Simulating “Stage” Theories: An Exploration with
Applications
Edmund Chattoe-Brown1
1
Department of Sociology, University of Leicester, University Road, Leicester, LE1 7RH
ecb18@le.ac.uk
Abstract. This paper presents a simulation of so called “stage” theories (ST),
systems in which agent states are constrained to follow sequences. Put more
simply, agents can only reach stage x from stage x-1. A general example is
provided by education (where one must understand arithmetic before algebra)
but stages are often found in social theories, for example, those of Becker
(marihuana use) or Rambo (religious conversion). Despite their ubiquity, ST
have received little attention as a class. This paper intends to clarify their
properties using simulation prior to empirical research.
Keywords: Stage theories, religious conversion, simulation, social theory.
1 Introduction
It is a commonplace of social science that certain processes occur in sequence. A
general example is offered by education in which new knowledge must build on old.
Extending this idea, we can view knowledge as a “tower” where the solidity of the
foundation determines the maximum height. 1
However, we also find stages in specific theories. For example, in a famous paper,
Becker [1] identifies stages in becoming a marihuana user. First the potential user
must learn to inhale effectively, then they must learn to recognise the state of being
high and finally they must learn to enjoy that distinctive state. At each stage, effective
use may by prevented by a failure to learn the appropriate skill. However, the
potential user always moves forward from the last stage they have mastered rather
than having to go “back to the start” as one might after “dying” in computer games.
This idea of stages is simple enough but although widely used in social science, the
foundations and formal properties of such systems seem to have received little
consideration. I shall postpone most foundational discussion until after a simulation
has been presented and analysed but, in the next two sections, I shall define the kind
of ST that will be discussed and examine their relation to existing simulations.
1
This is a more humanist view than the (often implicit) hypothesis that individuals have an
inbuilt “limit” but, to my knowledge, educational research maintains the ideology that everyone
can learn forever, thus neglecting such issues. To a practising teacher, this ideology is
obviously wrong even if limitations actually reside in teaching and not learning.
2 Micro and Macro ST
This paper will not explore what might be called macro ST, those in which whole
societies supposedly proceed in stages. An example is provided by Comte’s
hypothesis (the so called “law of three stages”) that all societies pass through
theological, metaphysical and positive phases [2]. It can be seen that (from the ABM
perspective) such theories are as unconvincing as many social scientists find them for
other reasons. If we regard stages as particular sets of social arrangements then macro
ST require implausible determinism without clear cause. For example, in undermining
theology, it is “necessary” that metaphysics must arise and prove its value. 2
This observation shouldn’t be over stated. Certain social arrangements may be
attractors or capable of reproducing themselves so macro societal patterns should not
be ruled out but the logic of robust sequences in these patterns is unclear.
Thus, this paper will only consider micro ST where sequences are supposed to
exist in attributes of individual agents. Apart from the interest arising in this general
class of theories as a result of their use in social science, they are also not so selfevidently unlikely. To foreshadow later argument, it is relatively easy to see how
some states of an agent can be logically prior to others. For example, it is hard to see
how agents can make choices when they don’t know the alternatives available and
especially when they don’t know choices are available [3].
3 Existing Simulations (and Other Research)
The ABM implementation of ST can be extremely simple. A sequence of states is
defined (for example as integers 1-10 constituting one attribute of an agent) and social
processes produce ordered transitions between states for each agent: 1 to 2 to 3 and so
on. It is the nature of these social processes that situate ST within existing simulation
research. For example, in social learning models, an agent may advance one stage
when it meets another at that later stage. This system is very close to a simple social
influence simulation [4] except that “influence” only moves agents one way. This
might be interpreted as an absence of “forgetting”. Once agents reach stage 5 they
cannot revert to stage 4. This can be contrasted with a standard social influence model
where an agent’s opinion may move from 4 to 5 and later reverse. 3 Micro ST can also
be distinguished from systems like Granovetter’s [5] threshold model. It isn’t the
number of other agents at any stage that directly determines “willingness to adopt”
that stage (although it does indirectly through the ecology of agents at other stages).
2
In the simpler case of technology, the development the wheel does not necessarily occur.
