An Expanded Feedback View of
Decision Maker Mental Models
Alexander Y. Lubyansky, PhD Student
Rockefeller College of Public Affairs and Policy, University at Albany
135 Westem Avenue, Albany, NY 12222
alubyansky@ gmail.com
Abstract
It may be useful to simulate the feedback dynamics of individual and group decisionmaking to
study certain problems, like the diffusion of insurgent tactics. A good place to begin is to expand
on Richardson, Andersen, Maxwell, & Stewart's (1994) SDS conference paper on mental model
research.
The main part of this paper elaborates on Richardson et al.'s causal map by incorporating
theories necessary to make a more “complete” representation of the decision process. The
theories include theories of cue perception and interpretation, mental models, decision-making,
attention (salience), and social influence. The paper concludes with a small, initial simulation of
part of the decision-making and social influence dynamics and shows how the model can
accommodate external datasets.
Key Words: Diffusion, Mental Models, Perception, Judgment, Social Influence, Salience
Introduction
Generic Problem
It is difficult to study the dynamics of systems where the important behavior comes from
heterogeneous decision makers communicating ideas with each other and making boundedly
rational judgments based on those ideas. Several features characterize this generic kind of
problem:
1. Data needed to understand decision maker mental models and social networks may be
qualitative, sparse, and imprecise. Despite this, the amount of data may be quite large
if it includes the issues, goals, actions, influence relationships, etc for all relevant
decision makers.
2. There may be no data about individual decision makers, but rather proxy data about
events in the world, with little or no idea about what particular individuals or groups
caused these events.
3. The important dynamics of decision maker social cognition and social influence are
theoretically complex.
4. The combination of complex theory and a set of problematic data make it very difficult
to analyze the whole problem using qualitative methods such as mental simulation and
role-playing.
Example Problem: Diffusion of Insurgent Tactics
A concrete example of this generic problem is the problem of predicting the diffusion of
insurgent tactics. Insurgents pose a difficult threat to counterinsurgents such as the US in Iraq
and Afghanistan. Cells can rapidly change their tactics to respond to and even anticipate
counterinsurgent actions (see Figure 1). It is too difficult to predict exactly which new tactics
insurgents will use, but it may be useful to understand how tactics “diffuse” throughout an
insurgent population.
IEDs destroy
HMMVWs
US deploys .. bigger IEDs
and EFPs
Figure 1. Counterinsurgent and insurgent adaptation to each others’ tactics.
The known data (START, 2009) about insurgent tactics is uneven:
1. We know most about what happened (group A attacked target B on date C using method
D).
2. We know a bit less about the networks involved (group A’s members, their interactions
with each other and their interaction with other actors). However, we can estimate the
composition and communication patterns of “typical” cells.
3. We know even less about mental models. How did the cell decide to use one tactic or
another? Interviews are difficult (impossible?) and self-reporting on these matters is
unreliable.
From the Global Terrorism Database (START, 2009), one of the most comprehensive open
source databases on terrorism, we can find or derive the following information:
e Who
o Insurgents — estimate their attributes and identities based on region,
demographics, or randomly; some groups claim responsibility for attacks or are
identified
e What
o Actions (insurgent attacks)
o Target type (government, military, etc)
o Target (in cases where the specific target is important)
e Where
o Countries, regions, cities, neighborhoods
e Why
o Self-claims
o By attacker identity
e When
o Date
e How
Suicide or not
Number of attackers
Weapons used
Vehicles used
o Method of attack
e Outcomes
Success or failure
Targets killed, wounded, captured
Perpetrators killed, wounded captured
Property damage
ooo0o°0
O°
oo°o
Approach
Given a problem, such as diffusion of insurgent tactics, with the above-mentioned theoretical and
data problems, one potential approach is to develop an integrated theory dynamics of decision
maker mental models, make that theory into a simulation model, and test the simulation model
against the existing data. This approach allows quantified, theoretically-sound modeling of data
otherwise unsuitable to model decision maker dynamics.
Theory
The proposed theory for the system dynamics model comes from an integrated and inherently
boundedly rational view of decision maker social cognition and social influence. This view
corresponds with the system dynamics assumption of bounded rationality and represents the
main processes within the “system boundary” of social cognition and social influence.
