I

ArticlesA Risk Economic
Approach to Nuclear
Power Generation
Are We Really “Strong in the Rain”?

Yasuhiro Sakai

Shiga University / Professor Emeritus“Strong in the Rain”:

Fukushima and Chernobyl

The purpose of this paper is to carefully discuss the problem of nuclear power generationfrom the viewpoint of the economics of risk
and uncertainty. In recent times, we have experienced the two major nuclear plant crises ─
Chernobyl in 1986 and Fukushima in 2011.
Those crises have repeatedly reminded us of thedangers of reactor explosions and their consequences such as radioactive soil, polluted areas
and abandoned towns. It is quite unfortunate,however, that risk-economic studies in nuclear
power generation have been amazingly rare although the economic theory of risk anduncertainty have been developed well since
Daniel Bernoulli, J.M. Keynes and Frank H.
Knight. Presumably, this paper is a bit ambitious attempt to fill in such a regrettable gap.
Kenji Miyazawa (1896-1933) is a very popular
Japanese writer who spent his whole life in
Iwate Prefecture, one of the stricken areas of
the 2011 Great East Japan Disaster. Out of his
famous poem “Strong in the Rain,” let us write
down some leading sentences of Miyazawa(1931):“ Strong in the rain.
Strong in the wind.
Strong against the summer heat and wintersnow.”In 11 March 2011, Japan experienced a tremendous trauma ; a massive earthquake ,followed by a big Tsunami and a tragic nuclear
disaster. As is seen in Miyazawa’s poet, some of
the Japanese people might be strong in the rain
and the wind, and also strong against the sum-

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mer heat and winter snow. We must point out,
however, that the 2011 East Japan Earthquake
demonstrated the scale of the disaster which
was perhaps beyond the bounds of Miyamoto’imagination. What was once regarded as unthinkable is now a thinkable reality.1)
George A. Bonnano (2011), a noted journalist, wondered how much trauma Japan could
take in the Fukushima nuclear disaster, andwrote the following impressive report in the
Newsweek, a world-famous journal: “First Japan was hit by a triple whammy. The countryof 127 million has just endured one of the largest earthquakes in recorded history, followed
by a shockingly voracious tsunami. ...... If only
the damage had stopped there. When thedeadly combo of earthquake and tsunami
breached the protective barriers and engulfed
one of Japan’s oldest nuclear power plants, a
nuclear nightmare began, one that at this point
has shown no clear signs of ending.” (Bonanno(2011), p. 8) 2)
Five years have passed since the Fukushima
nuclear accident. As McCurry (2016) has noted, those five years on, cleanup of Fukushima’s
reactor remains a far distant goal. Interestingly
enough, perhaps to the ears of non-Japanesepeople, Fukushima might sound like Hiroshima, the place in which the first atomic bomb
was dropped over a great number of innocent
residents. It is recalled that another nuclear accident, even worse than the Fukushima disaster,
took place in Chernobyl, the Ukrainian Soviet
Republic, on 26 April 1986. When Japan still
struggled with its nuclear disaster, Robin McKie (2011), a noted British reporter, returned tothe scene of the 1986 reactor explosion andfound many evils such as radioactive soil, abandoned towns, and polluted lakes. Another five
1) Birmingham and McNeill (2011), well-known report-

age writers, have offered the reader many interesting stories concerning the relation between Kenji Miyamoto
and the Fukushima disaster.
2) For a detailed discussion on the relation between

years have passed. On the 30th anniversary of
the nuclear accident, we can still eyewitness
many traces of the Chernobyl disaster. Surrounded by barbed wire, completely
abandoned by men, the Chernobyl exclusionzone may be regarded as a sort of hell. Authorities are said to make reconstruction plans
beyond the 21st century.3)
The contents of this paper are as follows,
Section 2 will discuss the role of risk and/or
uncertainty in economics. Section 3 will deal
with the traditional expected utility theory under risk and its economic applications. In
Section 4, we will attempt to adopt a risk-economic approach to nuclear power generation,with a comparison of the two opposing views,
the pros and cons of “the peaceful use of nuclear energy.” Section 5 will turn to the world ontrue uncertainty, with a discussion of the selection problem of appropriate projects. Finalremarks will be made in Section 5.

