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Risk Assessment 2 of 2
THE SCIENCE AND TECHNOLOGY JOURNAL
Copyright 1989 by William A. Manly
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STJ Column #2
THE RISKS WE REGULATE AND THOSE WE DON'T -- ARE WE ILLOGICAL?
Our first column showed that we tend to regulate and fear some risks which
are actually very small, and we put up with some which are large. There
seemed to be little rhyme or reason to why this was so. In trying to deal
with this exasperating situation, people have been called ignorant and
illogical. Massive education programs have been proposed to remedy the
first, and even the second, despite the lack of solid evidence that either of
these are the only causes. They may not be causes at all. For every example
given which "proves the point," it is easy to give a counter-example which
proves exactly the opposite.
As was mentioned in the first column, there is a science called GAME THEORY
which is essentially a planning method for deciding which risks to take.
Game Theory evaluates the "payoff" as a function of the probability that the
payoff can be achieved. This is essentially the method used by good bridge
and poker players to plan how they will play their hands. Game Theory is
also the prime component used by economists to make economic models. There
is presently much active research aimed at improving Game Theory. This
indicates that the applications of the science leave something to be desired.
If something is completely understood, there is nothing to attract anyone to
do research on it.
Game Theory and the theory of probability were simultaneously founded by the
French mathematician and physicist Blaise Pascal (1623-1662). He and Pierre
Fermat (1601-1665), in the seventeenth century, worked on problems sent to
them by a certain gentleman gambler and amateur philosopher who was puzzled
why he always lost money betting on certain combinations coming up in the
fall of three dice. In solving these problems, the two came up with the new
Pascal's formulation of the outcome of a gambling game was as follows:
a = p1 a1 + p2 a2 + p3 a3 + . . . + pn an (1)
(the numbers and n are subscripts)
where a is the expected outcome (in modern terminology, the PAYOFF) for many
repetitions of the game, p1 is the probability that event 1 will occur, a1 is
the payoff for event 1, and 1,2,3,...n are the (finite) numbers of n possible
events in the game. In this simple case, there is one player going against
Most modern formulations of game theory involve two players (or groups of
players) going against each other. In the early 1930's, the
Hungarian-American mathematician John von Neumann (1908-1957) got interested
in the application of probability to econometric problems. He wrote a
fundamental paper on the subject, and in 1944 published a classic book called
THE THEORY OF GAMES AND ECONOMIC BEHAVIOR. Von Neumann also made fundamental
contributions to the mathematics of both quantum mechanics and electronic
computers, and was one of the principal scientific contributors to the
Manhattan Project. He is prominently mentioned in the book ADVENTURES OF A
MATHEMATICIAN by Stanislaw Ulam (also a Hungarian-American mathematician),
who knew "Johnny" (as he calls him in the book) in Hungary, and worked with
him on the Manhattan Project.
Modern formulations of game theory utilize overdetermined sets of linear
equations which can be best solved (optimized) using linear programming
techniques. Some of the economic models have so many equations with so many
terms that they require large fast computers, so computer time is a real
limitation. Parallel processing may solve some of these problems.
Getting back to the use of game theory in risk assessment, remember that game
theory really involves only two things in this application: the possible
payoffs (which may be negative), and the probability that the payoff will be
made if the risk is taken. Two payoffs may be involved: the untoward results
of the risk, and a positive value for taking the risk. Thus we risk death or
injury by driving our cars on the freeway twice a day, but the positive
payoff is getting to work, which supplies us with money for our needs and
This simplistic view is necessary for formulating the equations of game
theory, but in my opinion is a real limitation on applying the theory to the
real world. For instance, the work may supply us with satisfaction, which is
difficult to put in the same equation with the paycheck amount.
Alternatively, the satisfaction may be negative (we don't like our work), and
this is difficult to add to the risk of death and injury.
Most of the examples in the books and articles on game theory are of
econometric models, or of poker-like games. The rating on the game is just
the payoff of a wager made on the hand, but there may also be a personal
satisfaction in playing, which is worth the losing of a small amount for the
social interaction, and this is never considered. This lack is bad enough
for a game, but in real-life complicated situations, such as whether we
support nuclear power plants or not, game theory falls short by a
considerable amount. It may be fine for fighting a war, but not so good at
determining whether we will tolerate Alar in our apples.
A RISK PERCEPTION SCHEME WHICH FITS REAL LIFE
In discussing some of the latest work on how people perceive risks, we "risk"
getting into some rather opaque psychology jargon. Their jargon really is
not any worse than that of other professions, but if you're not a
psychologist, and I'm not, it gives certain problems in understanding (though
jargon really aids fast understanding if you are in the profession). I'll
try to wade through this for you, but in doing so I will have to invent some
descriptive terms and names in English, and they won't be the same as in the
To show you one example of what you will be missing, we will next take up the
subject of the PSYCHOMETRIC PARADIGM. In English, this is just putting the
psychological factors in graph form, so that we can see what is going on.