The main inspiration for this integrated theory comes from the expanded dynamic hypothesis
(Figure 7) of Richardson, Andersen, Maxwell, & Stewart’s (1994) research into the feedback
dynamics of mental models. The integrated theory in this paper builds out on this hypothesis
such that the new hypothesis (Figures 3, 4, and 8) resemble Richardson, Andersen, Maxwell, &
Stewart’s (1994) hypotheses (Figures 5 and 7).
Ata high level, the theories used in this section fall under the subsections of Cue Perception and
Interpretation, Mental Models, Decisionmaking under Uncertainty, Salience, and Social
Influence. These theories largely coincide with the viewpoints of other system dynamics models
of integrated social cognition (Deegan, 2005; Martinez-Moyano, 2005; Martinez-Moyano,
McCaffrey, & Oliva, 2005; Rahn, 2005; Rich et al., 2005; Weaver & Richardson, 2006).
Cue Perception and Interpretation
Boundedly rational models of cue perception and interpretation come originally from the
Brunswik Lens Model (Brunswik, 1939, , 1952; Wolf, 2005). This model shows the perception
of data about an uncertain environment by the (human) organism as indirect. Basically, a given
phenomenon has various characteristics that can be perceived and interpreted by a person as
cues. Only via these cues does the person get an understanding of their environment, even
though this understanding is biased and uncertain.
In the policy process literature, there is a set of scholarly work (Baumgartner & Jones, 1993, ,
2002; Birkland, 1997, , 1998, , 2001; Jones & Baumgartner, 2004, , 2005a, , 2005b; Kingdon,
1995; Lindblom, 1959; Sabatier, 1999) dedicated to understanding policymaking from a
boundedly rational perspective. In their theory, Jones & Baumgartner (2005b) use a cue-based
model to describe individual and organizational policy maker perception and interpretation. In
their model, the policymaker only sees the world through a set of biased cues. Furthermore, the
policy maker can only perceive the cues by paying attention to them or making them salient
(more on salience later). This process is shown in Figure 2.
al
[Source] [Indicator ] a
oe | ===> [Decision ]
[ Source, ] ae
Figure 2. Baumgartner & Jones’ (2005b) depiction of cue perception and interpretation.
For the proposed method, the implication of a cue-based model of perception is that there are
four kinds of cue-related ideas and states:
1. A state of the world.
2. A cue about the state of the world.
3. A perceived state of the world. The speed with which states of the world are perceived
depends on the salience of the cues informing the perceived state. A decision maker can
only perceive a state of the world if he or she is paying attention to the relevant cues.
4. A goal. Both a perceived state of the world and a goal state of the world are necessary to
form a gap. The gap allows perceptions to be understood as a mental model idea about a
problem, a solution, or a causal explanation.
Figure 3 shows the part of the Dynamic hypothesis that relates to cues.
Decision Gap<+—__,
Maker's World Perception
of State yy
/ Cue
Cue Salience
Goal
State
Outside
"Physical" World
Figure 3. State of the world, cue perception, and cue interpretation.
Mental Models
Mental models are central to most models of boundedly rational cognition (Craik, 1943;
Johnson-Laird, 1983), certainly so in the system dynamics community (Sterman, 2000). In the
theory of mental models, a person has a representation of all their knowledge in the form of a set
of interconnected symbols or ideas.
Mental models may be divided into several kinds of ideas. The most relevant to the decision
maker decision view of mental models are ends, means, and means-ends ideas (Richardson,
Andersen, Maxwell, & Stewart, 1994). These correspond to the problems, solutions, and causal
explanations in the decision maker’s mind. This representation is backed up by organizational
and policy process theories of decisionmaking (particularly the Garbage Can Model of
Organizational Choice), even though these models often implicitly represent causal explanations
(Cohen, March, & Olsen, 1972; Jones & Baumgartner, 2005b; Kingdon, 1995).
There are three kinds of mental models ideas (aside from the aforementioned perceived states
and goals). These ideas come from perceived states and goals and are used to make decisions.
1. A “problem” idea is the “ends” part of a mental model. The statement behind a problem
idea is, "Problem X is important and needs to be addressed now."
2. A “solution” idea is the “means” part of a mental model. The statement behind a solution
idea is, "Solution Y is feasible and available for use now."
