302
74-A
SMIC
and
J.
method
constructing
scenarios
ranking
C. Duperrin
for
and
M.
Godet
A valid concept of what the future could be implies the existence
of an overall conjectural framework which makes full allowance
for the dynamics and complexity of the various systems involved.
Such a framework must integrate the variable factors which
determine the behaviour of all the economic and other agents
contributing to the shape of the future, even when these variables
are of a qualitative, subjective nature. A new method based on
the cross-impact analysis is proposed to improve decision-making
processes. A simple example is given to illustrate how this method
can be used in forecasting studies and scenarios.
SOCIALsystems are becoming increasingly complex and diversified, the factors
which influence them increasingly interdependent,
and the events which
occur within them increasingly interrelated.
Consequently, if we are to
control future events, we must first have some idea of the future context of the
system considered. Just as we can summarise past history by listing a sequence
of salient happenings, so can we visualise possible futures by envisaging a
series of impending events which, if they materialise, will have predictable
effects during the time period considered. Once established, this set of possible
events constitutes a frame of reference containing as many different versions
of the future as there are different combinations of those events. The question
which we will now attempt to answer is how it is possible to identify the most
probable events and thus the most probable future.
When we are considering the future, personal judgement is often the only
available means of assessing which events are likely to occur and to influence
those aspects of that future that we are trying to foresee. Some methods,
such as Delphi, are quite suitable for compiling a consensus of expert opinion
on the probability of occurrence of specified events to give a convergent view
of the future. However, such methods are imperfect in that they do not make
allowance for interactions between different events. By contrast, the crossDr J. C. Duperrin is with the Planning Department, French Atomic Commission, 33 rue de la F6d6ration, Paris XVe. Dr M. Godet is at SEMA Metra International, 16-18 rue Barbes, 92 128 Montrouge,
France. This article is adapted from a paper first published in French in Metra, Vol XIII, No 4, 1974.
303
impacts method has the advantage of both taking into account the opinions
which are expressed, and the interdependence between the factors to which
those opinions relate, so that it provides a more coherent frame of reference.
Critique
of the cross-impact
method
The cross-impact method is the general name given to a whole family of
techniques designed to evaluate changes in the probability of occurrence of
a given set of events consequent on the actual occurrence of one of them.
First of' all, the method takes the form of a list of events accompanied by the
probabilities., given by expert opinion, of the occurrence of each event. The
fundamental assumption of the method is that these probability ratings allow
for interactions between separate events, but these probability ratings are
incomplete. When allowance is made systematically for the whole gamut of
interactions, the pattern of "raw" probabilities becomes one of "finished", or
corrected, probabilities.'
This conversion from raw to finished probabilities is usually achieved by
the application of fairly sophisticated techniques, such as reiterated Monte
Carlo simulation models, etc. Several approaches have been put forward,
often consisting of an ingenious mixture of quadratic forms, mathematical
probabilities, and subjective-weighting coefficients. In practice none of these
formulas has come to dominate the field and as many different results emerge
from a problem as there are formulas being tried.22
Furthermore,
as
has
been
demonstrated
by
the
Battelle
Institute
team,3
3
the aim of the method should be to verify the consistency of the forecasts by
reference to standard probability theory. In practice, most of the methodshowever complex they may be-lead up to inconsistent "finished" probabilities
and give results such as P(i ) < P(ilj)P(j).
This is incompatible
with
=
which
should
be
measured.
P(i)
P(i/j)P(j) -}- P(i/j)P(j),
against
they
Most authors on the subject tend to mistake convergence for consistency:
the fact that a process is convergent does not necessarily mean that it gives consistent
results.
Scenarios:
sensitivity
and construction
The sensitivity analysis enables us to separate powerful or dominant events
from events which are subordinate to them. In most cases, this is done by
estimating the variation AP(j) of the probability P( j ) of the event j consequent
on a variation OP(i) of the probability P(i) of event i. The results are displayed
in the form of an elasticity matrix
where
Scenario construction is usually based on random selection, from which the
most probable chain of events can be generated.
In practice, when we consider a system of n events (el, e2, ... , en), that
system implies that 2n combinations or scenarios are possible. For example,
if we say that at a given date events el, e2, e4, ... , en will have occurred, but
not e3,this corresponds to one of the 2n possible scenarios.
304
The sum of the probability ratings for all the scenarios is unity, since they
are exclusive in relation to each other and one of them is bound to occur.
Examples of cross-impact applications to date show that the most probable
scenario has a probability rating of around 0. I . The exact figure depends on
the number of events considered and the size of the initial probabilities. There
are usually other quite different scenarios with probabilities which are only
slightly lower than this and which form part of the hard core of probabilities.