II

The Place of Risk andUncertainty in Economics

2-1. Individual Decision Making
under Risk: The General Framework
Let us consider the problem of individual decision making in the presence of risk. Its
general framework may be depicted in Table 1.
The set of possible choices is denoted by therow (a1, ..., ai, ..., am), and the set of possible
states of the world by the column (s1, ..., sj, ...,sn).4)Let us take a look at Table 1. When the individual has chosen a specific choice ai, and when
the nature reveals a specific state sj, we will havethe specific outcome that is represented by the3) See Oliphant (2016).
4) For the economic thought of risk and uncertainty

with a focus on the expected utility theory, see Sakai(1982,1991,2010).

risks and daily lives, see Sakai(1991, 2006). Also see Taleb (2007).

A Risk Economic Approach to Nuclear Power Generation

Yasuhiro Sakai

177element yij (i = 1,.., m ; j = 1,..., n). All the
combinations of those elements form the outcome matrix (yij). The probability that any
particular state sj actually occurs is denoted by
pj. Note that pj ≧ 1 for each j and Σj pj = 1.
When we face the payoff matrix as shown in
Table 1, we have to do the best possible judgment subje ct to the te chnolog ical andinformational constraints. Which is a better
allocation for the thermal power plant, in thecity or in the country? Let us introduce a particular form of judging criterion. Presumably,
the most popular criterion is provided by the
expected utility rule, which was first introduced
into human science very long time ago by Daniel Bernoulli (1738).5)
For any i = 1,..., m, let us define the expectedutility level of a choice ai as EUi = ∑j pj U (yij ).
Then we can state the expected utility rule as
one by which we select the act yielding the
maximum value among those expected utilities
EU1,..., EUi,..., EUm . Therefore, we find thefollowing formula:
Max i EUi = Max i {∑j pj U( yij)}.

(1)

Table 2 The allocation problem of a thermal
power plant: The city or the country?

alternative
choicestates of the world
non-accident
accidentstates of the world
…
…
sj

sn

a1

y11

…

y1n

the city2–2

the country

1

–1

yin

probability

1–p

p

…
yij

…

…

…

…

yi1

…

…

ai

y1j

…

…

s1

…

alternative
choice…

Table 1 The individual decision making underrisk: The general framework

2-2 The Allocation Problem of a
Power Plant
As an interesting application of the generalframework of individual decision making, let
us consider the allocation problem of a thermal
power plant. In order to meet additional electricity demand, suppose that we are going toconstruct a new thermal power plant. As isseen in Table 2, assume that there are two allocation choices available: the densely populated
city or the depopulated country. The thermal
power plant is not an absolutely safe facility
and may break down because of an accident.
There are two states of the worlds: The state of
non-accident and the one of accident, with therate of accident being p.
The construction of a thermal power plant in
the city instead of the country represents thecase of “high return and high cost”. On the one
hand, if no accidents occur at all, residents canenjoy the benefit of a shorter distance from thepower supply site to the power demand place :the transportation cost would be less. We assume that the payoff of the pair (the city, nonaccident) is as great as 2 (see Table 2). On theother hand, the thermal power plant may pro-

am

ym1

…

ymj

…

ymn

probability

p1

…

pj

…

pn

5) The general framework of individual decision mak-ing under risk and uncertainty, was systematically discussed by Sakai (1982).

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duce air pollution and noise in theneighborhood. Moreover, if an accident occurs
in the crowded city, the resulting damage
would be very serious. Hence the payoff of thepair (the city, accident) must be a negative value, say (–2).
The construction of a thermal power plant in
the sparsely populated countryside will give usa different story: In fact, we will enter theworld of “low return and low cost”. In the caseof non-accident, the net benefit will surely bepositive yet small because the power transmission to the consumption area will not be so
expensive: The payoff is assumed to be 1. In
the case of accident, the resulting damage
would be relatively small: The payoff is (–1).
We are ready to apply the expected utility
rule to the allocation problem of a power plant.
The levels of expected utility attainable fromthe power plant in the city and in the country
are respectively given as follows:
EU (city) = (1–p) U (2) + pU (–2),
(2)
EU (country) = (1–p ) U (1) + pU (–1). (3)The allocation problem of a thermal power
plant is depicted in Figure 1. For the sake ofpresentation, let us intentionally put p = 1/5,
which is a larger value than usual. Then the
point J on the line segment BC, and the point
K on the line segment DE respectively indicate
the value of EU(city) and EU(country). Notethat BJ : JC = DK : KE = 4 : 1. Since J is located higher than K, we can conclude that the city
is a better plant cite than the city. Needless tosay, the opposite conclusion would come if K is
located higher than J, which is another possible
conclusion under other circumstances.

