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Helping people make rational decisions using the principle of
satisficing
DJH Brown
Faculty of Science, Universiti Brunei Darussalam, Brunei.
The use of an intuitively simple reasoning language for constructing a
semiquantitative model of a communal world view to support decision making is
described. The language provides a medium within which decision makers can
express their thoughts about desiderata, choices and causal relationships. In the
course of searching for a solution to its decision problem by reformulating its model,
the decision makers’ collective perceptions are developed and refined until a feasible
alternative is revealed. The process is illustrated by a real-world decision problem.
1. Introduction
For a group to decide upon a collective action in the real world, its members need a means
of communicating their ideas and opinions to each other. This is a role of natural
language, but natural languages such as English are so expressively rich that there is
plenty of opportunity for miscommunication, even within a culturally homogeneous
group. As well, authority structures and other interpersonal relationships impact the
meaning and significance of things that are said, interpreted and acted upon during a
meeting.
For these reasons, an unambiguous written language having a simple and unequivocal
semantics might help decision makers clarify their arguments, viewpoints and predictions.
The language can be used to construct a shared model of rationality within which decision
options and their outcomes can be examined.
Such a language and a method of using it to make a decision is described that is intended
to be useable by people from all walks of life with no particular background. The
language is based upon logic and set theory and the method is an interpretation of the
behavioural theory of satisficing (Simon, 1955, 1979), but – it is claimed - no special
knowledge of any formal theory is required to make decisions using the language and
method.
2. The Basic Method
Levine and Pomerol (1995) characterise the task of a decision maker as being one of
performing a heuristic search through a state space of possibilities. Here, the task is cast
as a search through a space of possible models to find a satisfactory solution, as follows:
1. Create a causal model, comprising:
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- a state space described by a number of state variables and the domains of their values;
- action alternatives deemed potentially feasible, expressed as changes to the value of
state variables;
- desiderata upon the outcomes of the action to be taken;
- causal rulesi which infer the effects changes to the values of state variables in terms of
changes to other state variables - in general, a model contains several causal rules which
can produce chains of causes and effects.
2. Use the model to examine the correspondence between predicted outcomes and the
desiderata.
3. Modify the model until an alternative is found whose outcomes satisfy the desiderata.
In the course of model development, optimisation techniques such as linear programming
can be used to identify alternatives which are expected to optimise one or more outcomes,
and new knowledge thereby gained can be used to modify the desiderata. In this way, the
process can embrace the ideal of finding an optimising solution whilst operating within a
satisficing paradigm.
2.1 Model Representation Language
"Observing pouring rain and a river's steadily rising water level is sufficient to make a
prudent person take measures against possible flooding – without knowing the exact
water level, the rate of change, or the time the river might flood." -Yumi Iwasaki
The key role of the model in the method proposed here raises the question as to what kind
of model would be adequate for the purpose. It is commonly regarded that the more
precise the measurements, the more professional are the conclusions that depend upon
them - the proliferation of quantitative methods for decision support is one evidence of
the commonality of such a view. Here, a different approach is taken, for two operational
reasons. Firstly, the model needs to be created within the time perceived by the decision
makers to be appropriate to the task. Often this time is very limited. Secondly, the model
is created by the decision makers themselves, so its machinery should not require in-depth
knowledge of elaborate mathematical theories in order to build it.
Taking an action (implementing a decision) changes the world. General Systems Theory
(Klir, 1991) characterises a world model as a set of transitions between states, represented
as vectors of attributes (variables) where each attribute characterises an atomic component
of the world being modelled. Kirov (2002) noted the correspondence between a Model of
the predicate calculus (Suppes, 1969), and a System as defined by General Systems
Theory: predicate calculus syllogisms express what truths can be inferred from a given set
of conditions and state transition rules express how a state will change as a result of a
given action or event. That is, causation is equivalent to time-shifted implication.
Qualitative causal models (Weld and de Kleer, 1990, Parsons, 2001) use logical
representations to capture the essential aspects of a system using abstraction and
approximation methods. Whereas the basic mechanism of a numerical model of system
dynamics is the differential equation, in a qualitative formulation it is an "influence"
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(Forbus, 1984) or "confluence" (de Kleer and Brown, 1984) or “qualitative difference
equation” (Dvorak, 1992; Kuipers, 2001) whereat one or more inference rules express
under what conditions and how qualitative changes to the values of state variables are
made.
