1. Models and Methods of
Explanation
Dr. John Bradford

2. Overview
I. Types of studies: case study, cross-section,
longitudinal
II. Devising and Testing explanations
III. Unorthodox approaches to model-building
1. Dynamical Systems Modeling
2. Multi-agent modeling
3. Second-order cybernetics

3. I. What is being explained?
Types of Research
1. Case study (what • Often we aren’t
causes an event or interested in Y itself as a
condition) fact or event, but
changes in Y across
2. Cross-sectional study time (longitudinal
(comparison across study) or differences in
space) Y across space (cross-
3. Longitudinal study sectional study).
(comparison across
time)

4. Examples of Research Questions:
1. Why is the GDP per capita in
Swaziland in the year 2000
approximately $4,024 (PPP,
constant 1995 international $)?
(Case Study)
2. Why is Swaziland’s GDP per
capita far lower than that in the
US ($31,338)? (cross-sectional
comparison)
3. Why is Swaziland’s GDP
remained basically stagnant over
the past 20 years? (longitudinal,
or time-series comparison)

5. II. Steps to create and test a causal
hypothesis (‘explanation’)
Step 1: Create a model or hypothesis
1. Select something to explain, and establish it is
factually correct; -Establish that an event or ‘fact’
(pattern) exists!
2. Specify a causal hypothesis (from a more general
theory) that explains the phenomenon: if the
hypothesis (X) is true, the explanandum (Y) logically
and necessarily follows.
– If successful, this will show that your explanation is
‘sufficient’: it can account for Y

6. Steps in creating and testing a causal
hypothesis (‘explanation’)
Step 2: Testing the hypothesis/model
1. Identify other possible causes (rival accounts) of the
phenomenon.
2. Refute these other theories by showing that other
implications (which necessarily would occur if the
hypothesis were true) are in fact not observed
3. Show how other implications of your theory are in fact
observed.
– If successful, this will show that your hypothesis/model
is ‘necessary’, it best accounts for the phenomenon
because alternative explanations are refuted!

7. Steps in devising and testing an
explanation
• This is an ideal scenario,
whereby your hypothesis,
derived from a theory, is
validated, and alternative
hypotheses are refuted.
• “If this H is true, then X, Y,
and Z must also be true”
• Show that these other
implications are true for
your theory, and not true
for competing theories.

8. Key points about ‘explanations’:
1. Explanations must specify causal mechanisms
2. Correlation is not causation
3. Causal explanations can be distinguished from
‘just-so stories’ and ‘as-if’ explanations.
– just because a model can explain something, doesn’t
mean it does. Many hypotheses (models) can
account for the same Y. “Explanation” requires
further proof and refutation of alternative theories.
4. Explanation is not prediction!
– We can explain historical events only after the fact.

9. Key points about explanations:
• What is a mechanism?
– Elster provides this definition: “mechanisms are
frequently occurring and easily recognizable causal
patterns that are triggered under generally unknown
conditions or with indeterminate consequences” (36).
– I.e. we cite specific instances of a more general causal
pattern. Causal patterns are generalizable, but we don’t
know which causal pattern will be triggered in any
instance.
• Examples: conformism vs. anticonformism; underdog
mechanism vs. bandwagon mechanism; spillover
effect vs compensation effect; ‘forbidden fruit’ vs
‘sour grapes’, etc.

10. III. Unorthodox approaches to
Modeling (Hypothesizing)
1. Dynamical Systems Modeling
2. Agent-Based models: (aka “Artificial Societies”, Multi-
agent computational models, “generative social science”,
simulations).
• Note: These two methods pertain to STEP 1 above, namely, the
generation of models to account for some observed phenomenon.
They are “sufficient” in the sense that they can explain the
phenomenon, but this does not necessarily mean that they do.
There are always multiple ways of explaining any one
phenomenon.
3. Second-Order Observing (aka second-order cybernetics,
comparative sociology of the observer, systems theory,
autopoiesis, Luhmann)

11. 1. Dynamical Systems Modeling
 A system is a set of interrelating,
interconnected parts or elements that,
together, generate some distinct outcome or
behavior over time.
 In dynamical systems modeling, the behavior
that the system exhibits over time (i.e. its
dynamic) is generated from a model of the
systems structure (i.e. the elements and their
relations).