Fig. 1 A graphical interpretation of the allocation
choice of a thermal power plant

III Nuclear Power Generation:
Economic andPsychological Factors

3-1. The Two Opposite Views:
Pro and Con
We are now in a position to discuss the problem of nuclear power generation, which is avery sensitive and even political issue and has
been more or less neglected in the literature.
For instance, around 40 years ago, Kikuo Iwata(1981), then a rising star in Japanese economics
profession, frankly remarked with embarrassment: “I have so often been asked: ‘What domodern economists think of nuclear power
generation? What on earth are they doingright now?’ Alas, modern economists gave up
the idea of raising such an question per se. Thismight represent a sort of academic sabotage byirresponsible persons.” (Iwata (1981)) 6)
Iwata was not the only person to be blamedfor keeping us from the problem of nuclear
power generation. While Diamond and Rothschild (1978) was an excellent collection of
6) As of 2017, Kikuo Iwata serves as one of the vice pres-idents, the Bank of Japan. Time flies like an arrow!

A Risk Economic Approach to Nuclear Power Generation

Yasuhiro Sakai

179influential papers in the field of risk and uncertainty, none of the selected papers did notseriously discuss the possibility of nuclear power accidents. I myself was also to be blamed in
my earlier papers (see Sakai (1982)), but later
could successfully deal with the issue of nuclear
power generation from the viewpoint of risk
and uncertainty.7)
There are two opposing views on the efficiency and safety of nuclear power generation: thepositive view and the negative view. Before theGreat East Japan Earthquake took place in2011, the majority of the Japanese took the positive view. In fact, many people believed in the“myth of absolute efficiency and absolute safety”.
The second negative view was initially taken
by a limited number of scientists including
Takagi (1986) and Koide (2011). It has become
more popular since the 2011 Fukushima disaster. The myth of absolute safety is now almost
gone. The question whether and to what extent a nuclear power plant is economical,
however, remains a very controversial one, requiring the collection of more reliable data as
well as more interdisciplinary analyses. Not
only economic factors but also psychologicaland cultural factors must be taken into consideration.
Let us suppose that there are three types ofpower generation; nuclear, thermal or hydro.
We start our inquiry with the positive view.
Table 3 indicates the list of the technical cost of
power generation, which was officially announced by the Japanese Ministry of Economy,
Trade and Industry in 2010, just one year before the Fukushima Disaster. According to this
METI data, nuclear power is the most economical among the three (exactly, 5 to 6 yen

Table 3 The technical cost of power
generation (officially announced):
The positive view by the METI (2010)
Type of power generation
NuclearPower generation cost(¥/kWh )5~6

Thermal

7~8

Hydro

8 ~ 13for kilo watt hour), followed by Thermal, andHydro the most expensive. Since METI has
been strong and influential in the Japanese society, the conclusion that nuclear is the best
type of power generation has been more or lesstrusted by the majority of people for a longtime.
Let us turn to the negative view. Professor
Kenichi Ohshima (2011), an independent andenergetic researcher, has conducted a morecomprehensive inquiry than METI, having
come to an entirely opposite conclusion. His
method of analysis and acquired data can clearly be seen in Table 4. According to his
opinion, the real cost of nuclear power generation should be the sum of the direct technicalcost a la METI, the policy cost, and possibly
the environmental cost. The policy cost is calcu late d a s the sum tota l of a l l R & D
expenditures and the site location expenditures
including all subsidies necessary for the site
promotion to the local residents. The environmental cost includes all expenditures associatedwith environmental damage caused by the construction of power generation facilities.
Among those costs, Ohshima characteristicallyemphasized the importance of the policy cost,which was quite outside what the METI people had calculated , and succeeded in making

7) See Sakai (2004, 2006). While Arrow (1970) was amonumental work in the economics of risk and uncertainty, he did not discuss the economics of nuclear energy.