Consequently, we can say that the future trend cannot be identified simply
by taking the most probable scenario. For cross-impact analysis to overcome
this drawback, the methods employed would have to produce an order of
ranking of all the possible scenarios.
With a view to developing a method which complies with both these requirements, we decided to rethink the problem in all its aspects. None of the crossimpact formulas developed so far seems satisfactory. The results are not consistent with probability theory, nor do they give probability ratings for each
scenario evolved.
A new method
The principle underlying the method is extremely simple and is based on the
assumption that the experts consulted are able to give opinions concerning:
o The list H of the n separate events which are considered relevant to the
exercise in hand:
o The probability P(i) of the separate event e,, ie the probability of the
occurrence of ei within the period considered. When a person says "I
estimate at z 75 the probability of a given event" we subscribe to the opinion
of ProfessorVille4in interpreting this assessmentas meaning "ifyou consider
all the events whose probability I rated as 0-75, and record for a long
series of cases the frequency of the events actually occurring, I forecast
that that frequency will be in the region of 0-75".
o The conditional probabilities of the separate event taken in pairs:
P(i/j)is the probability of i if j occurs,
P(ilj) is the probability of i if j does not occur.
In practice, the opinions given in response to certain specific questions about
non-independent events disclose some degree of inconsistency with the overall
opinion (which is implicit although not expressed) revealed by the answers
given to all the other questions.
These "raw" opinions thus have to be corrected so that the "finished"
probabilities conform with the following constraints:
The framework of investigation is constituted by the probabilistic relationships
between separate scenarios and events:
305
o H is a finite set of separate events. These separate events are related
other.
9 We investigate the system S constituted by all the separate events
relationships between them.
o The separate events are considered to be non-recurrent, ie unable
more than once during the period T being investigated, and the
which they occur is neglected.
The "state of the system of separate
any combination of a certain number
period, to the exclusion of any other
For example, if the set H has three
which
corresponds
to el
and e2
occurring
to each
and the
to occur
order in
events" (E) is the term used to describe
of separate events occurring during the
events.
members el, e2, e3l then we may define
without
e3-
In a system S comprising n separate events, there will be r possible "states"
E, where r = 2n.
Each state, Ek, has an unknown probability ilk where
To each separate event ei we can then allocate individual and conditional
theoretical probabilities expressed in terms of the flk functions
306
The results must be in conformity with the following constraints:
Objectives
and principles
of the method
The method is designed to enable experts' estimates to be checked for consistency against the above constraints. The idea behind it is that each item
of information contributed by the experts allows for the interactions between
events but from a different standpoint than is usual, ie this allowance is made
only incompletely.
Consequently, the estimates need to be corrected and
the modus operandi for converting them into "finished" form must be based
on an objective rule, ie one which expresses the agreement of the estimates
with the constraints imposed.
One approach might have been to optimise a given factor of the individual
and conditional probabilities by reference to those constraints, but the nonlinear character of constraints on the probability of the separate events means
that special conditions would have to be observed with respect to the optimum;
consequently, we investigated the probability ratings of the different possible
states of the whole system made up by the separate events.
If we are able to determine the probabilities of these states, we can derive
scenarios based on the most probable sequence of possible futures.
The principle which we adopted, starting with a body of inconsistent and
incomplete information on the probability of separate events, was to strive
towards a consistent and complete "finished product" by considering the
probabilities relating to the possible states of the system composed by those
separate events. This is outlined in Figure 1.
Constraints (7), (8), and (9) are obeyed by the theoretical probability
ratings, but the personal estimates of the experts do not obey the constraints
(1), (2), and (3). Consequently, the objective function which we propose to
optimise is one which minimises the difference between the P(ilj) factors
resulting from the experts' conclusions and the theoretical P* (ilj)P* ( j) factors
expressed in terms of flk. This means that we must determine the probabilities
flr) of the r possible states which minimise, for
(II1, ll2, ... , I Hk, - - . )
example:
307
subject to the constraints:
This is a classic minimisation
straints.5 5
Results
programme
of quadratic
form with linear con-
-
The programme output gives us the probability ratings for the possible states
1 1-1 it,.I llr). From equations (4), (5), and (6) we can calculate
(nm
the finished probabilities P*(I),
which are not only consistent with
the experts' predictions but are also consonant with the probability constraints.
By this means we achieve a cardinal ranking of the possible states and can
thus circumscribe the area of plausible developments by retaining only those
states which have a probability greater than zero. Within this plausible area,
we can identify states which are more probable than others, ie trend-based
scenarios as opposed to divergent alternatives.
The next step in the method consists of an analysis of the sensitivity of the
system. An important part of this analysis is the estimating of the variation
AP(j) of P(j) consequent on a variation
of P(i).