This might be seen as a weakness. An agent could lose credibility or be unwilling to display
constant variation of opinions. Returning to a previous opinion might imply “mistakes” or lack
of justification. Memory/self-consistency in opinion dynamics is usually ignored in simulation.
3
4 Preliminary Analysis
Something can be understood about ST before simulation occurs. In a social influence
model where agents can only achieve stage x if they meet other agents already at that
stage, no agent can pass the latest stage in the initial population. A ST of this kind
lacks what might be called “self starting”.4 One strength of evolutionary theories (for
example) is that they only involve variation and selection but no quality requirement
on system initialisation. However awful the initial population, as long as some
instances are less awful, it is these that form the basis of subsequent populations and
gradual improvement will occur from whatever starting point. By contrast, social
influence cannot explain how initial populations achieve later stages. This seems
unsatisfactory. The obvious solution, that agents can progress through stages without
help seems to defeat the point of social influence. Why do we postulate social
influence when agents can proceed alone? Should we apply Occam’s Razor?
In fact, the situation isn’t quite so bad. Innovation and diffusion are conceptually
distinct and we can still ask two interesting questions of “pure” social influence. The
first is (given agents with infinite life times) what is the distribution of stages? The
second is (given agents with finite life times) what is the latest stage that is
sustainable in the population?5 In an educational context might we worry that, under
certain social arrangements, the latest stages would simply fail to reproduce
themselves effectively?
This raises a third issue. The system dynamics will depend significantly on
assumptions about the ability of those at later stages to adjust the stages of others. If
agents can only do this one stage at a time then, as already discussed, the system is
limited by latest initial stage. However, it is also potentially limited by the distribution
of stages. It is easy to see how an agent at stage 1 might be left behind by the
population. If all stage agents had moved on before they encountered the unfortunate
stage 1 agent there would be no subsequent opportunity for it to change stages. 6 By
contrast, this problem would not arise if agents at later stages could influence all those
at earlier stages rather than just those adjacent to them in stage terms.
In a teaching context, arguments exist for making different assumptions. On one
hand, teachers might be able (at least) to bring pupils up to their own stage. On the
4
This is also true of many innovation diffusion models.
Interestingly, the fact that all individuals may be “progressing” does not imply that societies
progress. In fact, in a pure social influence model, the best a society can hope for is stable
social reproduction and regression is perfectly possible. This in an interesting side light on the
relation between micro and macro ST.
6 An interesting application involves the interface between educational institutions. It is one
thing to bewail “dumbing down” in education as a whole but how much more damaging if gaps
arise between schools and universities such that most pupils simply cannot benefit from what is
traditionally regarded as “university level” education despite formal eligibility. How much
more difficult for each sector to close any such gap without co-ordination even assuming they
are willing. (In maintaining standards unilaterally, universities may simply make education
unproductive while believing they are being scrupulous.) Ironically, one way in which such
gaps occur may arise from ST. If teachers complete university education without really
understanding its goals, they cannot teach these and thus the gap is likely to be reproduced,
although individuals may transcend it at considerable effort through individual learning.
5
other, teachers might be most effective teaching somewhat below the limits of their
own knowledge. Too close and they might not understand themselves (and what is
understood and can be well explained may differ), too far and they might not be able
to recognise the state of the learner effectively. Such issues cannot be resolved by
“armchair theorising” (and it is possible that educational research has never cast the
issue of learning systems in quite this way) but it is important to recognise the
potential significance of the exact social influence assumptions for system dynamics.
The final issue to be considered is that of reproduction, both social and biological.
If the stage a child has reached when it starts school is determined by the stage of its
parents and the level at which teaching is “pitched” is determined by those who are,
themselves, at a particular level (teachers/policy makers), it is clear how a relatively
subtle but nonetheless divisive problem arises. Following Bourdieu and Passeron [7],
the “objective” educational failure of groups can actually be attributed to arbitrary
preconceptions and an explicit reliance on abilities not provided by the system itself.