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Table 4 to show his own list of the comprehensive cost for each type of power generation.
As can immediately be seen in Table 4, theintroduction of the new policy cost was quite
effective in the calculation of the comprehensive cost of power generation. In fact, the total
cost of nuclear power generation was calculated as 10.25 yen for kWh, which clearly exceeded
the thermal power (9.91¥/kWh) and the hydropower (7.19 ¥/kWh).
As Ohshima himself has noticed, the list of
direct and policy costs enumerated in Table 4
is certainly less than perfect. Indeed, there remain still missing items that must be taken into
account for the sustainable operation after theconstruction of power plants. One of thosemissing items is what we may call the backend
cost, which mainly consists of the expenditurenecessary for reprocessing and safekeeping radioactive wastes. And still another item to bementioned is the expenditure needed to carefully handle the phase-out process of nuclear
power. Remarkably, such a phase-out process
may be involved in a series of many difficultand long processes that no one may exactly
foresee. Besides, if any radioactive leakage occurs, then many residents will have to be
evacuated from the local area; the resulting expenditures for e conomical and menta lcompensations, hospitals, and possibly civil trials would be incalculably huge.

3-2. Psychological Factors: Their
Effects on Payoff Matrixes andProbabilities
Let us now introduce several non-economic
and psychological factors into our model analysis of power generation. For simplicity, there
are only two choices of the type of power
plants: namely, thermal and nuclear. Besides,
there are also two opposite views on the analysis ─ the positive view and the negative view.
Those views can easily be modeled in Table 5:
the positive view in the Upper Panel (A) andthe negative view in the Lower Panel (B).
Let us begin to take a look at Panel (A). We
would naturally expect that the rate of accident
differs between the two types of power plants.
Let us respectively denote the accident rate of athermal power plant and the one of a nuclear
power plant by p and q . According to the official view of the government authority, “going
nuclear" is much safer than "going thermal," sothat q is much lower than p, perhaps near zero .
We suppose that p = 1/5 and q = 1/10. It isneedless to say that local residents and liberalscientists may have serious objections against
such an optimistic view.
We assume that the thermal power plant
gives all the persons concerned (both the optimists and the pessimists) the solid payoff 2 if
no accidents occur, and the small loss (–1) if an
accident occurs. Besides, we also assume that

Table 4 The comprehensive cost of power generation(independently reevaluated): The negative view by K. Ohshima (2011)
Type of power generation Direct cost
NuclearThermal
Hydro

8.53
9.87
7.09

A Risk Economic Approach to Nuclear Power Generation

Policy cost
R & D cost Site subsidy
1.46
0.26
0.01
0.03
0.08
0.02

Yasuhiro Sakai

Total cost
10.25
9.91
7.19

181

the reliability of the thermal power plant, therate of accident p is largely objective and commonly shared by all the persons; therefore,
there are no special psychological factors working behind.
The difference of positions between the optimists and the pessimists appear when thereliability question of nuclear energy is on theagenda. According to the optimists or the people having the positive view, “going nuclear” ismuch more efficient than “going thermal”. After all, they are all strong believers of the “mythof nuclear energy”; the rate of nuclear accident
may be regarded as substantially zero. It is thereliability question of nuclear energy is on theagenda. According to the optimists or the people having the positive view, “going nuclear” ismuch more efficient than “going thermal”. After all, they are all strong believers of the “mythof nuclear energy”; the rate of nuclear accident

Table 5 The two opposite views of nuclear
power generation: How to deal withpsychological factors(A) The positive view
Payoff (probability)

Type of power
Psychological
generation
non-accident accident factors
Thermal

2
(1–p)

–1
(p)

none

Nuclear

4
(1–q)

–2
(q)

absolute safety(q is near zero)(B) The negative view
Type of power Payoff (probability) Psychological
generation
non-accident accident factors
Thermal2(1–p)

Nuclear

2
(1—q)

182

–1
(p)

none

–(4+α) unknown and(q)dreadful risks

may be regarded as substantially zero. It is assumed here that the nuclear power guarantees
4 unit of money, a handsome amount of gain,in the case of non-accident, whereas it may
yield (–2), a manageable amount of loss, in thecase of accident.
The whole situations would be drasticallychange if the local people decide to take thenegative or critical view. In a sense, “the windagainst nuclear” would blow strongly. The
people are no longer believers in the nuclear
myth, but are really concerned with the “nuclear enigma” which can be neither measurable
nor predictable. As is seen in Panel (B), there
are strong psychological and cultural factors
working behind. Although a nuclear power
plant can yield 2 unit of money when no accidents take place, it will cause a huge andperhaps non-measurable amount of loss shownby minus (4+α) unit when an accident occurs.
Presumably, the “plusαfactor” represents thenon-measurable dimensions of unknown anddreadful damages.