Conclusions
When seeking to comprehend the future development of a system, it is not
enough merely to pick out certain salient events and the corresponding possible
states of' the system. The possible states must be ranked by probability. The
SMIC 74 method does this.
This method is based on the principle of correcting the raw opinions expressed by experts, by allowing for the interdependence between the questions
formulated, and by constructing a coherent set of probabilities from the
individual probabilities of pairs of separate events. The sensitivity analysis
shows that SMIC 74 can evaluate the effects of action on an event and thus
help to choose between alternative strategies. This consideration of external
effects is in line with "technology assessment" thinking.
However, the improved cross-impacts method does not constitute a universal
panacea. Whatever the system being investigated, the choice of the variables
and their relationships depends on the subjective reference systems of the
experts consulted. We must thus be aware of the dangers involved in using
a method where the initial hypotheses have such an effect on the results.
Appendix
Example of SMIC 74 applied to a nuclear power system
The SMIC 74 method has already been applied by the Sema Metra International
Group, by the French Atomic Energy Commission, by Paris Airport, and by the
French Electricity Board. These applications were concerned with six or seven
events, ie 64 or 128 scenarios, and were therefore much more complex than the
following simple example.
308
We considered the events which could occur during the period 1974-1990. The
choice reflects the current concern about nuclear power in France, but it is purely
illustrative.
We have three separate events: river temperatures exceed 30°C (el); 75% of
and 200 000-strong protest march against
electricity is from nuclear sources
nuclear power stations
Their respective probabilities of occurrence between
1974 and 1990 are P(l), P(2), and P(3).
Of this eight (23) possible combinations of states, which are the most probable and
what are their probabilities?
The °raw"
opinion input
With a view to obtaining more reliable opinions, the expert panel is requested at
the outset to make explicit allowance for the relationships between events. Since
these relationships depend on the particular expert answering, there will be as
many types of relationship as there are different points of view.
In Figures 2 and 3 a solid line means a probable strong relationship between the
events, a broken line means a probable weak relationship. We will assume that the
expert panel reaches a consensus regarding a particular type of relationship between
events.
o A conditional type of relationship between e2 and el, where e2 is implied by el.
If el occurs during the period, there is a strong assumption that e2 occurred earlier.
At the same time, however, e2 may well occur without leading to el.
Explanation: given that the cooling techniques used by nuclear power stations
are one of the main factors leading to higher river temperatures, it can be fairly
assumed that a rise in those temperatures to more than 30°C will have been
caused by the nuclear power stations.
However, if other techniques are used to cool the nuclear power stations, it will
be perfectly feasible to produce 75% of the electricity supply from the latter
without bringing river temperatures above 30°C.
9 A causal type of relationship between el and
where e3 is a result of e, is shown
in Figure 3.
Explanation: if river temperatures climb above 30°C, then there is every chance
that a protest movement will emerge against the nuclear power stations which
are one of the main causes of river overheating.
309
However, a protest movement directed against the nuclear power stations
may emerge for different reasons than this (radioactive waste, fear of atomic
risks) .
The effects of each type of relationship on the probability ratings are as follows.
First, the conditional-type relationship between e2 and el gives the likelihood that
P(2). Second, the causal-type relationship between el and e3 implies that
P(l) $' P(3) .
The expert panel replies to the following three questions. What are the values
of P(i), P(ifj), and P (ifj) (where i, j = 1, 2, 3) for the period in question?
This system composed of three separate events can take on any of eight configurations (Ek), each of which can be given a probability index (lit). The eight states are
El =
(el, e2, e3) 12
E6 =
(QV e2l
17
=
(.F,, e2, e3) i E3
i and
(61, F2,
=
(ev C2' e3) E4
E8 = (il, j2,
=
(ev j2,
E5 =
(eh e2,
i
where
Individual probabilities may be expressed in terms of state probabilities:
where
Conditional probabilities may be expressed in terms of state probabilities as follows:
The experts' consensus is shown in Figure 4. The probability matrix derived from the
above equations is as follows:
The information supplied by the experts and shown in Figure 4 is inconsistent as
it stands, according to constraints (7), (8), and (9). In order to obtain corrected
310
results, we calculate the "state" probabilities, which were not expressed by the
experts but are implicit in their overall replies to the questionnaire. These state
probabilities are derived from the following programme:
subject to two constraints:
Results
We will first describe the corrected results for the individual and conditional
probabilities. The state probabilities which enabled us to adjust the original inThe "finished" information is shown in
formation are discussed subsequently.
5.
Figure
In
this
example,
the
individual
probability
which
is
most
modified
is
that
of
which rises from 0-5 to 0-62. By contrast, a large number of the conditional probabilities are substantially amended:
311
There is a simple explanation for this: it is often a great deal easier to give an
individual probability than a conditional one.