Instead of the statistical risks such as was published in the first issue of
STJ, we find that people make decisions based mainly on two psychological
factors: 1. Is the risk known or unknown; and 2. Does the thought of the risk
cause a great deal of apprehension. The first one is called "THE UNKNOWN
RISK," and the second one is called "THE DREAD RISK." I won't go into the
techniques used to make quantitative measurements of these factors, but such
measurements can now be reliably made.
Reference 1 contains two rather complex diagrams involving about 100 labeled
points on an X-Y plot (cartesian coordinates). The diagrams are too complex
to represent in this online column, so I'll have to describe it to you. The
coordinate system looks like this:
2 | 1
Small | Large
Dread Risk | Dread Risk
3 | 4
The first sector involves unknown risks with great associated apprehension;
the second sector unknown risks with small associated apprehension; the third
sector has known risks with small associated apprehension; and the fourth
sector involves known risks with great associated apprehension. Rather than
trying to explain to you why all unknown risks are not necessarily associated
with a lot of dread, I will give examples, and then I won't have to explain.
Sector 1 - Risk unknown, dread high:
DNA Technology (new or changed living organisms)
Nuclear Reactor Accidents
Nuclear Weapons Fallout
Sector 2 - Risk unknown, dread low:
Water Flouridation and Chlorination
Coal Tar Hairdyes
Darvon and Vallium
Sector 3 - Risk known, dread low:
Power mowers, Skateboards, Trampolines
Home Swimming Pools
Smoking (Fires and Disease)
Sector 4 - Risk known, dread high:
Nuclear weapons (war)
Nerve Gas Accidents
Coal Mining Accidents
Sport Parachuting, General Aviation
High and Underwater Construction
Whether it is explained or not, these lists all fit into intuitive
categories, even if the category name had not been listed at the top. I
think that most people, if asked to make four lists of the various
categories, would come up with four lists resembling those.
Now those are neat lists, but they don't mean anything just yet. To get some
meaning out of them, we look at another category: that of whether the general
public is in favor of regulation of the items. Now the pattern pops out!
The public is in favor of heavily regulating almost everything in sector 1.
They want to regulate about half the items in sector 4, and the regulation
intensity drops. There is some call for regulation on sector 2, and even
less in sector 3. There are some other factors involved for isolated items,
e.g., motorcycles are in sector 3, but there is a strong call for heavy
regulation. The reader can draw his/her own conclusions about that!
The list of psychological factors involved in making the assessments are as
Unknown to those exposed
Risks unknown to science
Known to those exposed
Risks known to science
Catastrophic, especially globally
High risk to future generations
Not easily reduced
Not globally catastrophic
Consequences not fatal
Low risk to future generations
Surprise! This whole thing is now beginning to look a whole lot more
sensible! The public idea is that if an adult individual wants to take a
risk, that is the problem of the individual, if no one else is involved. No
one wants to do something which will hurt our descendants, and everyone
believes that no one has any right to do something which will hurt "innocent"
It is difficult to argue with these ideas, and the general public turns out
to have a lot more sense than we might at first be led to believe.
Nevertheless, there are some anomalies which need to be changed. For
instance, we have no real choice but to go with nuclear power plants.
Barring an immediate breakthrough in solar power or hydrogen fusion, and with
an increasing population, we will either have to shut things down or build
nuclear power plants. We aren't going to start shutting things down, so the
conclusion is obvious. The attitude of the public is causing the regulation
to be so extreme, that the cost of these plants is going out of sight.
Education may be part of the answer, but it is not the complete answer, since
it will make little change in the dread risk. Changing something from sector
1 to sector 4 doesn't help very much. Look at the list above under "Dread
high." How do we go about changing those things, or the public's perception
of them? I don't have any quick and dirty answers, or even any good answers
at all. The only thing that we can say, is that the list of items under
"Dread high" is the most important list to remedy. Working on better
statistics and getting them out to the public is not going to make any
William A. Manly
Bibliography - these sources were consulted for this article:
1. "Perception of Risk", Paul Slovic, SCIENCE, V. 236, no. 4799, 17 April
1987, pp 280-285.
2. Van Nostrand's SCIENTIFIC ENCYCLOPEDIA, Fifth Edition, 1976.
3. ASIMOV'S BIOGRAPHICAL ENCYCLOPEDIA OF SCIENCE & TECHNOLOGY, Isaac Asimov,
Doubleday, 2nd edition, 1982.
4. "The Theory of Games" , H. Frederick Bohnenblust, in MODERN MATHEMATICS
FOR THE ENGINEER, McGraw-Hill, 1956.
5. THE RANDOM HOUSE DICTIONARY OF THE ENGLISH LANGUAGE, unabridged edition,
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