IV A Generalization of the

Expected Utility Theory:
J.M. Keynes andFrank Knight

In the above, we have intensively discussed
the effects of psychological factors on decision
making under risk. How to deal with thosefactors is really a controversial question. Since
there are the two opposing views of nuclear
power generation, it seems clear that a mere application of the traditional expected utility
theory a la Daniel Bernoulli does not work atall. In the history of economic thought, there
are several economists who had serious doubts

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about the applicability of the traditional Bernoulli principle. Among those economists are
J. M. Keynes and Frank Knight. Keynes (1936)
once remarked: “Human decisions affecting
the future, whether personal or political or economic, cannot depend on strict mathematical
expectation, since such calculation does not exist.” (Keynes (1936), pp.162-163) It would behigh time for us to establish a more ambitious
theory ─ a sort of generalized expected utility
theory a la Keynes and Knight ─ by appropriately incorporating psychological and cultural
factors into our theoretical framework.
In what follows, let us adopt a generalized
expected theory. Within such an expanded
framework, the utility function U is no longer
a function of one variable x such that U = U (x),but a more complicated function of a variable
x and a parameter β so that U = U (x ; β). The
new parameter β measures the degree of human sentiments, which may go in both ways ─negative or positive. Presumably, the presenceof fear or unknown risk would shift a person’sutility curve downward, whereas the optimistic
sentiments such as animal spirits would shift
the curve upward. When we evaluate the frequency of risky events, what matters is not theobjective probability p per se, but rather its
subjectively weighted value ω(p) filteredthrough a certain subjective filter ω. On the
one hand, when the local residents feel uneasy
about unknown and dreadful risks associatedwith nuclear generation, they may not totallytrust the officially announced accident rate, sothat the weighted value ω(p) tends to be higher
than p per se. On the other hand, as far as they
believe in the myth of absolute safety, they tend
to regard the accident rate p as near zero.

It should be noted that our generalized expected utility theory is even more general thanthe prospect theory of Kahneman and Tversky(1979). While they have newly introduced “theweighted filter of probabilities” into the traditional expected theory, we go even beyond
their approach in that we take account of “thepossibility of lower or upper shifts in the utility
function.” After all, there should be many other ways in which we can extend any existing
theory.8)
We are now in a position to get back to Table
2 in which the two opposite views of nuclear
generation are presented in the form of tables.
First of all, according to the positive view, theweighted values WV of the two power plants
─ thermal and nuclear ─ are provided in thefollowing manner:
WV (thermal) = ω(1–p) U(2 ; β)+ ω(p) U (–1 ; β),(4)

WV (nuclear) = ω*(1–q) U(4 ; β*)+ ω*(q) U (–2 ; β*).

(5)Fig. 2 evidently demonstrates the positive
view indicated by Panel (A). For the sake ofgraphical convenience, we put p = 1/5, which
is definitely larger than the real value. Since no
special psychological factors are considered forthe thermal power generation, no special attentions of the weighted filter of probabilities arenecessary, so that we should have ω(p) = p forany p. Therefore, for the case of the thermal
power generation, Eq. (5) may be simplified asfollows:
WV (thermal) = (4/5) U(2 ; β)+ (1/5) U (–1 ; β),(4*)8) Also see Kahneman, Slovic & Tversky (1982), Michel-

Kerjan & Slovic (2010). Akerlof & Shiller (2009) is aninteresting book which deals with the question how human psychology drives the economy and why it mattersfor the market economy.

A Risk Economic Approach to Nuclear Power Generation

Yasuhiro Sakai

183

The case of nuclear power generation requires a different treatment from the one ofthermal power generation. While the weighted probability filters should be considered
here, the myth of absolute safety leads to thesimplification of q = 0. Hence for the case of
nuclear generation, if we note that ω*(1) = 1
and ω*(0) = 0, Eq. (6) may be overly simplified
as follows:
WV (nuclear) = ω*(1) U (4 ; β*)+ ω*(0) U (–2 ; β*) = U (4 ; β*).

(5*)

According to the positive view, the midpoint
M lying on the line segment BC stands for thevalue of WV (thermal), whereas the end point
D on the line segment DE indicates the valueof WV (nuclear). Because the point D is located higher than the point M, the value of WV(nuclear) is greater than the one of WV (thermal). Therefore, the optimists can tell us that“going nuclear” is the best policy conceivable.