3. A “causal explanation” idea is the “means-ends” part of a mental model. The statement
behind a causality idea is, "Solution Y is effective at addressing problem X."
Operationally, the attributes that measure problem, solution, and causality ideas in the model are
certainty, and salience. Certainty is the degree to which the decision maker is convinced that the
statements in the above list are true. For example, a problem idea held with great certainty means
that the decision maker strongly believes that problem is important and urgent. Certainty changes
based on the gaps in perceived states and goals relevant to the mental models idea. For example,
if a principal’s goal compliance is much higher than perceived compliance, they will eventually
acquire the strong belief that compliance is a serious and urgent problem.
Maker's World
Ideas include
Problems,
Solutions,
and Causal
Explanations
Decision Gap<—__,
Perception
of State
Idea
Certainty
Cue Salience
Goal
q
Idea
Salience » Decision
Cue
State
/ Outside
Action — "Physical" World
Figure 4. Mental model ideas, decisions, and actions to change the state of the world.
Salience is the degree to which the decision maker is paying attention to an idea. The dynamics
of salience are explained later. Decisions are made based on the certainty and salience of mental
model ideas about problems, solutions, and causal explanations. A combination of certain and
salient problem, solution, and causal explanation creates pressure for a decision.
These decisions lead to actions which may be aimed at correcting the state of the world, forming
a long feedback loop. Figure 4 shows the part of the Dynamic hypothesis that illustrates this
process. This partial dynamic hypothesis highly resembles the system dynamics diagram of
Richardson, Andersen, Maxwell, & Stewart’s (1994) basic dynamic hypothesis in Figure 5.
Attention
(scanning, selection,
and measurement)
Interpretation
(information
processing)
Subjectively
interpreted cues
(perceptions)
Mental mode!
Cognitive model
of system function
iieicenagy)
\
Strategies and tactics
(means)
‘Assessment and
prediction of
system state
%
Planned
Internal
dynamics
Cues
="
State of
yy system
Action
\e
Desired state action
(ends)
Mental activity
‘System fuction (reality)
Figure 5. Richardson, Andersen, Maxwell, & Stewart's (1994) basic model of cognition.
Decisionmaking under Uncertainty
The model of decisionmaking in the proposed method comes from both boundedly rational
models of analytical decisionmaking and from a boundedly rational model of intuitive
decisionmaking. These models confirm the dynamic hypothesis in Figure 4 and suggest that the
decision maker’s actions include those shown in Figure 6.
The analytical models are the Garbage Can Model (Cohen, March, & Olsen, 1972) and its policy
process descendents (Jones & Baumgartner, 2005b; Kingdon, 1995). These models specify that
when there is an urgent problem, a feasible solution, and a believable causal explanation that
the solution addresses the problem, and then a decision is make to apply the solution to the
problem. Jones & Baumgartner (2005b) make the important amendment that these mental
models ideas must be salient for the decision to occur.
In Kingdon’s and Jones & Baumgartner’s models, there is also mention of actions other than the
enactment of policy to change the state of the world. Before, during, and after proper
“decisions”, the decision makers in policymaking change their goals, the attention that they pay
to cues and mental model ideas, and the mental model ideas themselves.
The intuitive model is the Recognition-Primed Model of Decisionmaking (Flin, 1996; Klein,
1998). This model, developed from empirical research into decisions taken under great stress and
time pressure in uncertain environments, suggests three types of intuitive decisions.
In a simple match decision, the decision maker perceives a situation through a set of indicators
and automatically matches the situation they indicate with an action. In a diagnosing the
situation decision, the decision maker has cues that don’t perfectly match potential actions. In
this case, the decision maker must think harder about the indicators, matching them up feature by
feature to possible actions. In the final type of decision, called evaluate course of action, the
decision maker cannot match the indicators to the action without a suspicion that something
important does not fit. The decision maker mentally simulates the situation to double-check the
decision and try to customize it to fit the environment.
Decision Ga
Maker's World a
of State
Ideas include \
Problems, Idea
Solutions, Certainty Cue
and Causal Cue Salience
Explanations
Goal
State
Idea
Salience _»-Decision é
N_. Outside
Action — "Physical" World
Figure 6. Different kinds of actions.
