and the other half were asked to predict the same for 20
mSv. Following Riddel et al. (2003) and Jakus et al. (2009), we provided a risk ladder (Figure4) to assist their predictions.6 Although these studies added scientific assessments for the target
6

Risk ladders are popular graphical communication tools to help people understand the relative
sizes of risks. However, they are known to influence their perceptions (see Nguyen et al.
(2010) for more details). In addition, it must be noted that expressing probabilities as ‘x per
million deaths’ might be an inappropriate form of information provision or risk
communication for the general public. Although we adopted such a frequency-basedrisk on the ladder, we did not do so, because providing such a reference point would cause
strong anchoring effects.
Figure 4. Risk LadderFigure 5 shows the actual format of the elicitation question. The interval alternatives were set
to be mutually exclusive and exhaustive. Notably, the bounds of each interval were set on thebasis of the risk ladder, so that respondents could directly refer to the ladder information. In
addition, we customized the response format, whereby when predicting the highest rate, each
respondent could not choose intervals lower than the lowest interval and vice versa (it waspossible to choose the same interval for both bounds). The responses are summarized in Table
2.

Figure 5. Risk Perception Question (for an additional dose of 1 mSv)

Table II. Frequency Distribution of Risk Perceptions

For simple comparisons with scientific assessments, the median and range of each
respondent were roughly calculated as follows. We denote respondent i’s lowest and highest
estimates as 𝜋 𝐿 and 𝜋 𝐻 respectively, and these are latent variables. If he (or she) chose the lthinterval as including 𝜋 𝐿 , then the following relationship is satisfied.

expression in this study because it is easy to understand, we accept that it might cause
cognitive biases (known as neglecting the denominator) and make people overestimate small
probabilities (see Slovic et al. (2000)).

𝜋𝑙 ≤ 𝜋 𝐿 ≤ 𝜋𝑙 if i chose l (l = 1, 2, …, 16),(9)where 𝜋𝑙 and 𝜋𝑙 are the lower and upper bounds of the interval (note that 𝜋1 = 𝜋1 = 0).
Likewise, a similar relationship is established for 𝜋 𝐻 , if he chose the hth interval.
𝜋ℎ ≤ 𝜋 𝐻 ≤ 𝜋ℎ if i chose h (h ≥ l),(10)where 𝜋ℎ and 𝜋ℎ are the bounds of the interval. Because the median of his subjective
distribution is defined as(𝜋 𝐿 + 𝜋 𝐻 ) 2, averaging equations (9) and (10) derives
𝜋𝑙 + 𝜋ℎ≤2≤𝜋𝑙 + 𝜋ℎ.
2(11)The left- and right-hand sides can be interpreted as the minimum and maximum of his possible
medians, and we call them the least median (LM) and the greatest median (GM) respectively.
On the other hand, the respondent’s range is defined as
substituting (9) from (10) derives the condition for𝜋 𝐻 − 𝜋 𝐿 . Therefore, if h > l,

. If h = l, another condition is derived.

That is,𝜋ℎ − 𝜋𝑙 ≤or 0 ≤≤ 𝜋ℎ − 𝜋𝑙 if h > l,(12)

≤ 𝜋ℎ − 𝜋ℎ if h = l.

Both sides in each condition can be interpreted as the minimum and maximum of possible
ranges, and we call them the least range (LR) and the greatest range (GR) respectively.
In Table 2, we calculated the individual approximate median as (LM + GM)/2 and the rangeas (LR + GR)/2 (we assumed that 𝜋1 = 0.

, because the Japanese cancer mortality rate

was already 0.301207 without additional exposure). Compared with the estimated rate based on
the linear no-threshold model, respondents tended to extremely overestimate for both 1 and 20
mSv. However, there seemed to be no proportional relationship between the exposure dose andrisk perception – the increase in the median or range of mortality rate due to an additional

exposure of 1 mSv is not one-twentieth of that by 20 mSv. Rather, the perceived effect of 1 mSv
was estimated to be much greater and more ambiguous.
Several factors could determine subjective distribution. In order to investigate therelationship, we asked about the variables shown in Table 3. In the structural analyses, we
assumed that all these can affect both the median and the range. In contrast, Riddel (2009) andNguyen et al. (2010) classified their independent variables into those that would relate only toperceived risk (median) and those only to ambiguity (which is, in fact, heteroskedasticity). For
example, gender was assumed to influence only the median, and risk information, only
ambiguity. However, such classification does not have much rationale and conviction. Why can
we exclude beforehand the possibilities that gender may also influence ambiguity and so on?