12. Steps to Dynamical Systems Modeling
1) Identify an empirical reference behavior patter, or
dynamic (typically time-series data)
2) Model the Stock-Flow Structure of the system that is
generating the observed behavior
3) Interrelate these stocks and flows with feedback
loops
4) Tie Structure to Dynamics via simulation: compare
simulation results with observed behavior
5) Further develop model (repeat steps 2-4)
6) Explore policy implications

13. System as cause vs. Laundry-list
approach
What causes the Slinky
1. Laundry-list approach
to oscillate?
– Gravity,
– Removal of Hand
2. System-as-cause
approach:
– The Slinky!

14. System as Cause Thinking
• The system itself is always the cause of its
own behavior.
• “Mental models should contain only those
elements whose interaction is capable of
self-generating the phenomenon of
interest" (Richmond 2010: 6).

15. System as Cause Thinking
Four assumptions that are almost always wrong
when dealing with systemic phenomena:
1. *Causes operate independently of each other:
(“laundry-list” thinking)
2. Causality runs one-way: no feedback
3. Effects are “linear” (fixed or proportional to their
effect)
4. Effects are instantaneous (no lags or delays)

16. Comparison of Methods
Comparative
Dynamical
Static, cross- Static Time Series
Systems
Capable of sectional (e.g. panel (e.g. ARIMA)
Modeling
regression)
depicting system
Dynamic?
X X ✔ ✔
depicting system
Structure?
X X X ✔
Linking Structure to
Dynamics via X X X ✔
Simulation?

17. Stocks and Flows
Stock
f lowing
Stocks
 “Nouns” that indicate conditions or states of
being at a point in time.
 Stocks are things that accumulate over time from flows
 They act as shock absorbers, or buffers, from the changes
in the flows
 They can physical or non-physical: non-physical stocks
“states of being” like anger, self-esteem, trust, etc.
Importantly, non-physical stocks need not obey the Law of
Conservation- they are not zero-sum.

18. Stocks and Flows
Stock
f lowing
Flows
 “Verbs” that represent activities or processes,
which exist over time.
 Flows fill and drain stocks, that is, they update the
magnitude of stocks.
 Flows are not “inputs” to stocks; they do not “influence”
them, and do not “have impacts” on them.
 Flows can by physical or non-physical. Non-physical flows
include: learning, getting angry, communicating, etc.

19. Invalid use of stock-flow language
 The language of stocks and flows is general, but not
universally applicable. It constrains possible ways of
representing the world.
 Example: it not valid to depict communication as a transfer of something
(information, meaning) from one person to another, despite our linguistic
habit. Why not? Because this model assumes that the sender (“ego”)
loses the meaning of the message once it is communicated!
Meaning f or Ego Meaning f or Alter
ego communicating to alter

20. Invalid and valid use of stock-flow
language
 In addition, there are three ways to link one simple stock-flow
structure to another, but only two that are permitted. They
are: 1) Stock to Flow links; 2) Flow to Flow links (Co-Flows),
depicted below.
Stock 1
Stock 1
inflow
inflow
Stock 2
Stock 2
inflow 2
 Note: Stock to Stock links are not permitted. Only flows
change the values of stocks.

21. Content-Independence
 The language of stocks and flows is content-independent:
apparently dissimilar phenomena can be generated by the
same stock-flow structure.
 For example: the following phenomena exhibit the same
behavioral patterns over time and can be depicted with the
same stock-flow structure:
 The boom and bust of a financial bubble
 The depletion of a resource
 Bacterial growth on a petri dish
 The life course of a new commodity
 These all follow the limits to growth archetype

22. Feedback loops
• A feedback loop occurs whenever a change in the magnitude
of a stock in turn affects a flow into or out of that same stock.
• Feedback implies that causality is not unidirectional. A → B,
but also B → A!
• Two types of Feedback:
1) Positive (reinforcing, amplifying) or
2) Negative (balancing, counteracting).
 Note that the terms “positive” and “negative” do not mean “good” and
“bad.” The terms “reinforcing” and “counteracting” are less confusing.