In decision making, some facts about the world are known quantitatively, and some
qualitatively. Semiquantitative reasoning is commonly used in medical diagnosis (Lowe
et al, 1994), environmental impact analysis (Environment Agency, 2004) and is the basis
of "Expert Systems" (Nii, 2004; AAAI, 2004) for representing and using domain
knowledge to solve problems of a given type within that domain. Programming
languages for building expert systems are often elaborate and complex, requiring
specialist knowledge to use. Building an expert system typically takes a team of specialist
"knowledge engineers" considerable time to construct. In contrast, ad hoc decision
making is typically performed, not by software, but by a group of people in the space of
few meetings. Hence a language for constructing semiquantitative causal models for use
by ad hoc decision makers should be as uncomplicated as possible, yet retain a clear an
unambiguous semantics.
The decision table (Pollack et al, 1971) is a representational device that has been used for
many years by computer systems analysts to represent logical confluences. Like
spreadsheets, decision tables use spatial contiguity for representing contextual
commonality and thereby offer a more cognitively accessible (Tufte, 1990) medium for
conceptualising logic than decision trees, just as the relational database model offers
conceptual advantages over the network database model. The “generalised extendedentry decision table”, or geedt (Brown, 1979), is a derivative of the standard extendedentry decision table in which object values are possibility sets rather than point values hence the qualifier “generalised”.
The model representation language used here is a set of geedts. Each geedt is a
confluence of semiquantitative inference rules having common antecedents or
consequents. Most people who have seen a geedt remark that it looks simple – this
provides some justification for the claim that no special knowledge is needed to use
geedts as a representation language, although the method does not depend upon their use.
A formal definition of geedt semantics is given in the Appendix. The following examples
use paper geedts; a software geedt processor (Simon et al, 1989) exists and was used to
build several decision support systems (Lock Lee et al, 1989), but its interface is not
perfectly adapted to the present purpose.
Flow-on effects can introduce nonmonotonicity or contradictions. Expert Systems
inference engines incorporate “conflict resolution” mechanisms to select between
different inferred values and van der Laan and Robins (2003) describe methods based on
probability theory of drawing inferences from censored data where a point value is known
only within a range. Geedt semantics adopt a different approach: geedt attribute values
and predicates are quality classes (sets of possible values) defined by enumeration or
extrema; ambivalences are propogated and no default assumptions are made about how
contradictory inferences should be resolved. An attribute value is deemed to match a
predicate whenever it has a non-null intersection with the range of the predicate.
Many mechanisms of representing uncertainty and propogating it through a causal model
have been proposed (Parsons, 2001). The approach taken here is to represent uncertainty
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at the object level within a model, rather than ascribing a measure of certainty upon
inferences.
As not all aspects of an outcome have equal significance to a decision maker, the notion
of “weighing things up” naturally led to the idea of using a weighted sum to relatively
measure the expected utilities of alternatives (Arsham, 2004), although the soundness of
aggregating heterogeneous variables has been questioned (Pomerol and Barba-Romero,
2000; Gal et al, 2002) and there is some evidence that people tend to rank the same
alternatives differently when they are characterised in terms of benefits or losses (Tversky
and Kahneman, 1981).
Nonetheless, weighted sums have become ubiquitous instruments for decision making.
They are standard practice in academic assessment, where student performance is
typically computed by a combination of coursework and examination results. Dawkins
(1976, pp 96-97) suggests that the evolution of altruistic behaviour can be explained in
terms of gene survival by a payoff function which sums risks and benefits of self-sacrifice
to aid relatives, weighted by their degree of kinship to the altruistic animal. In the world
of executive business decision making, the methodologies of Kepner-Tregoe (2004) and
the AHP, or Analytical Hierarchy Process (Wasyluk and Saaty, ibid), both based on
weighted sums, have gained widespread respect and use.
Using probability theory makes sense for casino owners and insurance companies, where
the empirical law that long runs of uncertain events produce actual distributions that
approximate theoretical ones allows mathematically sound policies to be created. But for
a one-off event, this law does not apply. However, from the historical record, it seems
that people in fact do often discount improbable yet mitigable adverse events, although
after one does happen within their realm of concern, great efforts are made to forestall or
mitigate a second occurrence – this common approach to risk management is summed up
by the aphorism “once bitten, twice shy”. Even in mandated Health and Safety Risk
Assessment (Ketz, 2003), the expected loss from improbable events is incoporated into a
wholesale figure such as Potential Loss of Life per year for an entire installation, which is
measured against an industry benchmark. Vose (2001) remarks: “A very common error
is to include rare events in a risk analysis model that is primarily concerned with the
general uncertainty of the problem... The problem would be better analysed by
considering the risk on its own and any risk reduction strategies that might be effective”.