Table III. Independent Variables

The variable selection was based on Sjӧberg (2000) and Dosman et al. (2001), who widely
reviewed the deterministic factors of public risk perception.
Slovic’s (1987) cognitive map showed that public perception was determined by twodimensions of risks: unknown and dread. However, according to Sjӧberg (2000), these factors
do not always determine the perception or sometimes affect it negatively. In addition, paststudies did not focus on the effects on ambiguity. To investigate these issues, we attempted toquantify unknown and dread by simply asking respondents whether the following sentences
corresponded to their images – ‘radioactivity was an unfamiliar and mysterious thing’ and ‘itwas somehow a terrible thing’.7 Only a few respondents stated unknown or dread contrary to
7

Although unknown and dread are usually quantified by factor analysis, we avoided thistraditional way, because it would have become burdensome for our respondents, and this kind

our expectation (21.9% or 16.6% respectively), although it might be because almost twenty
months had passed after the accident.
Dosman et al. (2001) reviewed the empirical results for the following socioeconomic factors:
gender, age, income, number of children, years of education, primary source of risk information,and political ideology (we excluded years of education and political ideology from among thesefactors, because we believed that it was a too delicate matter to ask these factors in this case).
Dosman et al. (2001) found that females, older people, people with lower income, parents ofyounger children, and less educated people tended to perceive larger risks. However, the results
pertaining to age and education level were not general. For example, while younger people may
be more familiar with new risks, on the other hand, they may be more impressionable towarnings from others who perceive risks negatively. Less educated people may not be too
conscious of several risks, but may feel more fear, because they do not know how to avoid or
mediate the risks.
Unfortunately, the results for the socioeconomic factors have sometimes (or often) beeninterpreted in confounding ways. For example, Dosman et al. (2001) mentioned that ‘as
individuals’ income levels increase, their overall perceptions of the world as a risky placedecrease. This may be because they are able to purchase products to minimize their exposure toor mediate the level of risk’. We must note that they discussed the effect of income on risk
preference (willingness-to-pay for risk avoidance) and not on perception.
In addition, there is scant evidence for the relationship between socioeconomic factors andambiguity. Cameron (2005) suggested that females and younger people have a larger variancein each subjective distribution. Although Delavande (2008) investigated the influence of age,of quantification was not of our interest.

the results for the influence on variance were not clear because of the beta distribution
assumption.
Risk information sources are also important factors influencing public perception. However,its effects are not clear and would vary accordingly to the time, place, and circumstance. For
instance, the primary role of mass media (TV, newspapers, and so on) is to inform the public ofrisks and help their correct understandings, which is important to avoid their dangerous
unconsciousness or extreme panic. Nevertheless, the media often cannot avoid providing
incorrect information. On the other hand, many people seem to believe that governments andthe a part of scientists often intentionally suppress negative information or have little concern
for public health, and do not rely on these avenues of information (Jenkins-Smith and Silva,
1998).
To understand how our respondents gather information, we asked them ‘how do you andyour family gather information regarding the health effects of radiation exposure’ and allowed
them to choose multiple alternatives. In addition to the six alternatives described in Table 3, we
also provided the following choices: ‘questioning your regular medical doctor’ and‘questioning the relevant department of the national, prefectural, or municipal government’.
However, a mere 4.7% and 3.7% respectively, chose these alternatives, and therefore, we
excluded them from our analyses. The primary source of information was the TV andnewspapers (55.0%), followed by the internet and SNS (29.2%), and conversation withneighbours (15.1%).
Moreover, we considered two other factors. The first was whether the respondents thoughtthat there might be other health effects besides the carcinogenesis. The other factor was whether
they lived in zones planned for decontamination. Municipalities in the intensive contamination
survey areas described in Figure 6 researched where additional exposure dose was expected toexceed 1 mSv/year, specified the zones where decontamination was needed, and planned its
implementation. However, we asked the question without presenting any relevant informationsuch as Figures 2 and 6, since individual perceptions could have changed otherwise. About
52.3% of respondents were aware that they lived in the decontamination-planned zones, 26.1%
were aware that they did not reside in such zones, and the rest were unaware.

Figure 6. Target Municipalities for Decontamination

The rates of having unknown and dread images, thinking possibilities of the other healtheffects, and gathering information are higher for those who knew that they lived indecontamination-planned zones (decon zone = 1). The higher rate of high family income forsuch respondents may have perhaps resulted from the fact that the distribution of relatively
high-level contamination (green-coloured area in Figure 2) nearly coincided with a series ofbasins stretching along the Abukuma River, which were highly urbanized (e.g. the Fukushima
and Kohriyama Cities, the largest cities in the prefecture) and the relatively high wage level.

5. MODEL SPECIFICATION
The median and range models were specified by expanding the interval data choice model ofHanemann et al. (1991).