23. Feedback loops
 Stock-flow structure of “Positive” (Reinforcing) and
“negative” (counteracting) feedback systems:
Reinforcing Loop: Counteracting Loop:
Exponential growth Exponential decay
Populat ion
Populat ion
declining
growing
growt h
decline
rat e ~ rat e

24. Components of the Structure
 The following model can be decomposed into two feedback
loops: one positive, or reinforcing, the other negative, or
counteracting.
Population
growing declining
growth
rate decline
~ rate

25. Feedback loop Dynamics
 When both positive and negative feedback are present in
the same system, three possibilities arise:
1. exponential growth: the reinforcing loop will dominate the
counteracting loop.
2. exponential decay: the counteracting loop will dominate the
dominate the reinforcing loop.
3. equilibrium: they balance each other out.
Population
growing declining
growth
rate decline
~ rate

26. Feedback loops
– A reinforcing feedback loop will exhibit exponential growth..
– The rate of change becomes faster: accelerating growth. This is opposed to
“linear” growth or decay in which the rate of change remains constant.
NO SYSTEM CAN GROW FOREVER!

27. Dynamics of Depletion: Overshoot and Collapse
The Stock-Flow Structure looks The Behavioral Dynamic looks
like this: like this:
Populat ion
growing declining
Population: 1 - 2 - 3 -
1: 1800
growt h
rat e decline 3
~ rat e
Resource
consuming 2
1: 900
3
2
1
1
2 3
1 3
1: 0 1 2
~ 0.00 5.00 10.00 15.00 20.00
Page 1 Years 1:16 AM Wed, Feb 24, 2010
resources
per pop Sensitiv ity Results f or Population

28. Dynamics of Depletion: Overshoot and Rebound
 If the resource is renewable, it is possible that it can rebound, but
the in order for this to occur, the resources per population must go
to zero before Resource does,
 In the context of economics, this periodic growth, collapse, and
regrowth can be considered as a process of Schumpeterean
“creative destruction”
Population
growing declining
1: Population
1: 4000
growth
rate
decline
Resources ~ 1: 2000
consuming rate
regenerating
1 1
1
1: 0 1
~ 0.00 15.00 30.00 45.00 60.00
Page 1 Years 10:10 AM Wed, Mar 03, 2010
regeneration
Population
rate
~
resources
per pop

29. Stock-flow diagram of system exhibiting overshoot
behavior
Popul ati on
initi al 10
being born
dying
Death rate
D=1-R(t)/R(0)
Birth Rate
consumi ng
Resource
consumpti on
per capita

30. Overshoot and Collapse of Population
Population: 1 - 2 - 3 - 4 - 5 -
1: 1800
3
2
1: 900
3 4
2
1 5
5
4 1
2 3
1 3
1: 0
4 5 1 2 4 5
0.00 5.00 10.00 15.00 20.00
Page 1 Years 2:06 PM Tue, Mar 02, 2010
Sensitiv ity Results f or Population

31. 2. Agent-based computational
models
• Agent-based models
explain social phenomena
by generating them (in the
simulation) from the local
interactions of
heterogenous actors, or
“agents.”
• They specify how macro-
NetLogo simulation
level patterns may emerge
from the bottom-up.

32. Agent-based computational models
• We view artificial societies as laboratories, where we
attempt to ‘grow’ certain social structures in the computer-
or in silico- the aim being to discovery fundamental local or
micro mechanisms that are sufficient to generate the
macroscopic social structures and collective behaviors of
interest” (Epstein and Axtell 1996: 4).
“Indeed, the defining feature of an artificial society model
is precisely that fundamental social structures and group
behaviors emerge from the interaction of individual
agents operating on artificial environments under rules
that place only bounded demands on each agent’s
information and computational capacity” (ibid. 6).