3. Model Abduction
"There are two things which are very apt to be confounded, but which it imports us
carefully to distinguish:- the motive or cause, which, by operating on the mind of an
individual, is productive of any act: and the ground or reason which warrants a legislator,
or other bystander, in regarding that act with an eye of approbation. " - Jeremy Bentham.
Decision makers do not reason about the world as it actually is, but about their images of
it in their minds. Simon (1972) characterised this as “bounded rationality”. Using the
method described here, the rationality is bounded by the statements of the model. When
the method is used by a group, this rationality is explicit and visible to all members.
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For non-trivial decision problems, the purpose of decision analysis is not simply to
discover which alternative action leads to the desired outcome, but to identify a feasible
objective and formulate an action or policy that will achieve it, insofar as the bounded
rationality of the decision makers can see. The process of doing this is a stream of
rethinking. Rethinking the possible actions, rethinking the feasible goal(s), rethinking the
causal laws. The bounds of the rationality shift as new ideas are introduced into the
model in the quest for a satisficing solution to the decision problem.
Pierce (1902) defined abduction as “reasoning which professes to be such that in case
there is any ascertainable truth concerning the matter in hand, the general method of this
reasoning, though not necessarily each special application of it, must eventually
approximate to the truth.” According to Sullivan (1991), “The objective of abduction is to
determine which hypothesis or proposition to test, not which one to adopt or assert”.
Using Sullivan's meaning of Pierce's term, abduction is a creative process by which
desiderata are created and examined. But this involves more than just creating hypotheses
and testing them within a fixed model. It involves reconstructing the model, including its
axioms.
3.1 Using Diagnosis as an Abduction Search Heuristic
Clinical diagnosis is a search through the past to identify what underlying condition could
have caused the current symptoms, whereas decision making requires a prognostic search
through the future to identify which alternative course of action can reasonably be
expected to achieve the desired objectives.
At first sight, diagnosis and prognosis seem to be opposite modes of reasoning. In
diagnosis, one is presented with the effects and seeks to determine the causes, whereas in
prognosis, one is presented with the causes and seeks to determine the effects. However,
in both cases, the task is to establish a chain of causal links between the prior and the
posterior states of the world.
In both tasks, a model, whether implicit or explicit, is constructed and developed as the
investigation proceeds. And in each case, the process involves reasoning in both
directions, from the prior to the posterior and vice-versa. In clinical assessment, modelbased prognosis is used to identify which additional clinical evidence should be sought to
verify hypotheses. And in decision making, model-based diagnosis can be used to identify
what qualities a satisficing alternative should possess. The analogy between decision
making and diagnosis maps symptoms to desiderata and hypotheses to alternatives.
The method of differential diagnosis involves constructing tests that can eliminate one or
another candidate hypothesis of cause. This general approach is also applicable to
decision analysis: a key feature of the abductive method is the testing of the satisfiability
of desiderata and modifying them to find which ones are feasible. The same is true of
alternatives.
3.2 An Example
“You can’t think seriously about thinking without thinking about thinking about something” – Seymour
Papert
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In southern Europe, eating outdoors during the warmer months is a traditional pleasure.
Mr and Mrs Smith were dismayed to learn that the courtyard of their newly-purchased
house in a small village was – despite being part of their property - the entrance to their
neighbour Mrs Jones’ garage. As well as making it impossible for the Smith family to
dine al fresco in their courtyard, exhaust fumes from Mrs Jones’ car entered their kitchen
window each time she drove in or out of her garage. The Smiths’ kitchen had no other
windows.
Mrs Jones was a friendly person but on the subject of her garage access she was
immovable. The Smiths’ house was a subdivision of a larger property Mrs Jones’ family
had owned for many generations. Her internal garage had been used by her for many
years before the Smiths bought the subdivided property. Mr Smith had offered to share
the cost of building Mrs Jones another garage in her garden on the other side of her house,
away from the Smiths’ courtyard, but she had refused. She did not want the beauty of her
garden despoiled by an outbuilding, nor did she want to spend her own money to solve
someone else’s problem.