5.1. Median Model
We assumed= Φ(𝜇 ) for each respondent i in order to assure[0,1] and specified

the structure of 𝜇 as follows.
𝜇 = 𝛽 ′ 𝑋 + 𝜈𝜇 , 𝜈𝜇 ~𝑁(0,1)(13)

where 𝑋 is a vector of independent variables, 𝛽 is a parameter vector, and 𝜈𝜇 is the stochastic
term. Then, based on equation (11), the contribution to the likelihood for respondent i wasderived as
𝐿 = Pr(LM ≤
= Φ(Φ

−1 (

′

≤ M)

M) − 𝛽 𝑋 ) − Φ(Φ−1 (LM)(14)′− 𝛽 𝑋 ).

However, in order to compute the log-likelihood, two conditions must be satisfied: (i) LM > 0
and M > 0, because the domain of Φ−1 (∙) is (0,1), and (ii) M > 𝐿 , because 𝐿 must belarger than zero. The only case contrary to these conditions is the respondent choosing the firstinterval for both the lowest and the highest estimates ( 𝜋 𝐿 = 𝜋 𝐻 = 0 ), in which case
LM = M = 0. Therefore, we replaced the likelihood for this case as follows. Among the othercases, LM is minimized when = 1 and= 2 (if 𝜋 𝐿 = 0 and 0.000001 ≤ 𝜋 𝐻 ≤ 0.0000

then LM = 0.000000 ). Then, we assumed that the respondent’s choice of =that his or her median was lower than the minimum (,= 1 means< 0.000000 )8. Finally, the likelihood

was summarized as𝐿Pr(< 0.000000 ) = Φ(Φ−1 (0.000000 ) − 𝛽 ′ 𝑋 )⁡⁡if⁡⁡ = = 1,
Pr(LM ≤≤ M)=
𝜋𝑙 + 𝜋ℎ𝜋𝑙 + 𝜋ℎ= Φ (Φ−1 () − 𝛽 ′ 𝑋 ) − Φ (Φ−1 () − 𝛽 ′ 𝑋 ) ⁡⁡otherwise.
2
2
{

8

(15)

Another approach is to combine the first and second intervals into a new interval [0,0.000056]. In this case, if the subject’s choice was = 1⁡or⁡2 and= 1⁡or⁡2, then LM = 0,

and condition (i) is violated. Therefore, we neglected LM and just considered≤ M whencomputing the likelihood. However, the estimation results were not much different from theapproach in the main text.

5.2. Range Model
Likewise, we assumed
of

= Φ(

) in order to assure[0,1] and specified the structure

as follows.
= 𝛾 ′ 𝑋 + 𝜈𝜔 , 𝜈𝜔 ~𝑁(0,1)(16)

where 𝛾 is a parameter vector and 𝜈𝜔 is the stochastic term. Then, equation (12) establishes thecontribution of respondent i to the likelihood.
𝐿𝑅 = Pr(LR ≤≤ R) = Φ(Φ−1 ( R) − 𝛾 ′ 𝑋 ) − Φ(Φ−1 (LR) − 𝛾 ′ 𝑋 ).

(17)

The similar conditions must also be satisfied: (iii) LR > 0 and R > 0, and (iv) R > 𝐿𝑅.
These conditions are violated only when = . If = , then LR must be zero, and condition(iii) is violated. In particular, if == 1, then R is also equal to zero, and condition (iv) isviolated. Therefore, we replaced the likelihood for these cases as follows. First, for =we neglected LR and just consider
for another case of =≠ 1,

≤ R (note that R = 𝜋ℎ − 𝜋ℎ in these cases). Second,= 1, the same approach with the median model was applied. Amongcases satisfying conditions (iii) and (iv), the LR is minimized when = 1 and
LR = 0.000000 ). Thus, we assumed that his or her choice of =range was lower than the minimum (= 2 (then,= 1 meant that his or her< 0.000000 ). Finally, the likelihood was summarized

as
𝐿𝑅
Pr(
Pr(

=

< 0.000000 ) = Φ(Φ−1 (0.000000 ) − 𝛾 ′ 𝑋 )⁡⁡⁡if⁡⁡ = = 1,⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(18)≤ R) = Φ(Φ−1 (𝜋ℎ − 𝜋ℎ ) − 𝛾 ′ 𝑋 )⁡⁡⁡if⁡⁡ = ≠ 1,⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡

Pr(LR ≤{≤ R) = Φ(Φ−1 (𝜋ℎ − 𝑙 ) − 𝛾 ′ 𝑋 ) − Φ(Φ−1 (𝜋ℎ − 𝜋𝑙 ) − 𝛾 ′ 𝑋 )⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡otherwise.⁡⁡⁡⁡