Like the analytical models, this model suggests that the decision maker’s decisions include
changes to cue salience, goals, idea certainties, and idea saliences. The dynamic hypothesis in
Figure 6 shows these additional decisions and largely overlaps with the representation of these
decisions in Richardson, Andersen, Maxwell, & Stewart’s (1994) expanded dynamic hypothesis
shown in Figure 7.
Attention
(scanning, selection,
and measurement)
Interpretation
(information
processing)
Judged adequacy of
assessments and
forecasts Ps
Changes in cue selection mace Subjectively =
and interpretation rarer percent ae
erceptions|
Cognitive model suador
of system function— tate o
(means-ends) . the system
. Assessment and
prncccampeiied \ prediction of Internal
Sree system state dynamics
Strategies and tactics
(mearis) .
Action
Modification of Planned || |
strategies and tacti Desired state action
(ends)
System fuction (reali
Modification
of goals
Base Judged adequacy of
planned action
Mental activity
Figure 7. Richardson, Andersen, Maxwell, & Stewart's (1994) expanded model of
cognition.
Salience
Salience means prominence and is used in theories of social cognition and social influence to
describe the degree to which a person pays attention to an idea or cue (Wikipedia, 2009). There
are several basic determinants of salience.
The first determinant of salience is direct experience. The more exposure a decision maker has
to cues and communications from other people (social influence is discussed later), the higher
the salience of the perception of the relevant cues and mental model ideas. This can be
extrapolated into the idea that changes in cues and mental model ideas also create salience. If
something changes rapidly, the more one can be said to “experience” it.
The second and third determinants of salience are the degree to which ideas relate to
consequences for- and aspirations of- the decision maker. This means that important problems,
feasible solutions, and convincing causal explanations have more salience. In summary, high
idea certainty leads to high idea salience and low idea certainty leads to low idea salience.
Jones & Baumgartner’s (2005b) understanding of salience in a policy process context also adds
the following properties of salience:
1. Attention inertia: Attention, once focused on a given cue or mental model idea, tends to
stay there by default. This suggests that the salience allocated to a given cue or mental
model idea is a system dynamics stock.
2. Attention shifting: Powerful government decision makers tend to stop paying attention
to a policy once it has been dealt with, as new and different issues demand attention. This
goes along with the positive effect of idea certainty on idea salience.
3. Threshold effects: Policy makers will not perceive information to be serious enough to
act upon, until it passes some threshold of importance. This threshold is variable, and
shifts over time for various reasons. This goes along with the conclusions of the Decision
Making under Uncertainty section, where a combination of problem, solution, and causal
explanation needs to be certain and salient for a decision to occur.
4, Agenda crowding: An organization can only pay attention to so many issues at once.
Agenda crowding makes it harder for new issues to get attention. This suggests that total
salience is limited, a bottleneck on the amount of attention that can be focused on any one
cue or mental model idea.
5. Friction/overreaction: If policy makers have been ignoring or not adequately dealing
with pressures for change, the acknowledgement of these pent up pressures often leads
policy makers to overreact in their response to a policy issue. This rule is not immediately
applicable to the proposed model.
6. Cascades/herd mentality: The more a given issue, problem, or solution gains attention
with policy makers, the more others mimic this attention. This suggests that salience
positively affects idea certainty, which therefore positively affects idea salience, creating
a positive feedback loop.
7, Sieves/sequential selection: Policy makers go sequentially through alternative sets of
policy issues, problems, and solutions, rather than paying attention to all of them at once.
This conforms to the “agenda crowding” idea.
Social Influence
Social influence models have two roots. The theoretical root is in organizational behavior and
social psychology studies, including pioneering work by Asch (1956), Festinger (1954), and
French (1956). The methodological root is in dynamic network models of contagion and
diffusion, including research by Schelling (1971), Friedkin & Johnson (Friedkin, 1993, , 1999;
Friedkin & Johnson, 1990, , 1999), Axelrod (1997), Sznajd-Weron & Sznajd (2000),
Hegselmann & Krause (2002), Deffuant, Amblard, Weisbuch, & Faure (2002), Lorenz (2007),
and Stauffer (2007).