The Smiths had appealed to the village mayor to adjudicate on their behalf, but, although
sympathetic to their situation, he had said he could not do anything. Both parties had then
sought legal advice from professional lawyers. For a fee of e300, the Smith’s lawyer had
provided the advice that he would be willing to represent them in a civil suit against Mrs
Jones using her garage entrance through the Smith’s courtyard. Mr Smith estimated the
cost of litigation would be about e3000 – e10000. The Smiths hoped that the outcome of
a civil suit would be that the lawyers would agree an out-of-court settlement whereby they
would pay Mrs Jones some money in compensation for losing her garage entrance access.
Mr Smith had estimated it would cost e10000 to build a garage in her garden, and half of
this was the sum he had in mind for a settlement.
A friend had suggested building a wall across the courtyard to deny Mrs Jones access to
her garage entrance, but although the suggestion had been made facetiously, it was an idea
Mr Smith was starting to consider seriously. Mrs Smith contended that to create an
obstruction would make them look bad and might prejudice a later court verdict. Mr
Smith argued that if they built a wall, there would be no need to go to court – it would be
a fait accompli. But Mrs Smith repeated that she did want them to be the “bad guys”.
At the behest of the author, the Smiths looked at their decision problem using the method
described herein. They began by listing the alternative courses of action, as they saw
them at that moment:
1. litigate
2. build a wall to deny Mrs Jones access to her garage entrance
3. talk to her again
The aspects thus far considered are:
image = the Smith’s self-image
car
= the continuation of Mrs Smith’s car entering their courtyard
cost = the estimated cost of the action in euro’000
The Smith’s desiderata and their expectation of the outcomes are expressed by the model
in Figure 1. The outcome of litigation is uncertain. If they estimated the probabilities of
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each litigation outcome they could use a weighted sum or expected value calculation to
obtain a quantitative estimate measure of the utility of the litigation option. Doing the
same thing with the other alternative actions would enable a decision to be made, but
would it be a sensible one?
desiderata
alternative actions
litigation
wall
talk
litigation outcomes
win
lose
settle
cost
<5
image
good
car
no
0.2
bad
no
yes
cost
3 - 10
3 -10
5
image
bad
car
no
yes
no
Figure 1 Expected outcomes
In his celebrated treatise on The Art of War, Sun Tzu advises against fighting any battle
you cannot afford to lose unless you know you can win. If the Smiths lost their case, they
would lose all hope of any future negotiation with Mrs Jones, be deemed to be the party at
fault in the eyes of the neighbours and incur considerable expenses on lawyers’ fees and
court costs.
Looking at the decision problem that would be faced by a court judge, it can reasonably
be assumed that his decision desiderata would be that his judgement be consistent with
the cuurent rules of law and, if extending them by predcedent, be just. He could find in
favour of either party, or dismiss the case.
The Smiths believed they held the moral ground, but the legal position was more on the
side of Mrs Jones. The Smith’s courtyard served as a right of way for three other
properties as well. Unlike Mrs Jones’ car, the other residents’ vehicles did not need to
pass directly beside the Smith’s kitchen, but any judgement against Mrs Jones having a
right of way through the Smiths’ courtyard would necessarily apply to the other
householders. And the other residents had no other means of access to their properties.
The model of Figure 2 projects that the judge would have to reason that to find in favour
of Smith, the principle of right-of-way would have to be contradicted, which is unlawful
and would thereby create an unjust precedent. It did not look as if the Smiths would be
successful in a court case. And presuming Mrs Jones’ lawyer was aware of the legal
position, it was unlikely he would advise her to settle out of court.
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Desiderata and Alternatives:
desiderata
alternative judgements
Smith
Jones
dismiss
legality
legal
predecedent
just
outcomes
Considerations:
causes
judgement
Smith
Jones
effects
neighbours’ rights of way
causes
neighbours’ rights of way
maintained
impeded
effects
right-of-way principle
upheld
contradicted
causes
right-of-way principle
contradicted
upheld
legality
unlawful
lawful
impeded
maintained
legality
unlawful
lawful
effects
precedent
unjust
unjust
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Expected Outcomes:
desiderata
alternative judgements
Smith
Jones
dismiss
legality
lawful
predecedent
just
outcomes
unlawful
unjust
lawful
just
Figure 2 Modelling the judge’s expected reasoning
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Thus taking Mrs Jones to court would be inneffective as the Smiths were sure to lose the
case. Because of this, building a wall would most likely result in the Smiths being sued
by Mrs Jones and losing that case, so it too is not a feasible alternative.