5.3. When or How Can We Use Range to Analyse Decision-Making under Uncertainty?

Range is a simple measure of perceived ambiguity, but as Larson (1980) pointed out, it is nota sufficient measure in many cases. Suppose that there are two persons having the same range[𝜋 𝐿 , 𝜋 𝐻 ] but with different distributional shapes. For example, the first person has a unimodal
shape while the second person has a uniform one. In this case, the first person puts some degreeof confidence on a particular probability and is less ambiguous than the second person. Thus,
only with the information of range, we cannot distinguish the difference between them.
This is the tradeoff of the assumption-free approach; we can obtain only limited information
about subjective ambiguity while being able to avoid the constraints of distributional shapeassumptions. Therefore, considering this tradeoff, characteristics of the uncertain situation andpurpose of the study, researchers have to determine which approach is applied: the approachdeveloped here or the traditional one assuming some distributional shape.
For example, recall the situation of Ellsberg’s experiment (1961). The respondents did nothave any information about a proportion of red (or black) balls in the uncertain urn. In otherwords, they were completely uncertain, and thus, many of them might imagined only a uniform
likelihood distribution over [0, 1] about the probability of red ball. In this situation, range
becomes an appropriate measure of subjective ambiguity (Becker and Brownson, 1964). We
can easily create similar situations on a laboratory basis – especially gambles for which the
respondents are informed only intervals of the winning probabilities (e.g., Becker and
Brownson (1964), Yates and Zukowski (1976), Larson (1980), Curley and Yates (1985) and
Kahn and Sarin (1988)). However, such a situation would be rare in the real world. We
recognize that today’s Fukushima would also be far from it but practiced the distributional-free
approach in the next section as the first attempt.
Even when range is not a sufficient measure of subjective ambiguity, we can use it to analyse
human preference if accepting the α-maxmin rule (Jaffray, 1989; Marinacci, 2002; Ghirardato

et al. 2004) instead of accepting any distributional shape assumptions. For example, consider
an α-maxmin person who is uncertain about whether a bad event will occur or not. That is,whatever the shape of his (or her) subjective distribution is, he considers only the worst and bestcases in decision-making. Denote his status dependent indirect utility as
and as1 if the hazard occurs

if it does not. If his perception for the hazard-occurring probability ranges from 𝜋 𝐿 to𝜋 𝐻 , the willingness-to-pay (WTP) for him to exclude the uncertainty is defined as

where

|

( −

P)

=

( )|

𝐿

=

( )|

𝜋 1 + (1 − 𝜋)

∙

( )|
− [
𝐿

𝐻

( )|
−

+ (1 − ) ∙𝐿−[ ( )−

( )|

( )|
1(

if

]

(19)

)]

is expected indirect utility, y is status quo income, and[0,1] is a weight put on the worst case of 𝜋 = 𝜋 𝐻 . Since
increases with𝐻

𝐿

is an increasing function of y and

( )−

1(

) > 0, his WTP> 0.

Especially, if WTP is included in the indirect utility in an additive way (for instance,
( −

P) =

( ) − 𝛽ln

P where 𝛽 > 0 is marginal utility of income), its function isderived as a somewhat simple from.
ln

P = 𝛽 −1 (𝜋 𝐿 +)[ ( ) −

1(

)]

(20)

Despite of the above usage, we could not conduct CVM questions in the survey to ask WTP
for excluding the radioactive contamination or willingness-to-accept for bearing thecontamination because (i) it was quite difficult to find out ethical or moral validities for ahypothetical scenario that Fukushima residents were to pay the decontamination cost and (ii)their unease was thought to be too serious to accept in exchange for monetary compensations.
Trials of welfare analyses using the range information are remained in the other case studies.

6. EMPIRICAL RESULTS
The estimation results are summarized in Table 4. First, we discuss column (1), in which all
variables are considered.

Table IV. Estimation Results of the Median and Range Models

Significantly positive parameters on d20mSv in both models indicate that those who
predicted a rise in the cancer mortality rate due to additional exposure of 20 mSv tended toperceive larger and more ambiguous risks than those predicting the same for 1 mSv. These arequite interpretable results.
Unknown and dread images for radioactivity positively relate to both perceived risk andambiguity, although the parameter on unknown is not significant in the median model and isless significant in the range model. Notably, the results suggest that both images determinedsubjective ambiguity and add fresh evidence to a series of works pioneered by Slovic (1987).
The parameter on other effects is significantly positive in both models and indicates thatthose who thought of the possibilities of other health effects tended to perceive the cancer
mortality rate as larger and more ambiguous.
The respondents who knew that they lived in zones planned for decontamination, that is,
those who recognized that their living environment was contaminated to some degree,
perceived larger and more ambiguous risk. The result in the median model is consistent withthose of Riddel and Shaw (2006) and Riddel (2009), who showed that respondents living near
the route of nuclear waste transportation perceived a larger mortality rate. It also agrees with
Nguyen et al.’s (2010) findings for increased perceived risk on account of arsenic concentrationin tap water.