Unless the state undertakes to rear all children from birth, a “handover” from parents
to schools is inevitable. However, it is far from inevitable that the consequences of the
relation between the stages of pupils, parents and teachers should be blamed
exclusively on the pupil nor (to return to the practical use of simulation) that the
consequences of such a potentially complex system should be susceptible to “linear”
policy. Returning to the issue of interfaces between educational sectors, we can see
how the ability of the whole system to deliver a particular distribution of stages in the
population might depend crucially on the ability to maintain the latest stages. 7 Failing
this, social “regression” may occur by a kind of “unravelling” process.
5 A Case Study: Rambo’s ST of Religious Conversion
In this section, I discuss a significantly different application of ST. The purpose is
firstly to demonstrate (within the relatively small compass of a single paper) that these
issues are of general relevance and secondly to analyse the detailed foundations of
ST. By this I mean that it is easy enough to specify a ST but less clear why this
general class of theories exists and when it applies. For example, how likely is strict
logical priority of stages in a typical social system? In what social settings are stage
processes likely to be found? What kinds of social processes (collective or individual)
are likely to produce movements between stages? The example is Rambo’s [6] ST of
religious conversion. This involves the following stages:
Context: All the things that brought the person to their current state where the study
of the conversion process is supposed to start. [A biography of person x.]
Crisis: What happens to destabilise their belief system. [The death of a loved one.]
Quest: The search for an alternative belief system resolving the crisis. [A need to find
a supernatural rationale for death absent from an atheist or agnostic standpoint.]
7
There is also an issue about the law of large numbers. Probablistic “gaps” in the learning
ladder are unlikely to occur in big populations. However, they are presumably more likely in
the small populations found at later stages.
Encounter: A meeting with a person (or perhaps artefact?) which embodies the belief
system resolving the crisis. [A conversation with a sympathic Anglican priest.]
Interaction: Based on the encounter, the quester interacts with the relevant religious
community and establishes that the faith does in fact meet his/her needs and that s/he
is willing and able to commit to its requirements. [Visits to a local Anglican church.]
Commitment: The seeker joins the religious community and commits to a role within
it. [Tithing/other moral actions arising from membership, attendance, church duties.]
Outcomes: The convert does (or doesn’t) find what they sought. [The death is at least
accepted or the supernatural rationale doesn’t provide lasting comfort.]
There is a lot for foundational understanding of ST here. Firstly, while context doesn’t
look like a stage, it explains why other stages do in fact have that property. For
example, different events will destabilise different belief systems (a death may
destabilise an agnostic while encounters with evil may destabilise a Christian) and
quest, interaction, commitment and outcome stages depend on the psychology,
experience and so on that the person carries with them. The mistake is perhaps only to
think of context as an undifferentiated “heap” of variables rather than (in ABM terms)
time dependent specifications of agent state determining environmental interaction.
Secondly, several stages involve external events but the nature of these can vary
considerably. Crisis might involve a losing a loved one, “putting two and two
together” about beliefs one previously thought made sense, witnessing how other
people treat each other and so on. The same diversity can be imagined in the
encounter and interaction stages. From an ABM perspective we need to allow for
shifts that may occur cognitively without outside cause, on the basis of social
encounters and through encounters with “artefacts” or any combination of these.
Thirdly, choice is an important element in ST despite their apparently
“deterministic” character. Context initially implies no choice. Crisis creates the need
for choice. Quest identifies alternatives. Encounter and interaction sketch out
potential costs, benefits and moral conflicts. Each of these stages seems strongly (if
perhaps not logically) prior to the others. Without crisis, psychology urges “If it ain’t
broke don’t fix it”. Without quest, there is no resolution to the crisis and no set of
alternatives over which to decide. Thus a ST is deterministic in regard to the logic of
the choice process and that, given a crisis, there will be quest till resolution (or death)
but there is no determination of what faith will be chosen or how long the process will
take. There may be other common social actions that “create” stages in this way.