Sensitivity analysis
The sensitivity analysis consists in measuring the variation AP(j) of P(j) consequent
on a variation AP(i) of P(i). The elasticities are calculated on the basis of the corrected results, and are shown in Table 1 where OP(i) = 0. for all i.
The horizontal totals in Table I show that event el is more of a prime mover
than the others, with an elasticity of -0-51 as compared with -0-32 and -0. 18
for e2 and e, respectively. The vertical totals show that event e2 is the most conditioned of the three, ie is the most sensitive to occurrence of the other two ( -0.51) ,
whereas the least sensitive is the prime mover el. This means that the development
of nuclear power stations is highly sensitive to the other events in the system considered, especially to the rise in river temperatures which is the prime mover in that
system.
All the elasticities are negative; their interpretations are as follows.
'E12== - 0-33. This means that when the probability of river temperatures rising
above 30°C increases by 100%, the probability of 75% of electricity being generated
by nuclear power stations declines by 33%, so that river temperatures will have
exceeded 30°C before the 75% nuclear level is reached.
e21= - 0. 14. If the probability of 75% of electricity being generated by nuclear
power stations increases by 100%, then that of river temperatures having exceeded
30°C declines by 14%, which is consistent with the above result. If river temperatures had risen above 30°C, this would have occurred before the 75% nuclear
level had been reached, and thus would have reduced the probability of the latter.
632= - 0. 1 8.If the probability of a 200 000-strong protest march against nuclear
power stations increases by 100%, then the probability of nuclear power generating
75% of electricity declines by 18%.
E23== - 0. 1 8.If the probability of 75% of electricity being from nuclear sources
increases by 100%, then the probability that a mass protest against nuclear power
stations has occurred decreases by 18%.
Scenario probability ratings
We can see from the following probabilities that only scenario E, has a nil probability,
meaning that it is not plausible: rI, = 0-279, II1 = 0-234, fl, = 0.201 , 11, = 0. 103,
ll7 = 0-073, Ila = 0-066, f'3 = 0-044, fl5 = 0-00.
312
In other words, it is not conceivable that there could occur a combination of
over 30°C without
75% electricity from nuclear sources and river temperatures
there also occurring a popular demonstration against nuclear power stations.
E,, EI, and E4 constitute the hard core of the trend-based scenarios, there being
more than two chances out of three that one of them will correspond to the situation
in 1990.
is the "technological"
scenario: 75% of the electricity supply is
Ee = (ii, e2,
whereas technological innovation has made it possible to avoid
nuclear-based,
over-heating the rivers and the population is accustomed to the idea of nuclear
energy.
El = (e,, e,, e,) is the "conflict" scenario: technocratic authority has imposed
nuclear power generating despite overheating of rivers and despite public discontent.
the "conservation"
scenario: river temperatures remain below
E4 =
30°C and nuclear power stations account for less than 75% of total electricity supply,
but this does not prevent antinuclear demonstrations.
The other scenarios can be described as "divergent".
They are less probable
situations, such as E, = (e,,
e,) with a probability of 0-044, ie it is not likely that
there will be a combination of anti-nuclear protest and river temperatures above
30°C, at the same time as nuclear power stations account for less than 75% of total
electricity production.
References
1. T. J. Gordon and H. Hayward, "Initial Experiment with the Cross Impact
Matrix Method of Forecasting", Futures, December 1968, pages 100-116; Howard
E. Johnson, "Some Computational Aspects of Cross Impact Matrix Forecasting",
Futures, June 1970, pages 123-131; Julius Kane, "A Primer for a New Cross
Technological Forecasting and Social Change, Vol 4,
Impact Language KSIM",
No 2, 1972, pages 129-142; N. Dalkey, "An Elementary Cross-Impact Model",
Technological Forecasting and Social Change, Vol 3, No 3, 1972, pages 341-351.
2. J. P. Florentin and J. M. Dognin, "Utilisation de l'Analyse d'Interaction
(Cross
Impact Analysis) dans la Planification Strat6gique", These de doctorat de 36me
cycle, June 1973, Universite de Paris IX, Dauphine, France.
3. E. Fontela and A. Gabus, "Events and Economic Forecasting Models", Futures,
August 1974, pages 329-333.
4. J. Ville, Etude critique de la notion de collectif (Paris, Gauthier-Villars,
1967).
5. The computer programme
achieving this was developed at the Compagnie
Internationale
de Services Informatiques
by J. Lieutaud from Ravindran's
algorithm, Communications of ACM, 1972, Vol 15, No 9.
6. J. C. Duperrin, M. Godet, and L. Puiseux, "Energy and Society, Scenarios for
Atomic
2000", Rapport Economique du CEA (to be published, Paris, French
'
Commission, 1975).