Regarding the other socioeconomic factors, the risk perceptions of females and respondents
with low income also tended to be more negative and ambiguous. Gender effect on ambiguity is
consistent with Cameron (2005), who showed that females had larger variances under thenormal distribution assumption. In addition, older respondents perceived larger risks.
Regarding risk information, the most popular media (TV/newspaper, internet/SNS, andconversations with neighbours) positively relate to both perceived risk and ambiguity, although
we could not identify the kind of information gathered, particular programs watched, the extent
to which these pieces of information conflicted with each other, and so on. In contrast,
respondents who gathered information from relevant books had less ambiguous perceptions.
Importantly, it must be noted that we should interpret the results on information just as
correlations with perceptions, and not as causalities, because the parameters might suffer fromself-selection biases – those who perceived larger or more ambiguous risks might want togather information more actively. On the other hand, we should also note that excluding
information variables causes omitted variable biases. Compare columns (1) and (2); theparameter on unknown increases in both models when information variables are excluded.
Taking the positive parameters on the popular media in column (1) into account, this upwardbias is caused by positive correlations between unknown and information gathering (see Table5). While these correlations seem to be counterintuitive as people should have gathered
information to make up for their lack of knowledge, the result is not surprising because theirunfamiliarity to radioactivity might have been amplified through information gathering in thesituation mentioned in section 2. The increase of the parameter on other effects would suggestthat gathered information makes people more conscious of the other health effects. Also, deconarea is positively correlated with information variables, and its parameter increases in column(2).

Table V. Correlations between Information and Other Variables

7. CONCLUSION
This study developed new simple methods to elicit and analyse ambiguity in public risk
perception and applied them to the problem of radiation exposure in Fukushima, which is a real
uncertain problem. The empirical analyses suggested a potential for the expansion of the workby Slovic (1987) and of other works investigating the influences of socioeconomic factors on
risk perception. The results suggesting that usage of popular risk information media relates tomore negative and ambiguous perception seem to reflect reality in the given case, namely, thedelay in sharing scientific knowledge pertaining to the health effects of radiation exposure,conflicting scientific beliefs regarding the effects of low-dose exposure, the shortage of
epidemiological evidence, conflicting public information, false rumours, and so on. Because of
these factors, the popular media could not exclude imprecise or conflicting information.
Our methodology is applicable for any unknown matters for which people cannot easily
estimate precise values, such as probabilities for outcomes that rarely happen or have neveroccurred, willingness-to-pay for non-market goods, and so on.
We hope that this method will be applied in the future studies and that its potential drawbacks
will be clarified and improved. For example, a clear drawback in our survey is that the medianand range might systematically correlate to each other, because the ranges of the alternatives in
Figure 5 were designed to become gradually larger on the basis of the risk ladder (nevertheless,the ladder itself would provide appropriate information in predicting the rate of new mortalityrisk, as it was constructed from real mortality data). Was the similarity between estimation
results of the median and range models caused by this systematic correlation? Prior to that point,
does the range or something else indicating ambiguity generally have a positive relation withthe central tendency (median or mean)? To examine these questions, we propose to attempt toelicit risk perceptions in a gradually wider form like figure 5 for a part of sample and in an equalinterval form for another part in order to compare the estimation results between them for futureapplications.

ACKNWLEDGEMENTS
This study was carried out as a part of “Monetary Evaluation of Mitigation Measures for the
Fukushima Daiichi Accident,” a research project commissioned by the Ministry of Education,
Culture, Sports, Science and Technology.

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Yamagata
Prefecture

MiyagiPrefecture

Evacuation Area

Fukushima Daiichi
nuclear power plant

20km
Fukushima
Prefecture
Fukushima Daini
nuclear power plantTochigi
Prefecture

Ibaragi
Prefecture

Note: This map was drawn using Kenmap, a blank map drawing software. The evacuation area
consisting of the ‘restricted zones’ and the ‘deliberate evacuation zones’ is coloured dark. From
April 2012, this zoning was re-examined and re-designated into five categories: (i) the
conventional ‘restrictive zones’ which the general public is prohibited from entering, (ii) the‘deliberate evacuation zones’ where evacuation is requested, (iii) zones where the return ofevacuees will be difficult for a long time (the exposure dose is expected to exceed 50 mSv/year),(iv) zones where habitation is restricted (20-50 mSv/year), and (v) zones where cancelling of
evacuation order is prepared (less than 20 mSv/year).
Figure 1. Location of the Fukushima Daiichi Plant