It seemed an impossible situation.
But their analysis of their situation thus far was limited to only trying to find ways of
stopping Mrs Jones car passing through their dining area close to their kitchen. They
needed to probe more deeply into the decision problem.
They have three ways to continue their abductive search:
modify their objectives (desiderata)
modify their action choices
modify their cause-effect model.
They had set themselves the objective of stopping Mrs Jones’ car disturbing them. It
certainly was a problem, but it was not their fundamental problem. This was that they
were dissatisfied with their present situation. They had to either change it or change their
perceptions of it.
What could they change? Changing residence would be a major upheaval. They did not
want to move house, as aside from the issue of Mrs Jones’ car, they were very satisfied
with where they lived. It was otherwise quiet, in a pleasant village with a good school for
their young daughter, close to many of Mrs Smith’s old friends, near to pleasant
recreational facilities and areas, and it had a nice view of the French Alps from its upstairs
balcony. Mr Smith had done a lot of renovation work on it and their investment in the
house was more than merely financial. To find another affordable property with similar
advantages would be difficult and stressful at the very least.
Changing their dining place was feasible, for they had a pleasant garden at the rear of their
house, although it was less convenient than the courtyard, requiring more time to carry
things there and back. The problem of the exhaust fumes from Mrs Jones’ car entering
the kitchen could be resolved by keeping the window closed and constructing an alternate
means of ventilation at an estimated cost of 200 euros. A more radical option would be
to, at an estimated cost of 3000 euros, reorganise the ground floor of the house,
converting the the guest bedroom at the rear of the house into a kitchen. Here it would be
close to their garden. Unfortunately, this would place the new kitchen next to the rear
driveway used by their other neighbours for vehicle access, so it would also require
ventilation other than by a window. However, their self-image would be good and Mrs
Jones’ car would no longer impede their dining al fresco.
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alternative actions
litigate
wall
talk
move house
dine in garden and reventilate kitchen
dine in garden and move kitchen
cost
3 - 10
3 - 10
image
downside
?
0.2
3
good
stress
carry
good
car
yes
yes
yes
no
no
no
Figure 3 Revised prognosis and new alternatives
Dining in the garden seemed a promising option despite the tedium of having to carry
things back and forth, as it was a more pleasant spot than the bare gravelled courtyard.
However, when they tried it, an unexpected consequence manifested itself.
Their daughter often played in the garden, but when they went there to eat, she became
disturbed by the insects that were attracted to the sweet food. She was inconsolably afraid
of being stung by bees. Dining in the garden on a regular basis was clearly impossible.
Now what?
Looking again at Figure 1, it can be seen that the only optional action that had not been
thoroughly explored was “talk”. But what was there to talk about? Mrs Jones had
rejected the Smiths’ idea of building a garage for her in her garden. One of the things she
liked about her garage was that it was internal, which made it very convenient for her
when transporting heavy objects such as grocery bags.
For an agreement to be accomplished, the Smiths needed to find a way to satisfy Mrs
Jones’ desiderata as well as their own. Mrs Jones requirements were simple: she wanted
to use her garage. Was there a way she could do this yet not disturb the Smiths? Clearly,
the only possibility was for her to have a differently located entrance to her garage.
It was a large room, formerly used for storing farm equipment. She used the outer part as
a storage area and the inner part – the part closest to the Smith’s kitchen – as her garaging
area Would she agree to switching these around so that her car would not have to pass so
close to the Smith’s kitchen? Mr Smith was unsure; he had not seen inside Mrs Jones’
house and Mrs Jones was away on holiday. It was a possibility though.
Thinking about the internal structure of Mrs Jones’ house led to another idea. Her house
was not much wider than a car-length garage would be long. It seemed likely that her
garage extended the whole width of her house. Hence there was a possibility that an
entrance could be constructed at its other end. That way she could enter and leave
without entering the Smiths’ courtyard at all. To construct such an entrance would
require building a door into the wall that was the front of her house, knocking a gateway
in her garden wall and building a short driveway. There was even an ancient gateway that
had been bricked up which could be modified for the purpose.