Fig. 2 The positive view184

Now let us turn to the negative view, whichis graphically presented in Fig. 3. This figure isapparently more complicated than Fig. 2, andthus requires a more careful analysis than before. As far as the thermal power generation,
there should be no fundamental difference between the negative and positive views. Henceas before, the midpoint M on the line segment
BC indicates the value of WV (thermal).
When we are dealing with the nuclear power
generation, however, the negative view is definitely at variance with the positive view. The
critical people do not believe in the myth of
nuclear energy. Even if no nuclear accidents
occur, the payoff we can obtain is no longer
four unit , but merely two unit; which is thesame amount of money we can get from thethermal power generation. Besides, the nuclear
accident ratio q is no longer near zero , butrather may be substantially larger than p, thethermal accidental ratio.

Fig. 3 The Negative View

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At this stage, we must not forget the fact thatthe pessimists have extraordinary fears against
nuclear energy such that their utility curves are
no longer stable but may shift downward. If
the utility curve shifts downward from U (x, β)
to U (x, β*) under the heavy stress, then thevalue of WV (nuclear) is no longer indicatedby the midpoint N, but rather the midpoint H
on the shifted curve. It is noted that as thepoint H lies in the fourth quadrant, WV (nuclear) is forced to take on a negative value. In
short, we may enter into the world where nuclear generation per se is a negative asset.
To sum up, a risk economic approach involves a fundamentally difficult problem. First,
human attitude toward nuclear generation differs from person to person: there exist a varietyof optimists and pessimists. Second, the utility
curve per se may not be stable, but possibly
shift upward or downward. Third, the official
opinion for the reliability of nuclear generation
may not necessarily supported by the local people. Honestly speaking, there remains still along way to go in this field.

V

Selection of Appropriate
Projects in the Worldof True Uncertainty

Paul Slovic (1987), a famous psychologist,
once reported the results of his empirical research on many risk perceptions of theAmerican people. He classified many conceivable items into just two items, unknown risk
and dreadful risk. According to his research,
nuclear power plant is regarded as both highly
unknown and highly dreadful risks. Psychologically speaking, it is the most dangerous
thing the people want to avoid. Althoughmine accident represents highly dreadful risk,
its danger is rather known to all the people.
The risk of microwave is highly unknown but
not so dreadful. Finally, bicycle is the most familiar and the most risk-free good.8)
In his well-known book (1921), Frank Knight(1921) emphasized the role of uncertainty inthe working of the market economy. According to Knight, risk is a measurable concept in
the sense that it can be represented by the normal or other specific distribution functions.
Uncertainty, however, is radically different
from risk since the former is no longer measurable at all. The notions of psychological risks
including unknown and dreadful risks are very
closely related to the one of non-measurable
uncertainty. We might to add that it is thistrue uncertainty, but not risk, which may form
the basis of a valid theory of nuclear generationfrom the economic-psychological viewpoint.9)
The myth of nuclear energy is now vanishedamong the people. Let us go with Knight’s argument. Then we are ready to investigate theselection problem of power generation withspecial reference to with non-measurable uncertainty. One thing is certain. The direct
application of the traditional expected utility
theory would not be appropriate. In the worldof true uncertainty, risks may not be measurable, so that many formulas of mathematicalprobabilities are now worthless. In order to
conduct our analysis further, it is necessary to
introduce some forms of selection rules. Theremight be the plain average rule, or the very aggressive maximax rule. We do think, however,that the more prudent maximin rule is the best
selection rule when the people face unknown
and dreadful risks.

9 ) F o r K n i g h t o n t r u e u n c e r t a i n t y, s e e S a k a i(2015,2016).

