Models and methods of explanation: dynamical systems, agent models, reflexive

Models and Methods of Explanation

Dr. John Bradford

Overview

I. Types of studies: case study, cross-section, longitudinal

II. Devising and Testing explanationsIII. Unorthodox approaches to model-building

1. Dynamical Systems Modeling2. Multi-agent modeling3. Second-order cybernetics

I. What is being explained?

Types of Research1. Case study (what

causes an event or condition)

2. Cross-sectional study (comparison across space)

3. Longitudinal study (comparison across time)

• Often we aren’t interested in Y itself as a fact or event, but changes in Y across time (longitudinal study) or differences in Y across space (cross-sectional study).

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)

II. Steps to create and test a causal hypothesis (‘explanation’)

Step 1: Create a model or hypothesis1. 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

Steps in creating and testing a causal hypothesis (‘explanation’)

Step 2: Testing the hypothesis/model1. 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!

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.

Key points about ‘explanations’:1. Explanations must specify causal mechanisms2. Correlation is not causation3. 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.

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.

III. Unorthodox approaches to Modeling (Hypothesizing)

1. Dynamical Systems Modeling2. 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)

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).

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

System as cause vs. Laundry-list approach

1. Laundry-list approach– Gravity, – Removal of Hand

2. System-as-cause approach:

– The Slinky!

What causes the Slinky to oscillate?

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).

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 feedback3. Effects are “linear” (fixed or proportional to their

effect)4. Effects are instantaneous (no lags or delays)

Comparison of Methods

Capable of Static, cross-

sectional

Comparative Static

(e.g. panel regression)

Time Series(e.g. ARIMA)

Dynamical Systems

Modeling

depicting systemDynamic?

X X ✔ ✔

depicting systemStructure?

X X X ✔

Linking Structure to Dynamics via Simulation?

X X X ✔

Stocks and FlowsSt oc k

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.

Stocks and FlowsSt oc k

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.

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 A lt er

ego c om m unic at ing t o a lt er

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.

Note: Stock to Stock links are not permitted. Only flows change the values of stocks.

St ock 1

St ock 2

inflow

St ock 1

St ock 2

inflow

inflow 2

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

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.

Feedback loops Stock-flow structure of “Positive” (Reinforcing) and

“negative” (counteracting) feedback systems:

Reinforcing Loop: Counteracting Loop: Exponential growth Exponential decay

Populat ion

growing

growt h ra t e

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Components of the Structure The following model can be decomposed into two feedback

loops: one positive, or reinforcing, the other negative, or counteracting.

Populat ion

growing

growt h rat e

dec lin ing

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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.

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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!

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The Stock-Flow Structure looks like this:

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Sens it iv it y R es ult s f or Populat ion

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Populat ion: 1 - 2 - 3 -

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The Behavioral Dynamic looks like this:

Dynamics of Depletion: Overshoot and Collapse

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”

Populat ion

growing

growt h rat e

dec lin ing

dec linerat e~R es ourc es

c ons um ing

res ourc esper pop

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regenerat ing

regenerat ionrat e

~10: 10 AM W ed, Mar 03, 2010

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1: Populat ion

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Stock-flow diagram of system exhibiting overshoot behavior

Population

initial 10being born

Death rate

dying

Birth Rate

Resource

consuming

consumption

per capita

D=1-R(t)/R(0)

Overshoot and Collapse of Population

2: 06 PM Tue, Mar 02, 2010

Sens it iv it y R es ult s f or Populat ion

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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-level patterns may emerge from the bottom-up.

NetLogo simulation

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).


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 interactions4. 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


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.

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


• 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.


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!


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!


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)


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)


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.


Example: Segregation and unintended consequences

• Thomas Schelling (2005 Nobel Prize winner) famously 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.

Thomas Schelling


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!


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!

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 XY 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!

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!

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.


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.

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)


• 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!


• 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.


• 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.


• “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.

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).

Triple Helix Model

Models and methods of explanation: dynamical systems, agent models, reflexive

Technology

based computational

based computational

triple helix

dynamical

based models

feedback loops

reinforcing

unorthodox