Fourthly, this kind of ABM specification can be used to identify stages which lack
structural significance or have only “narrative” importance. For example, the first
encounter with the faith that eventually resolves the crisis will be an important relief
but little follows about its stage status. The encounter need not be a person, it might
be as mundane as a story in a magazine bringing back memories of comfort from a
neglected faith. In this case, while we can “define” the encounter as an event, it isn’t
clear how this changes the dynamic of subsequent events. Given the definition of the
ST, it isn’t clear that someone can “stick” at the encounter stage in the same way they
can stick at the quest stage. From the ABM perspective, there is perhaps a
requirement that a stage needs to involve elements outside the agent’s control.
Questing doesn’t guarantee finding but a positive encounter makes it extremely
unlikely that an agent wouldn’t search extremely actively for the corresponding
interaction. (One could tell a contrived story about meeting a priest from an obscure
faith and a seeker discovering that there was no church of that faith in his/her country
but generally encounters strongly imply the possibility of realising interaction.)
Finally, the example of reinvigorated faith in the face of crisis and the need to
evaluate a faith (potentially resulting in further quest) draw attention to the possibility
of loops. These should be distinguished from branches (to be discussed later) in that
they do not violate the assumption of deterministic sequence used to define ST.
6 A Basic Simulation, Results and Discussion
As befits an exploratory simulation, the model is extremely simple. Each agent has an
attribute definining its stage (a positive integer) and, during interaction (based on
random mixing), one agent at a higher stage may change the stage of another (at a
lower one) by “teaching” it in a small number of distinct ways defined below. User
controlled features are the population of agents, the number of those agents who are
“starters” (not initialised at the earliest stage and thus serving as potential “teachers”
in the system) and the number of stages.8 Different assumptions can be made about
the distribution of stages for “starter” agents. These may all be at the same stage (call
this the “homogeneous starters” condition, HoS) or distributed randomly up to that
stage (“heterogeneous starters”, HeS). Different assumptions can also be made about
how one agent may learn from another. Agents may only learn from those at the next
stage (“Adjacent Learning”, AL9), from those at all subsequent stages (“Inclusive
Learning”, IL) or from those up to x stages later than them (“Nearby Learning”, NL).
Finally, the extent to which agents are able to “learn for themselves” can be varied
(“Self Learn”, SL, and “No Self Learn”, NSL conditions).
Even for this simple simulation 12 experimental conditions exist in addition to
variation introduced by number of stages and proportion of agents who are starters. I
shall only look at outcomes of the experimental conditions and user controls
separately. For experimental conditions, I used a standard setting of 200 agents and 30
starters in a 20 stage process. In each case the variable for comparison is the “steady
state” average stage in the population after 1000 periods.10 All agents live for 80
periods and spend the first 10 of these being “socialised”: receiving learning mainly
from their (single) “parent” rather than from the community at large.
Figure 1 shows a typical run in HoSALSL condition.11 The starters clearly fail to
transmit later stages to the wider population before they die and there is a drop to a
steady state which can reproduce itself (societal “regression”). Even with SL, there is
little variation in the latest stage attained by the most “advanced” agent and thus little
opportunity for the population to move further through the stages. 12
8
Some stage processes may be open ended (have no latest stage) but I neglect this possibility.
Here, for a 20 stage process, “nearby” is defined as within 4 stages in all conditions.
10 Because many runs show “regimented” behaviour, this value depends on when sampling
occurs. To minimise this, samples are averaged over a “lifetime” from 920 to 1000 ticks.
11 The title reflects an ordered sequence of stages as a kind of “learning ladder”.
12 It is possible that under conditions yet to be identified endogenous “renaissance” may occur.
9
Fig. 1. Latest, Average and Earliest Levels for a Typical Run in the HoSNLSL Condition.
Figure 2 shows the other common regime in the system (HoSILSL condition). Here
the latest stage attained by starters is maintained and the average stage of the
population is enhanced (societal “progress”). Interestingly, as usually occurs in this
regime, the pattern of average stage is quite “regimented” despite the probabilistic
nature of the system. This surprising result will be investigated further.
Fig. 2. Latest, Average and Earliest Levels for a Typical Run in the HoSILSL Condition.
Table 1 shows the twelve possible experimental conditions. The first finding is that
the system is relatively stable, without large variations in steady state values.