A Risk Economic Approach to Nuclear Power Generation

Yasuhiro Sakai

185

Let us discuss the maximin rule in greater detail. It requires the people for playing safe inuncertain situations. We must first think of
the worst possible scenario for every project,and proceed next find the best one out of
those worst scenarios. Suppose that there arem projects, a1,..., am ,and n states of the world,
s1,..., sn. Note that no probabilities pj are associated with the state s j. Further let y ij be thepayoff we can get when the project i is taken
and the state j is realized. More mathematically, let us define the worst scenario Ni for the
project i as Ni = Minj {yi1, ..., yij ,...,yin}. Thenthe maxmin rule requires that the project yielding the ma ximum va lue of N i must b echosen:10)
Maxi Ni = Maxi Minj {yij}.(6)Now, let us get back to Table 2. We are dealing with the selection problem of power
generation types, thermal or nuclear. In theworld of true uncertainty, numerical probabilities become meaningless, so that the accident
rates such as p, 1–p, q and 1–q should not bereferred at all. If we side with the positive view,
as is seen in Panel (A), the payoff of the thermal power takes on the minimum value (–1)
when an accident occur, whereas the one of thenuclear power, the minimum (–2) also in thecase of accident. While those two values areboth negative, (–1) is larger than (–2). Therefore, according to the minmax rule of decision
making, the thermal power generation is better
than the nuclear. Presumably, a stronger argument would be applied to the negative view.
As in Panel (B), while the payoff of the thermal
power takes on the minimum value (–1) whenan accident occurs, the one of the nuclear isthe minimum (–(4+α)) also in the case of accident. Between those two values, (–1) is clearlya much better value. This shows the superiority of the thermal power over the nuclear.
It is noted that the above argument is totallydependent on the reliability of the minmax
rule of decision making. In the world of nonmeasurable uncertainty, the people are involvedin many risks of unknown and/or dreadfultypes. As common sense tells us, the principleof “safety first” constitutes one of the golden
rules in human life.

VI

Concluding Remarks

Louis Pasteur (1822-1895), a renowned
French chemist and microbiologist, once remarked: “Chance favors the prepared mind.”This maxim is important and persuasive when
we are eager to discover hidden laws in the fieldof natural science. Its applicability may besomehow limited, however, if we take a look at
the history of human disasters. Even if we focus on nuclear disasters in modern times, there
are too numerous to list. Among them are theThree Mile nuclear accident (1979), the Chernobyl nuclear accident (1986), the Great
Hanshin-Awaji earthquake (1995), and theGreat East Japan disaster (2011). It is fair to saythat when those disasters stroke the regions ,the local people were not prepared at all.
Torahiko Terada (1934), a legendary Japanesescientist and essayist, noted that a natural disaster unexpectedly struck the people who wereso busy in their daily lives and conveniently
forgot the past experience of disasters. Therefore, in line with Pasteur’s famous sentence
aforementioned, we might say the following:“Disaster strikes the forgetful minds.”

10) For the maxmin rule, see Sakai (2004).

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As we repeatedly noted, it is quite unfortunate that risk-economic studies in nuclear
power generation have been extremely rare so
far. In closing this paper, we would like topoint out one important exception. In his outstanding book, E.F. Schumacher (1973) wasbrave enough to regard the problem of nuclear
energy as the one to choose the way to salvation or damnation.
In spite of Schumacher’s warning, the mainstream economics has consistently ignored theimportant problem of nuclear energy under
uncertainty. It is recalled that Schumacher was
once a research associate under J.M. Keynes.
Moreover, we would like to point out that
Schumacher’s view of nuclear energy as incalculable danger is in line with Knight’s notionof non-measurable uncertainty.
This paper may be just one step forward toward a more systematic approach to nuclear
power generation. No doubt, so many unsolved problems remain. They will be left for
future research.
【Acknowledgment】
Financial support from the Japanese Ministry of Education, Culture, Sports, Science andTechnology through Grant-in-Aid for Scientific Research (C) No.16K03837 is gratefully
acknowledged. All remaining errors are solely
my responsibility.
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A Risk Economic Approach to Nuclear Power
Generation
Are We Really “Strong in the Rain”?

Yasuhiro Sakai

This paper aims to discuss the problem of nuclear power generation from the viewpoint of
the economics of risk and uncertainty. Although we have experienced the two major
nuclear disasters, Chernobyl and Fukushima,
in recent times, it is quite unfortunate that riskeconomic studies in nuclear power generation
have been extremely rare so far. This may show
intentional neglect in the academic circle. The
purpose of this paper is to duly mend such a regrettable tendency. Before 11 March 2011, there
were many people who more or less believed in
the myth of absolute safety. The Great East Japan Earthquake, however, has completelychanged their concept of risk for nuclear power
generation, thus requiring the need to take a
new risk-economic approach to nuclear energy.
As saying goes, we can learn new lessons in oldteachings: we have to reexamine the economics of J.M. Keynes and Frank Knight. There aremany possibilities for future research.
Keywords: Risk, uncertainty, nuclear power
generation, Keynes, Knight

A Risk Economic Approach to Nuclear Power Generation

Yasuhiro Sakai

189