33. Agent-based computational models
Agent-based computational models are capable of modeling:
1. Agent Heterogeneity
2. Agent Autonomy
• Macro-structure emerge from agent interactions, which then feedback upon
these interactions. Is capable of modeling the co-evolution of macro and
micro-level phenomena.
3. Local interactions
4. Bounded rationality*
5. Ontological correspondence (from Gilbert 2008)
• In contrast to equation-based models, an agent-based model is an analogue of
the process it models. It represents the process which generates the observed
pattern, not just the pattern itself.
6. Adaptation/Learning (from Buchanan 2007, and Miller and Page 2007)
7. Non-equilibrium outcomes

34. Agent-based computational models
Summary:
• All models simplify. In this respect, all models are
wrong. The problem is not that models simplify
reality per se, but rather, that some models leave
out the most important aspects of the social
objects they seek to describe. They distort rather
than simplify.
• Agent-based models simulate the local
interactions of heterogenous actors who influence
one another, are capable of learning, and who do
not possess perfect knowledge and
foresight. These models explain social
phenomena by generating them.

35. Logical structure
• Agent-based models demonstrate what would happen
if agents behave in in the ways specified in our theory.
• The results of a simulation show the “outputs”
(consequences or results) that logically follow from the
“inputs” (our hypotheses).
• A simulation can be treated as a method of deductive
reasoning, in which the “premise” (hypothesis) is
specified in a computer programming language.
• The simulation has the following logical structure:
IF THE ASSUMPTIONS ARE TRUE, THEN THIS IS WHAT
WOULD HAPPEN

36. Agent-based computational models
• Compare to the prevailing ‘rational actor
model’, which explicitly assumes that:
– agents are homogenous or ‘representative’;
– agents are omniscient;
– agents don’t influence one another;
– agents are incapable of learning;
– preferences never change;
– outcomes are always equilibrium conditions.

37. Agent-based computational models
Example: How to model a standing
ovation?
• A “standard” way would be to
observe the number of people
standing and sitting over time,
and then to find some equation
that ‘fits’ this pattern.
• But this exercise in ‘curve fitting’
would tell us nothing about how
this pattern emerges!

38. Agent-based computational models
Example: How to model a standing ovation?
• A second approach (e.g. ‘rational actor
model’) would assume that everyone sits or
stands based on his/her individual evaluation:
some stand because they like it, others don’t
because they dislike it.
• One might infer from this approach which
individuals liked the performance, which
didn’t, and its overall evaluation.
• But these inferences would be wrong, and
again, the model would fundamentally
mislead us about how humans actually
behave!

39. Agent-based computational models
Example: How to model a standing ovation?
• Finally, in an agent-based approach, one can
generate the aggregate (macro) pattern by
simulating the local interaction of
heterogenous agents.
• Unlike the other approaches, such a
simulation can specify that:
1. People influence one another (including
watching and observing)
2. People can adapt (or change their minds)
3. People are heterogenous (spatially and in
terms of their behaviors and preferences)

40. Agent-based computational models
Example: Swarm of Bees
• When modeling the position of a
flying swarm of bees, it might be okay
to treat the average position (in the
center) as representative of the
whole. This would be a
representative-agent model:
assumes agents are homogenous.
• Average behavior, however, can also
be misleading. Sometimes
differences cancel each other out,
but other times not! (Miller and Page
2007)

41. Agent-based computational models
Example: Swarm of Bees
• Genetic diversity among bees enables
them to keep the hive cool, at a steady
temperature, because different bees will
begin to cool the hive at different
temperatures.
• If they were homogenous, however, then
they would have a much more difficult
time keeping the hive at a constant,
average, temperature. This is because all
bees would act to cool the hive at once,
causing it become too cold, generating a
violent oscillation in temperature!
• One can only generate the (homogenous,
constant) temperature of a beehive in a
simulation by modeling the heterogenous
behaviors of bees.

42. Agent-based computational models
Example: Segregation and
unintended consequences
• Thomas Schelling (2005 Nobel
Prize winner) famously Thomas Schelling
demonstrated that racial
segregation of neighborhoods
would arise, even in the absence
of racist sentiments, so long as
individuals prefer to live adjacent
to some neighbors similar to
them.

43. Agent-based computational models
Example: Segregation and unintended
consequences
• The point is not that prejudiced
individuals don’t exist, but rather, that
one should not expect policies directed
towards changing individual attitudes to
have much effect on the macro-level
regularity of neighborhood segregation.
• Moreover, racist sentiments may often
result from the pattern of segregation
itself rather than vice-versa!