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Her garden would not be the same, but it would not be despoiled by the presence of a
garage. A brief survey of the external configuration of the front of Mrs Jones’ house
showed that there was indeed an ancient bricked-up doorway just where the new entrance
would need to be constructed. It would have to be widened to accomodate a car, but it did
suggest that Mrs Jones’s garaging area did indeed extend the whole width of her house.
Putting in a new garage door at the front would not impact any of her accomodations.
The Smiths could offer to pay all the costs, estimated at around 1000 euros. Mrs Jones
would actually benefit, as the new entrance would be easier for her to access than having
to turn her car around in the limited space of the Smith’s courtyard. She would only have
to suffer the temporary inconvenience of the building alterations. It was a win-win
option.
alternative actions
litigate
wall
move house
dine in garden and reventilate kitchen
dine in garden and move kitchen
new garage entrance
cost
3 - 10
3 - 10
?
0.2
3
1
image
downside
good
good
good
good
stress
carry
none
car
yes
yes
no
no
no
Figure 4 A way out for the Smiths: a new way in for Mrs Jones
This potential solution did not emerge magically from the method, but the principle of
seeking a satisficing solution did encourage a deeper assessment of the litigation option,
leading to its elimination as a feasible alternative. The process of looking for things to
change in the model prompted ideas about moving the dining place, but when these too
were found to be infeasible, the decision makers were obliged to reconsider their
judgement that it was pointless talking to Mrs Jones again.
The principle of satisficing encouraged the Smiths to consider that a negotiated settlement
must be satisfactory to both parties and they were thereby prompted to think about the
situation from Mrs Jones’ point of view. Her sole objective was that she be able to
continue to use her garage. It was fortunate that the garage was potentially accessible
from both directions. Had this not been the case, the Smiths would have had to just put
up with the situation as it is, or move house or come up with a more inventive solution.
But at least they would not have incurred the stress and cost of a sure to be unsuccessful
legal battle.
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5. Discussion
The model that is put together by a committee might be called a summary expression of
its “collective memory” insofar as its contents impact the deliberation of the issue under
debate. As Haseman et al (2003) observe: “The advantages of capturing collective
memory are many, including simplification of the process, codification of decision
strategies, carryover of knowledge when group composition changes, etc.”
Putting together a semiquantitative model is not timeconsuming - indeed, using a written
shared model can actually make the decision making process shorter because its explicit
display tends to avoid endless going over of the same ground as often happens during the
debate of controversial or delicate issues.
Because the process is not elaborate, little briefing of participants is necessary; it is
obvious to everyone how it operates once they see it in action. They do not need to know
its underlying mathematical theory, just as a car driver does not need to know the laws of
thermodynamics. The geedt notation does not obscure the process with jargon or
symbolism, lending it the “readiness to hand” (Heidegger, 1962) of a useful “object-tothink-with” tool (Papert, 1993).
Brown (2006) lists six essential requirements of a useful decision aid. Below, his list is
reordered and classified:
Operability - Address the decider’s real concerns
- Call for input that people can provide
- Produce output that the decider can use
Acceptability - Fit the institutional context
Functionality - Draw on all the knowledge he has
- Represent reality accurately
The method described here focusses on the first group: it is a process that enables
deciders to express their concerns in the form of a semiquantitative model and
communicate with it, because it is their own creation.
But the method falls short of meeting the second and third groups of requirements Brown
regards as essential. The geedt notation and the principle of using a semiquantitative
values are markedly different from the prevailing culture that cherishes quantitative
measurement. For example, Brown (ibid) remarks: “I now believe that nothing short of
reporting a credible and highly visible quantitative measure of research usefulness will
move researchers and sponsors to take it seriously”. Hence the method is unlikely to fit
existing institutional contexts. It also does not draw on all the knowledge deciders have,
but only on that knowledge they decide to apply to the problem and/or share with the
group. And the method’s ideological orientation is much more aligned with the principle
of representing reality “sufficiently unto the purpose”, rather than “accurately”.
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This means the method is unlikely be accepted within the world of large organisations.
But it may find a place in a decision aid toolkit for ordinary people deciding things where
professional image is not at stake.
5.1 Applicability
Real world decisions are made in the context of a complex system of market, physical,
ecological, sociological and political dynamics. These complexities, however, do not
place such decisions beyond the scope of semiquantitative logic. For example, Brown
and Osunkoya (2004) discuss the potential of semiquantitative modelling to the problem
of deciding whether a proposed Acacia plantation would present a threat to biodiversity.