However, allowing for variation, 3-4 distinct output regimes exist. The first is “high
learning” (average stage values around 15 out of 20 available) for conditions 2, 5, 8
and 11. Here the effect of IL, largely independent of SL/NSL is to ensure that later
stages are rapidly transmitted to the population. In terms of process, the IL condition
most rapidly blurs the initial distinction between starters and “others”. The second is
“intermediate learning” for conditions 3, 6, 9 and 12. Here NL does not allow
transmission as rapid as IL but it is still effective largely regardless of SL/NSL. The
third condition is “low learning” for conditions 1, 7 and 10. Here, the potentially
limiting effects of AL (agents can only learn if there happens to be an agent at the
next stage in the population) is meliorated by SL but still severe. Condition 10 is the
only one that looks like it may be significantly different from other runs in its output
regime (with values around 0.9 rather than 1.2 – this will be investigated further).
Finally, there is a unique “no learning” regime (condition 4). Here, with NSL, starters
simply cannot transmit to other agents as they are too many stages apart.
Table 1. Average Stage of Population Under Full Set of Experimental Conditions.
Starter Condition
HoS
HoS
HoS
HoS
HoS
HoS
HeS
HeS
HeS
HeS
HeS
HeS
Social Learning
AL
IL
NL
AL
IL
NL
AL
IL
NL
AL
IL
NL
Self Learning
SL
SL
SL
NSL
NSL
NSL
SL
SL
SL
NSL
NSL
NSL
Average Stage
1.25, 1.37, 1.25
15.1, 15.39, 15.44
11.62, 11.41, 11.64
0, 0, 0
15.23,15.27, 15.16
11.19. 11.83, 11.35
1.21, 1.31, 1.4
15.4, 15.59, 15.36
11.45, 11.65, 11.61
0.99, 0.99, 0.99
15.18, 15.36, 15.12
11.58, 10.94, 11.57
These condition combinations do not lead to outcomes in a simple linear way.
Different “factors” dominate the outcome in different combinations making the
system unsuitable for reliable narrative or statistical characterisation. In retrospect,
this justifies the decision to simulate. Recognisable regression occurs in conditions 1
and 4 and progress in the other conditions.
The sort of regimented outputs shown in Figure 2 made me want to try and “break”
these results. I have not done this for all twelve conditions but for a single condition
(HeSNLSL chosen randomly), it proved encouragingly hard. Table 2 shows the
outcome of exploring the parameter space. 13 Columns 1 and 2 show the effect of
changing the number of stages. Column 1 gives the number of stages. In column 2,
the steady state average is expressed as a fraction of the number of stages “available”.
The system reproduces short stage sequences much better than long ones. This
outcome is non linear and draws attention to the importance of “demographic” and
“structural” issues like lengths of socialisation, schooling and learning “lifetime” in
the social reproduction of “hard” skills (those involving many stages). Columns 3 and
4 show the effect of varying the population size (keeping the fraction of starters
constant at 10%). This effect is fairly small and relatively linear. Columns 5 and 6
show the effect of number of starters (out of 200 agents) on average stage level. This
effect is very small until the fraction of starters gets very high and even then it is not
particularly large. This suggests both that it is the behavioural regime that dominates
and that, fairly soon, the clear distinction between starters and others in the population
at large breaks down as knowedge spreads and the population replaces itself.
13
Because of the relative reproducibility of runs shown in Table 1, these are the results of
single runs.
Table 2. Effects of Various Parameters on Average Stage in the Population.
Stages
1
10
20
30
40
50
60
70
80
Fraction
0.99
0.8
0.575
0.39
0.32
0.28
0.21
0.17
0.17
Population
10
30
50
80
120
150
180
200
Average
11.7
11.4
11.2
10.9
11
10.4
9.6
9.4
Starters
1
5
10
30
50
80
120
150
200
Average
11.8
11.8
11.6
11.7
11.5
11.9
12.1
12.3
13.1
Finally, there is a concern that this system may be sensitive to initialisation
assumptions about the age distribution of starters and the stages of the other agents at
the start of the simulation. In fact, at least for the condition chosen for further study,
the steady state shows almost no sensitivity to these factors. These findings provide
encouragement that any results discovered are not intolerably brittle (as the
“regimented” output might have suggested).