Evacuation Area

Fukushima Prefecture

Fukushima
Daiichi nuclear
power plant
Fukushima
Daini nuclear
power plant

Note: This map is adapted from the Extension Site of the Distribution Map for Radiation Dose, a website published by
the Japanese Government (http://ramap.jmc.or.jp/map/eng/). The evacuation area was not covered in the survey.
Figure 2. Objective Area and Radiation Dose Distribution (Air Dose Rate (μSv/hour))Explanation 1: Change of the Legal Standard on Radiation Exposure Dose
Before the accident, other than natural and medical exposures, the maximum allowable radiation dose forthe general public was 1 mSv/year in Japan. This standard was based on the recommendation of theInternational Commission on Radiological Protection (ICRP), a committee establishing international
standards for radiation protection, according to which the reference levels for normal exposure situations
should be set to 1 mSv/year or less.
After the accident, the legal standard was changed to 20 mSv/year or less. This change was also based on
the ICRP’s recommendation that reference levels for emergency exposure situations should be set in theband of 20-100 mSv/year. In April 2011, the national Nuclear Safety Commission (corresponding to thepresent-day Nuclear Regulation Authority) suggested the government should adopt the minimum value ofthe band as the maximum allowable dose for the general public.
Explanation 2: Goals of Decontamination Projects
The ICRP also recommended that the reference levels for long-term post-accident situations should be set
to 1-20 mSv/year. The present decontamination projects target reducing the contamination to its minimum
level (1 mSv/year) as a long-term goal. In order to achieve that (i) the national government is to initiatively
implement decontamination in zones where the additional exposure dose is expected to exceed 20 mSv/year,
and (ii) under technical and financial support from the government, each municipality is to plan andimplement decontamination in zones such that the additional exposure dose to be 1-20 mSv/year).
The above explanations cite concrete values, namely 1 or 20 mSv. Even such levels of exposure may raise thepossibility of carcinogenesis. Please predict how much it rises.

Figure 3. Explanations before the Risk Perception Question

The rate and frequency of each cause of death in Japan in 2009 were as follows. Refer to this while making
your prediction.

100%

Cause of death: 30.12%00 (per million deaths)

Cancer

: 30.12%00 (301,207 deaths)

Heart disease: 15.82%00 (158,156 deaths)

Cerebrovascular disease : 10.71%00 (107,087 deaths)
10%

1%

0.1%

0.01%

0.001%

Pneumonia: 09.80%00 (098,012 deaths)

Senility: 03.38%00 (033,846 deaths)

Suicide: 02.68%00 (026,840 deaths)

Traffic accident: 00.43%00 (004,297 deaths)

Tuberculosis1: 00.20%00 (002,008 deaths)

Fire accident: 00.17%00 (001,653 deaths)

Work-related accident: 00.094%0 (000,941 deaths)

Influenza: 00.055%0 (000,547 deaths)

Homicide: 00.042%0 (000,417 deaths)

Natural disaster2: 00.010%0 (000,101 deaths)

AIDS1: 00.0056% (000,056 deaths)

0.0001%* Each rate was calculated on the basis of the Demographic Statistics in Japan, Statistical Handbook of Japan,
Survey on Industrial Accidents in Japan, data of the Fire and Disaster Management Agency, and
Demographic Yearbook (United Nations).
Note 1: The rates for tuberculosis and AIDS (Acquired Immunodeficiency Syndrome) are for 2008.
Note 2: The number of deaths by natural disaster varies greatly every year. The number in 2009 is theapproximate average yearly value.

Figure 4. Risk LadderQ. To what extent will cancer mortalities per million people increase due to an additional dose of 1 mSv otherthan natural and medical exposures? Choose an appropriate alternative from the following list for both yourlowest and highest estimates.
Lowestestimate

Highestestimate

nobody (the rate will not rise)

1

1

more than 000,000 person, but 56 people or less (the same applies hereafter)2

2

more than 000,056 people: AIDS

3

3

more than 000,101 people: Natural disaster44more than 000,417 people: Homicide

55more than 000,547 people: Influenza

66more than 000,941 people: Work-related accident

7

7

more than 001,653 people: Fire accident

88more than 002,008 people: Tuberculosis

99more than 004,297 people: Traffic accident

10

10

more than 026,840 people: Suicide1111

more than 033,846 people: Senility

1212

more than 098,012 people: Pneumonia

13

13

more than 107,087 people: Cerebrovascular disease

14

14

more than 158,156 people: Heart disease

15

15

more than 301,207 people: Cancer not caused by radioactive contamination

16

16

Figure 5. Risk Perception Question (for an additional dose of 1 mSv)

Special contamination area

Intensive contamination
survey areas

Note: This map is adapted from the Decontamination Information Plaza, awebsite published by the Japanese Government and Fukushima Prefecture(http://josen.env.go.jp/en/). Decontamination in the special contamination
area and the intensive contamination survey areas is planned andimplemented by the government and the concerned municipality
respectively.
Figure 6. Target Municipalities for Decontamination