While differing in their focus and algorithms, these models share the same heritage and many of
the same features. Broadly, social influence models are subsets of contagion/infection/diffusion
models (Monge & Contractor, 2003, pp. 173-182) such as the SIR and Bass Diffusion models
with which system dynamics scholars are familiar (Sterman, 2000, pp. 295-347).
In a generic social influence model, the “disease” being spread is an opinion. At the beginning, a
group of people have a set of different opinions; as they communicate with each other, changes
in opinions spread from person to person. The basic dynamic is a negative feedback loop where
the receiver’s opinion seeks to match the sender’s opinion, given several factors. Possible
outcomes of such a model include convergence to a single equilibrium opinion, a “fracturing” of
the group into two or more equilibrium opinions, oscillations in opinions, and various other
behaviors.
In social influence models, the following factors may affect the process of spreading an idea
from a message sender to a message receiver:
1. The inherent persuasiveness of the sender to the receiver. This is a catch-all constant
that encompasses charisma, power relationships, social similarity, institutional reporting
structures, etc. This factor is not immediately applicable to the proposed model.
2. The frequency, length, and intensity of communication by the sender to the receiver.
The more the amount of communication, the more salient the sender’s message is to the
receiver and the more chances the sender has to sway the receiver’s opinion.
3. The difference between sender and receiver opinions. This is known as “bounded
confidence”, where the more of a gap there is between sender and receiver opinions
(certainties of mental model ideas), the less the sender’s opinion will change. However,
since the difference between opinions is what drives social influence, if there is little gap
then the receiver’s opinion does not change much. Therefore, the largest change in
receiver opinion comes from a “medium size” gap.
4. The certainty of the receiver’s opinion. The more certain the receiver is of a mental
model idea, the harder it is to sway them. For example, if a principal becomes convinced
that there is a compliance problem, it becomes more difficult for social influencers to
convince the principal otherwise.
Figure 8 shows the basic “macro” factors of social influence in the dynamic hypothesis.
Decision Gap<+—_,
Maker's World Perception
of State
Ideas include
Problems, Idea
Solutions, Certainty Gui
and Causal Cue Salience
Explanations
Goal
State
Idea
Salience —»Decision fp
ices : Outside
Action — "Physical" World
Social Influence P
; Social Influence
Messages Received
Messages Sent
Outside
"Social" World
Figure 8. The final dynamic hypothesis, showing social influence inputs and outputs.
Simulations
Inspirational Simulation Models of Diffusion
The simulation models that are most relevant to diffusion (Monge & Contractor, 2003, pp. 173-
182) come from the marketing, epidemiology, sociology, and econophysics communities. The
main examples of these models are the Bass Diffusion model, the SIR model, the Friedkin &
Johnson model, and the Hegselmann & Krause model. The basic stock and flow dynamics of
these models are shown in Figure 9.
Simplified Bass Diffusion (Marketing) Susceptible Infectious Recovered (Epidemiology)
Adopting from
innovation
Coefficient of
Innovation
ISusceptib! 4 Infected >} Recovered
R
a ingeed 7 x ae
Potential
Adopters Coefficient of Coefficient of
Adopting
\ ( / Infection Recovery
Coefficient of “adopting from
Imitation Imitation Hegselmann & Krause (Econophysics)
Adopters
bounded confidence bounded
‘rutipler to opinion change confidence
? mutter to
certaity growth
Friedkin & Johnson (Sociology)
Bs T. harciening of opinions
fs oniric|
PRS. Bs opinion ai
aoe rato of rexienurn 7
ee wD opinion gap to absolute certainty
ae fy Poon
clos =I 18} “i
PRG ES OF x: ‘confidence
time to C
time to ( i gap between B's ,
jap sien Bs 's opinion "and A's opkion’
Ass opinion 9 Te ie Tnaxirrum opirion gap
and A’s opinion absolute gwenA’s confidence
+ gett ap bounds
Bis weight on A
B's weight on A
Figure 9. Various diffusion models.
The prototype model of decision maker idea diffusion developed comes from all these models.
The next few figures show how this new model is related to the more common diffusion models,
using the Bass Diffusion and SIR models as an example. Figure 10 shows the loop common to
both these models from Figure 9, but with different names for the relevant variables.
Sender's Idea Receiver's
Certainty Sender Transmitting | dea Certainty
Idea to Receiver
|
|
|
a
Figure 10. Basic diffusion model.