What can be learned? At best, these simple (but I believe novel) simulations have
shown the possibility of societal regression (failure of social reproduction) and the
potential hazards of “gaps” (especially in the AL condition) informally raised earlier.
Also, this approach casts a different light on stage systems, revealing their connection
to macro phenomena of social reproduction in an interesting way. This kind of
simulation steps back from the individualised approach to learning and sees teachers
and learners as operating within a macrosocial context with a potential for collective
action failure. If any one group fails to pass learners up the “ladder of learning”
effectively, this affects the system as a whole and not just the learners concerned. It
may also feed back unpredictably to the structure of the learning ladder itself.
However, given the simplicity of the model and lack of calibration/validation, it
would be unwise to draw conclusions about when progress or regression occur.
(Comfortingly, regression appears to be rare, occurring mainly in ALNSL conditions.)
However, because (to my knowledge), there are no other models of this kind in the
literature, even a preliminary analysis still adds value in opening up this set of ideas.
7 Possible Extensions and Conclusion
There are several ways in which this research could usefully be developed:
7.1 Modelling “Real” ST
It would be relatively straightforward to simulate Rambo’s theory. 14 In addition to
understanding limitations of that theory by simulation, deepening understanding of
14
The core element might be some sort of bit string representation of religious faiths which
“matched” (or did not) the current state of the agent. Mismatch would constitute a crisis.
the “building blocks” of ST15 and comparing real and simulated data (for example the
distribution of times spent in various stages based on biographical data), this exercise
might also illuminate an important foundational issue. Is the existing social scientific
notion of “stage” simply sloppy thinking for the precise specification of process
practiced in ABM? As suggested above, it may be that some stages turn out to have
no substantive “underpinning” in the ABM. Conversely, others may serve as
workable (and measurable) summaries of particular stages real social actors go
through. We can see how a social actor could realistically be put in the “quest” stage
given its behaviour and reports of a past crisis. Finally, by recognising the distinction
between the agent and environment, we may be able to provide a formal definition of
a stage in terms of the agents inability to move to the next without some external
input. It may be the existence of exogenous processes which defines stages.
7.2 “Solving” the Problem of Regression
The notion that (even with personal and social learning operating) social reproduction
may fail is a disturbing one. It is too early to say much about when and why this
might happen but even the thought that it might is salutary. This way of thinking
about learning systems suggests topics for both empirical research and further
simulation. Empirically, it would be interesting to look at classroom dynamics in
terms of information transfer between teachers and pupils. The ability of education
systems to “pass on” students and avoid “learning gaps” would also make a good
topic of study. In particular, can “mental models” of students and their congruence
with the goals of learning serve as predictors of success? What happens to students at
university who believe their task is to fill a “bucket of facts” as they did at secondary
school? Such explicit attempts to match the state of the learner with the state of the
teaching might even have important policy implications for educational success. 16
On the simulation side, there are also interesting issues to be explored. The role of
artefacts in social simulation is often neglected, perhaps on the grounds that “things”
don’t matter to social interaction. In this simulation, however, artefacts (in this case
“books”) have a distinct role to play. In a sense, what is “wrong” with the simulation
above (which allows regression to occur) is that everyone learns only from each other
or from themselves and the system lacks an anchor in the non social world. If a gap
occurs in the knowledge ladder, this is a bottleneck until it is filled. How likely self
learning is to fill such gaps is a matter for conjecture. At low levels (getting the back
off a computer), it seems reasonable. At high levels (learning calculus), much less
so.17 On the other hand, the presence of durable artefacts at each stage of the learning
process is an obvious resolution to the bottleneck problem and, furthermore, gives
artefacts a distinct role in the system as things that do not have constantly changing
15
In what sense, for example are simulated versions of Rambo’s stages processually “similar”
to any of Becker’s stages? Is there an atomic “set” of common kinds of stage from which all
extant ST can be reconstructed? If so, this would be a useful theoretical generalisation.
16 My own direct experience suggests both that it is ineffective to “take for granted” any
obvious skills in modern students and that it is actually quite hard to figure out what their
model of the university educational process must be from their behaviour!