Acacia is very popular among foresters but receives a very bad press from
conservationists; the real truth about the species and its ecological impact probably lies
somewhere in between the points of view that are argued by the opposing sides.
Using a semiquantitative model does not beget taking advantage of the wealth of
operations research models available for finding optimising choice combinations. On the
contrary, such models can be used very beneficially as sources of attribute values within a
broad-ranging model that can also take into account factors and aspects of reality that are
not susceptible to numerical simulation. One such case is a decision faced by one of the
author’s students in deciding when she and her husband should have a baby. Financial
projections of family income and expenditure provided quantitative estimates which were
combined together with qualitative factors such as the psychological effects of
motherhood upon her studies, the reduction in mobility occasioned by new responsibility
and so forth.
The method does not provide a mechanical means of solving the decision problem, but it
does have the virtue of making it clear what the issues are. In the example, the principle
of searching for a model-theoretic certain outcome pushed the decision makers to look
more deeply into what at the surface appeared to be an uncertain outcome.
5.2 Causality
McCarthy (1996) observed a systematic inadequacy of rule-based expert systems; namely
that because their knowledge is limited to particular cause-effect relationships, they lack
the general knowledge he calls common sense that could be needed to reason sensibly
about a situation not explicitly covered by the rules the expert system has. Ad hoc
decision making is concerned only with the particular decision at hand, rather than an
entire class of decision problems. Nevertheless, if some practicable way to model
common sense were developed, its deployment in ad hoc decision making would relieve
some of the effort necessary to build a causal model.
One can find many examples of circular arguments being used to justify assumptions.
Sometimes this is just political “spin”, but sometimes it is genuine misunderstanding. For
example, Davis (1979) writes: “On the basis of his new theory of relativity, Einstein
concluded that an observer would measure this particular speed for light, quite
irrespective of his own speed or that of the source of the light”, whereas Einstein (1905)
Page 14 of 20
writes: “We will ... introduce another postulate … that light is always propogated in
empty space with a definite velocity c which is independent of the state of motion of the
emitting body”. In Einstein’s account both the constancy of the speed of light and
Relativity Theory are causes (postulates), whereas in Davis’s account Relativity Theory is
the cause and the constancy of the speed of light is the effect. If, as most physicists do,
we accept Einstein’s algebra, there is no doubt that the two propositions are correlated –
each leads to the other. But which idea came first to him? Einstein’s later anecdotal
remarks suggests he conceived of the constancy of C in his early teens, long before his
PhD on relativity was published.
In the decision making method described here, the alternatives lead to the effects and the
desiderata test the effects, so there is no such “chicken or egg” quandry. Or is there?
The “leading to” and “testing” both depend upon the model, which in turn can be
constructed so as to prove a given alternative satisfies the desiderata - the method is not
immune to “spin”.
5.5 A Role for an Automatic Theorem-Prover?
To use logical causal model for decision analysis, two general techniques can be applied.
Natural deduction involves, for each decision alternative, inferring all its effects and then
seeing whether they satisfy the criteria and, if so, backtracking through the chain of
deductions to form the rationale. Proof-finding involves, for each decision alternative,
setting up the desiderata as a conjunctive theorem, adding the alternative as an axiom of a
logical model, and using a method of proof-finding to establish whether the theorem is
satisfiable within that model.
In both modes of operation, a separate application of an automatic inference engine would
be required for each alternative. This is technically simple, but it has the disadvantage
that it does not provide a direct visual comparison of the merits of the alternatives. One
could not include all the alternatives as axioms in a single model, as they may have
combined effects that would interfere with the logic - axioms are inherently conjunctive,
whereas alternatives are by definition disjunctive, if not necessarily exclusively so.
However, by looking at causality from the other side of the coin of time, a causal model
can be viewed as a "forensic logic” model of rules of the form:
IF effect has occurred THEN it may be because of cause
It is rather like looking at causality from an Archimedian "view from nowhere" (Price,
1996), as if there were no arrow of time. Forensic inference deals only with possibilities,
not certainties, and does not preclude there being other reasons why an effect may occur,
so the law of the excluded middle and the principle of bivalence still hold. Modal logics
(Marcus, 1962) use special operators to symbolise different semantics such as “must be
true” or “may be true” and n-ary logic predicates (Yamamoto and Mukaidono, 1988) map
elements of a domain to a set such as {T, F, maybe}. A forensic logic predicate simply
maps a subset of a domain to the set {T, F}, so no special operators or semantics are
required.