Table I. Comparison with Official Statistics for the Socioeconomic Characteristics ofFukushima Residents
Official statistics
Frequency%
Gender15 years and over (n = 1,740,909)
M ale
978
(58.5)
835,901(48.0)
Female694(41.5)
905,008(52.0)
Age
15 years and over (n = 1,740,909)
Less than 20 years old
7(0.4)
101,390
(5.8)
20s
124
(7.4)
193,177(11.1)
30s
425(25.4)
249,957(14.4)
40s
510(30.5)
243,861(14.0)
50s
419(25.1)
293,886(16.9)
60s
150
(9.0)
273,682(15.7)
70s
35(2.1)
221,226(12.7)
80 years and over2
(0.1)
163,730(9.4)
Sample mean
45.3 years
51.7 years
Number of household members
General households (n = 719,441)
1 person218(13.0)
188,617(26.2)
2 people440(26.3)
185,294(25.8)
3 people377(22.5)
135,403(18.8)
4 people381(22.8)
108,945(15.1)
5 people142(8.5)
50,887(7.1)
6 people80(4.8)
28,708(4.0)
7 people
22(1.3)
14,438(2.0)
8 people
9
(0.5)
5,076
(0.7)
9 people
2
(0.1)
1,478
(0.2)
10 people or more
1
(0.1)
595
(0.1)
Sample mean
3.1 people
2.8 people
Housholds with two or more persons
Family income(n = 890)
x < 2 million yen
180(10.8)
33(3.7)
2 million ≤ x < 4 million yen
421(25.2)
230(25.8)
4 million ≤ x < 6 million yen
449(26.9)
243(27.3)
6 million ≤ x < 8 million yen
335(20.0)
168(18.9)
8 million ≤ x < 10 million yen
162
(9.7)
94
(10.6)
10 million ≤ x < 15 million yen
102
(6.1)
84
(9.4)
15 million ≤ x < 20 million yen
13
(0.8)
23
(2.6)
20 million yen ≤ x
10
(0.6)
15
(1.7)
Note: Official statistics for gender, age, and number of household members are sourced from the Pupolation Census in2010 . Official statistics for family income are sourced from the National Survey of Family Income and Expenditure in2009 .
This sample (n = 1,672)
Frequency%

Table II. Frequency Distribution of Risk Perceptions

Interval alternatives≤ π = 0 (nobody)
0.000001 ≤ π ≤ 0.000056
0.000057 ≤ π ≤ 0.000101
0.000102 ≤ π ≤ 0.000417
0.000418 ≤ π ≤ 0.000547
0.000548 ≤ π ≤ 0.000941
0.000942 ≤ π ≤ 0.001653
0.001654 ≤ π ≤ 0.002008
0.002009 ≤ π ≤ 0.004297
0.004298 ≤ π ≤ 0.026840
0.026841 ≤ π ≤ 0.033846
0.033847 ≤ π ≤ 0.098012
0.098013 ≤ π ≤ 0.107087
0.107088 ≤ π ≤ 0.158156
0.158157 ≤ π ≤ 0.301207
0.301208 ≤ π ≤ 0.698793
Total
Sample mean of approximate median
Sample mean of approximate range(Reference) Estimated rate based on
the linear no-threshold model

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.

Cancer mortality rate raised byan additional exposure dose of 1 mSv
Lowest prediction
Highest prediction
153(18.9%)
44(5.4%)
210(26.0%)
131(16.2%)
92(11.4%)
67(8.3%)
86(10.6%)
96(11.9%)
19(2.3%)
37(4.6%)
52(6.4%)
48(5.9%)
20(2.5%)
34(4.2%)
20(2.5%)
26(3.2%)
27(3.3%)
39(4.8%)
35(4.3%)
61(7.5%)
23(2.8%)
39(4.8%)
10(1.2%)
20(2.5%)
10(1.2%)
29(3.6%)
9(1.1%)
34(4.2%)
9(1.1%)
10(1.2%)
34(4.2%)
94(11.6%)
809 (100.0%)809 (100.0%)
0.051887 (s.d. 0.120695)
0.054317 (s.d. 0.122194)
0.000050 (s.d. 0.000000)

Cancer mortality rate raised byan additional exposure dose of 20 mSv
Lowest prediction
Highest prediction
109(12.6%)
28(3.2%)
174(20.2%)
82(9.5%)
112(13.0%)
79(9.2%)
97(11.2%)
87(10.1%)
27(3.1%)
42(4.9%)
53(6.1%)
48(5.6%)
38(4.4%)
37(4.3%)
25(2.9%)
33(3.8%)
45(5.2%)
47(5.4%)
48(5.6%)
77(8.9%)
40(4.6%)
57(6.6%)
17(2.0%)
31(3.6%)
14(1.6%)
45(5.2%)
17(2.0%)
32(3.7%)
16(1.9%)
22(2.5%)
31(3.6%)
116(13.4%)
863 (100.0%)863 (100.0%)
0.059967 (s.d. 0.121117)
0.066261 (s.d. 0.130128)
0.001000 (s.d. 0.000000)