17 Another refinement is that higher levels of education explicitly try to turn students into more
effective self learners.
stages. On the other hand, this clearly isn’t a panacea. Even with a book on calculus,
it would be unreasonable to assume that everyone could teach themselves that skill!
7.3 Details of the Learning Process
For simplicity, this model involves the typical “random wander on a flat plain”
assumption. In practice, education is obviously much more structured. Pupils are put
in classes, classes in educational institutions and educational institutions into
educational systems. What consequences do these kinds of structures have for the
overall distribution of stages? What effect does it have if teachers and institutions
only operate over a fixed range of stages/ages under a division of labour? 18 What
happens if these stages somehow fail to join up?
One example is provided by the concern with class origins in education. The
simple simulation only looks at average stage, earliest and latest. Because there is
random mixing, we are unlikely to see polarisation of learning with successful and
disaffected groups [8]. On the other hand, without random mixing and with
homophily in class groups and selection into schools, we can much more easily see
how the learning dynamics of good schools might become a virtuous circle while that
of “sink” schools becomes a vicious one. In the real world, it is known that children
from some backgrounds arrive at school “behind” and are much less likely to catch
up. Add to this the “comprehensive” notion (captured by this simulation) that the
better students may “draw up” the less able and it is possible to see how phenomena
like selective education, streaming and changes in the “stages” of schooling (and the
corresponding testing regime) may have important effects on the overall efficacy of
the system that are very hard to predict. That would be a classic opportunity for social
simulation in a new area of social science!19
7.4 Formal Developments to ST
We can think of ST as a hypotheses with varying degrees of “strength”. The strongest
possible is that all cases follow a single sequence barring measurement error. Weaker
is that a certain number of stages can be “missed” or occur in non standard order.
Weakest of all is just that a sub set of stages should occur more often than any other
sub set of possible stages. Simulations of ST (and their extensions) can be used to
explain why such strong or weak patterns might exist in terms of underlying (and
potentially less observable) behaviour [9]. What will happen to the robustness of a
sequence when there is probabilistic transition between some or all stages? For
example, in the Rambo model, what impact does the choice of different possible
religions have on the overall properties of the sequence? Once such multiple routes
18
It is possible that as a first approximation such issues could be explored by making agent
interactions conditional on things like the age and “type” of the agent. At present, everyone
teaches everyone. It could be this assumption that might be relaxed in the first instance rather
than focusing on the details of the spatial and administrative details of education systems.
19 There is, of course, a large literature on organisational learning but the structures of firms and
schools are so different that the findings would be unlikely to be comparable. In addition, these
models (to my knowledge) deal with the efficacy of individual firms rather than systems of
firms.
exist, it may also be possible to carry out some of sort of Markov chain analysis of the
resulting systems and there is also an interesting theoretical question about when it is
useful to view learning as a “tower”, a “network” or some other structured object.
7.5 The Problem of Data and Self Delusion
This paper deliberately seeks to meet the criteria of the conference in describing a
simulation and its outcomes. However, the comparison with evidence is more
problematic and needs further work. Governments have a considerable incentive not
to draw attention to failing education systems. There is also an argument that says that
it makes no sense to talk about quality independent of particular measures of it.
Nonethless, there is anecdotal evidence (for example from individuals informally
administering the same test year on year) that ability may be going down while
measures of that ability go up. Further, it is possible (though not easy) to think of
ways that quality might be observed unobtrusively regardless of its formal
assessments. For example, A level markers might covertly be given essays to mark
that were actually written several years ago or students might be asked to take old
exam papers without knowing they were old.20
At the same time, there is also a potential problem of self delusion. We tend to be
uncomfortable with the idea of “Ages of Gold and Lead”. Who wants to be the best
social scientist in a deeply mediocre era? Although it is a commonplace that older
people always think they live in the worst of times, it is possible (and worthy of
empirically grounded social scientific study) to consider whether and when that might
actually be true!
Acknowledgments. I am grateful to Asiyah Kumpoh whose interest in religious
conversion in Brunei drew my attention to this class of theories.
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20
Both approaches have obvious problems but are better than nothing.