Page 15 of 20
Diagnosis of cause, whether in medical, judicial or other retrospective enquiries, always
proceeds by the making of inferences from the forensic evidence available. In standard
logic, cause implies effect and effect can be inferred from cause. But in diagnosis, one
can only see the effects and is trying to "prove beyond reasonable doubt" what the cause
was. MYCIN (Shortliffe, 1976) used forensic logic rules annotated by estimates of the
strength of inferences (and algorithms for amalgamating strengths) for differential
diagnosis of bacterial infections. Notwithstanding the functional limitations of its
representation (McCarthy 1996), MYCIN’s approach gained widespread approval and
was very influential in the development of the field of Expert Systems (McCorduck,
2004).
Given a causal model couched in classical logic form, an automatic proof-finding
procedure can interpret the rules as forensic logic rules by reading antecedents as
consequents and vice versa. It could then find those qualities of each alternative that are
logically implied by the desiderata, which are precisely those that would partially satisfy
them in a classical logic model, notwithstanding the fact that logical implication is not
symmetric, as only those cases where both an antecedent and its consequent are valid are
of relevance.
The extent to which an alternative’s qualities are deducible from the desiderata is an
indication of how near it is to being a satisficing choice. An automatic theorem prover
that performed the deduction and highlighted the partial matches could thus provide
visual heuristic diagnostic guidance for the abductive process.
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Appendix
Generalised Extended Entry Decision Tables
Definitions
A quality q is a set of symbols or a range of numerical values.
A state is a tuple S = <q1,..,qn> designating a subspace of a universe
U = Q1 x Q2 x ... x Qn where (i) (q i  Qi)
A geedt is a mapping {R}: U → U delineated by a set of state transitions from S to S’
where R = (<c1,..ci,..cn>,<d1,…dj,..dn>) where ciQi and dj Qj ,
interpreted by a rule of inference:
(i) (R.ci = {}) v (S.q iR.ci) ≠ {})├ (j) (S’. dj = R. dj S. dj)
Local Consistency and Completeness

A geedt T ={Rj}, j = 1,..,m is locally consistent iff it contains no two rules which match a
situation that make different inferences:
 Ri, Rji#jk Ri.ckRj .ckmRi.dm Rj.dm
Let D = (D1,..,Dn) be the universe of domains of antecedents of state variables, where
Di Rj cij = 1,..,m
Then T is locally complete iff there is no state in D that does not match the antecedent of
some rule in T.
The computation of completeness is achieved by subtracting the state spaces
circumscribed by the antecedent of each rule from D. If the remaining space
L = (…((D - R1) – R2) -…- Rm) is empty, T is complete.
L - R = ((L1 - R.c1), L2, …, Ln) 
(L1, (L2 - R.c2), …, Ln))  ….
….  (L1, L2, …, Ln - R.cn)
The recursive subtraction performs its function in less than exponential time, as many
remaining subspaces quickly become empty before the entire enumeration of
combinations is made. Because rules are conjunctive, once any dimension of a remaining
subspace becomes empty, no state could match it, whereupon that line of the recursion
terminates.
Page 20 of 20
Notes
i
The foundation of classical logic is the axiom of Modus Ponens (Suppes, 1969), which asserts that given
an inference rule that a conclusion can be deduced from a premiss and evidence that the premiss is true, the
conclusion may be deduced.
Of course, just because one can write down a rule does not necessarily mean that the rule is valid. In
general, the empirical veracity of a causal rule is context-dependent, but contextual dependency can be built
into the definition of the cause and can also be expressed within a model by its structure – ie how chains of
causal rules fit together. How well a (bounded rationality) model reflects reality is largely a function of how
well its rules are circumscribed and organised.
In the predicate calculus, the logical operator of implication is so defined that an inference rule is defined to
be true even in the case where the premiss is false and the conclusion true, but Mackie (1974) imposes a
condition of necessity upon the antecedent of a causal rule. That is, X implies Y is true when X is false and
Y is true, but X causes Y is false when X is false and Y is true.
The method described here is based upon a different type of causality, one equivalent to the semantics of
logical implication, which might be written in English as:
“If (but not only if) X is true
Then it causes Y to become true”
No condition of necessity is imposed upon its antecedent for a rule to be valid within a model; (the value
inferred by) a consequent can arise from any number of causes, not just the (value of the) antecedent of a
single onmiscient rule.