Table III. Independent Variables

Variables
Exposure dose
d20mSv
Images for radioactivity
unknown
dread
Perception for other health effects
other effects
Socioeconomic characteristics
decon zone
femaleagehigh income
number of children
Information sources
TV/newspaperinternet/SNS
neighbours
magazinebookhearing meeting/symposium

Definition

Total

M ean
Decon zone Decon zone=0=1

= 1 if asked to predict the effect of 20 mSv or = 0 if 1 mSv

0.516

0.521

0.511

= 1 if thinking that radioactivity is an unfamiliar and mysterious thing= 1 if thinking that radioactivity is somehow a terrible thing

0.219
0.166

0.204
0.155

0.232
0.175

= 1 if thinking that there may be other health effects besides cancer

0.847

0.803

0.887

= 1 if knowing that his or her residence is located in a zone planned for decontamination,= 0 if knowing that the residence is not located there or not knowing either way= 1 if femaleage (years)= 1 if family income is 6 million yen or morenumber of children aged 6 years or less (people)

0.523

0.000

1.000

0.415
45.3
0.372
0.20

0.419
44.7
0.335
0.18

0.412
45.8
0.406
0.21

= 1 if watcing relevant TV programs/news and reading newspaper articles
0.550
0.475
0.619
= 1 if gathering with internet and social network services
0.292
0.234
0.344
= 1 if hearing from the neighbours
0.151
0.107
0.191
= 1 if reading relevant articles of magazines
0.111
0.058
0.160
= 1 if reading relevant books
0.071
0.040
0.098
= 1 if participating in relevant public hearing meetings and symposiums
0.070
0.040
0.097
Sample size
1,672
798
874
Note: The threshold of high income stems from the fact that the average family incom in Fukushima was 6.482 million yen according to the National Survey of Family
Income and Expenditure in 2009 .

Table IV. Estimation Results of Median and Range Models
M edian model(1)(0.335) ***-4.639(2)(0.331) ***Range model(1)(0.337) ***-4.105(2)(0.332) ***0.240(0.041) ***

0.137
0.213

(0.051) ***(0.057) ***0.641(0.061) ***

0.156
0.146
0.069
-0.1920.029(0.041) ***(0.043) ***(0.085)(0.043) ***(0.041)

Constant-4.478-3.969Exposure dose
d20mSv
0.242 (0.040) ***0.257 (0.039) ***0.222 (0.041) ***Images for radioactivity
unknown
0.061 (0.051)
0.097 (0.050) **0.094 (0.052) *dread
0.193 (0.058) ***0.201 (0.057) ***0.200 (0.058) ***Perception for other health effects
other effects
0.566 (0.057) ***0.642 (0.056) ***0.559 (0.062) ***Socioeconomic characteristics
decon zone
0.099 (0.041) **0.149 (0.040) ***0.104 (0.043) **female0.123 (0.043) ***0.129 (0.042) ***0.132 (0.044) ***ln(age)0.210 (0.085) **0.269 (0.084) ***0.015 (0.087)
high income-0.304 (0.042) ***-0.288 (0.042) ***-0.211 (0.044) ***number of children-0.001 (0.039)
0.027 (0.038)-0.001 (0.042)
Information sources
TV/newspaper
0.187 (0.043) ***－0.197 (0.045) ***internet/SNS
0.222 (0.046) ***－0.259 (0.047) ***neighbours
0.119 (0.058) **－0.248 (0.057) ***magazine
0.052 (0.070)
0.008 (0.072)－
book-0.107 (0.085)－-0.165 (0.090) *hearing meeting/symposium
0.023 (0.079)-0.069 (0.087)－
Log likelihood-4771.1-4792.0-3613.6
Sample size
Note: Standard errors are shown in parentheses. ***, **, and *: significant at 1%, 5%, and 10% respectively.

－
－
－
－
－
－
-3640.3
1,672

Table V. Correlations between Information and Other Variables

TV/newspaperinternet/SNS
neighbours
magazinebookhearing meeting/symposium

unknown
0.11230.04510.1004
0.09790.01230.0135dreadother effects decon zone
0.02450.19320.14460.03950.09030.12090.07310.10480.11810.00090.08700.1629-0.0223
0.05230.1137-0.0150
0.02550.1119female0.0589-0.0549
0.0726-0.0471-0.0189-0.0265

agehigh income number of children
0.07240.04350.07200.01170.01480.04580.00080.0364
0.09640.07230.0488-0.0177
0.00220.04290.05850.10690.08020.0458