44. Agent-based computational models
Example: Income distribution and development.
• Similar models have been developed to explain
income distribution, and also to predict the likely
consequences of policy interventions.
• Because of compounding growth (i.e. reinforcing
feedback), wealth will tend to accumulate in the
hands of a small minority of individuals, even in the
absence of coercive force, and even when all
individuals are endowed with equal access and
equal talents.
• Pure luck will initiate this chain-reaction unless
direct redistributive policies are implemented!

45. Why Agent-based computational
models?
Why is this important/interesting?
• Agent-based models are a unique tool that enables us to simplify
without making crazy assumptions about human behavior.
• They enable us to specify hypotheses and to demonstrate exactly
how these phenomena can arise.
• They force us to specify the causal mechanisms implied in our
theories: in this sense, they are a tool of theory development.
• They enable us to think creatively, and to model causal processes
that go beyond XY models.
• They enable us to tell stories (along with systems dynamical
approaches) and to do social science visually.
• Agent-based models are only sufficient accounts, but in the social
sciences, providing any adequate account of social emergence is a
vast improvement!

46. 3. Second-Order Observing
• I called dynamical systems models
and multi-agent models “methods”
to deal with or observe social
phenomena. This isn’t the whole
truth. The ‘methods’ are always
modes of observing the world that
constitute in some ways that which
they observe.
• Second-order observing (aka second-
order cybernetics) focuses not on
explaining social phenomena per se,
but explains the explanations
themselves!

47. Second-Order Observing
• “Second-order” observing = observing observing.
Just as “second-order” explaning explains
explanations. And “second-order” dreaming
dreams dreams.
• This method of applying a process to itself is
known as recursion.

48. Second-Order Observing
3 important contributors to this tradition:
1. G. Spencer-Brown:
• Logician
• Developed a “calculus of indications”, a formal
theory of distinguishing distinctions.
2. Heinz von Foerster:
• Cybernetician
• Developed ‘second-order cybernetics’ as an
observer-dependent theory of observing.
3. Niklas Luhmann:
• Sociologist, systems theorist
• Devised a theory of self-referential social
systems.

49. The Role the Observer
• The dream of science was
originally to describe a world in
which there were no observers (a
subject-less universe). Then came
two amendments:
1. Observations are not absolute but
relative to an observer (Einstein)
2. Observations affect the observed
so as to render impossible
accurate prediction (Heisenberg)

50. The Role the Observer
• Heinz von Foerster proposed the
following:
1. A description (of the universe) implies
one who describes (a truism)
2. One therefore needs a theory of the
observer: we are challenged to write
a “description invariant ‘subjective
world’” (259)
3. Must ask: “How do we know”, rather
than, “What do Know”
• In everyday language, it’s difficult if
not impossible to distinguish what
you observe from how you observe
it!

51. The Role the Observer
• Compare the following number sequences:
A- 1 2 3 4.
B- 8 5 4 9.
• Both have order! A is in numerical order. B
is in alphabetical order.
• Order does not inhere in things.
– Order or pattern is observer-dependent:
observing order reflects ordered observing.

52. Second-Order Observing
• To “observe” is to distinguish, in order to indicate
one side of a distinction.
• Observing has two levels:
– First order observing = the what
– Second order observing = the how; observes how
others observe what they observe, by distinguishing
(comparing) the distinctions that make possible that
observation with other possible distinctions (and
hence other points of view).
• All observing has a blind-spot: one cannot observe
both the world and one’s observing at the same
time. Every observation is therefore incomplete.

53. Second-Order Observing
• “Second-order” observing =
observing observing. Just as
“second-order” explaning
explains explanations. And
“second-order” dreaming
dreams dreams.
• This method of applying a
process to itself is known as
recursion.

54. Second-order explanations of
development?
• I bring this reflexive turn in the social sciences to your
attention to expand your potential object of inquiry.
• One may attempt to explain, not “development”, but
the explanations themselves.
– Are there certain institutional, or system attributes that
tend to correlate with certain epistemological or
cognitive styles (cf. Fuchs 2001)?
– This approach has recently been formalized quantitatively
(using entropy statistics to analyze social sciences) by
Loet Leydesdorff, who also posits a triple helix model to
depict recursive causal relationships and complex
dynamics arising between three or more social systems
and/or institutions (e.g. government-industry-university
relations).

55. Triple Helix Model