Notably, in Figure 10, the “susceptible” population is actually a stock of a sender decision
maker’s certainty of some idea (see theory in the previous section) and the “infected” population
is a similar stock of a receiver decision maker’s certainty of that idea.
The unit of analysis has moved from a population to an individual and the scale of the idea has
moved from present/absent to a range of certainty/uncertainty. People are not “converted” by an
idea. Rather, the ideas are in various individuals’ heads to some degree and change due to
communication.
Unfortunately, Figure 10 violates the laws of physics. Information does not obey the law of
material conservation and thus the flow structure needs to be changed, as shown in Figure 11.
Sender's Idea
Certainty oO
—$—$___ |
Sender Transmitting
\ Idea to Receiver
\ ;
Gap between Sender's
and Receiver's Certainty
Receiver's
Idea Certainty
Figure 11. Revised diffusion model.
Figure 11 shows the proper information structure. The remaining changes needed to get the
model in Figure 11 to the mostly complete model in Figure 12 are the additions of the “bounded
confidence” loop and exogenous placeholders for more theory on social influence, salience, and
network effects.
The Prototype Model of Decision Maker Idea Diffusion
The simulation model in Figure 12 shows the basic dynamics of social influence, with italics text
indicating constants than can become feedback structure in order to simulate the rest of the
theory. This prototype model can simulate social influence and the explicit change of ideas from
a sender decision maker to a receiver decision maker.
The model in Figure 12 needs elaboration and testing to accurately describe the theory of
perception, interpretation, mental models, judgment, decision making, salience, and social
influence written about in this paper. This may be the subject of future work.
In addition, the model in Figure 12 is not suited to represent more than 2 decisionmaking
“agents”. It is also unsuited to run on subscripted data from spreadsheets and databases. Figure
13 shows a subscripted version of the Figure 12 model.
Receiver's Maximum
Certainty Gap
\
Network Effects /
Use-Usefulness of
Relationships / Etc
Contact Rate
Salience...
Minimum Time to
Transmit 1 Unit of
— Certainty
Acceptability per
Certainty
y
Social Influence Acceptability of ‘i é
Factors / Believability Sender's laximum Certainty
Message to Transmission Rate
Reciever
/ Receiver's
Absolute fun ‘Sender Transmitting Idea Certaint
Certainty Gap A+) Idea to Receiver
Sender's Idea
—
Bounded Confidence
Closing Idea Gap
Gap between Sender's
and Receiver's Certainty
Figure 12. Full diffusion model.
Basic Mechanics of
idea Transfer
The model in Figure 13 has removed the twin decision maker roles of “sender” and “receiver”
and replaced them with a set of subscripted matrices. The model in Figure 13 can simulate a
potentially large number of agents representing individual decision makers or groups of decision
makers. This subscripted model is also configured to take data from spreadsheets, with some
mock data shown in Figure 13. Work is ongoing to take actual data series from sources like the
Global Terrorism Database (START, 2009), transform them into spreadsheet
variables
representing decision makers, communication networks, ideas, and events, and use them to
populate the model shown in Figure 13.
Idea (Problem, Solution, Causality)
INumber| Receiver's Maximum
a i . .
i me a Certainty Gap Minimum Time to
C Transmit 1 Unit of
‘3UseMortar Contact Rate ~~ Certainty
4UseRPG Acceptability per \ y
ee oe Certainty
TUselED Acceptability of
Li aUsensssune Sender's Message to Initial Idea
Person to Person Reciever Certainty
(Connection) __
Number [To... 1 2 ?
From..._ame—_Abdulah Zaitulah | Absolute ———_— Idea Certainty
[Abdullah Certainty Gap Sender Transmitting
itullah Idea to Receiver
Person to Person (Contact Rate) SN a
[Number |To... | - at
rom..._ [Name \dullah _|Zaitullah_| Sender Receiver “
Abdullah, \dea Certainty Gap “
2Zaitullah Sender Receiver
Sender Receiver
Idea Certainty. <——
Figure 13. Subscripted diffusion model.
Connection Matrix
Discussion
This paper has described a possible feedback simulation approach to study the dynamics of
individual and group decisionmaking. The paper theoretically elaborates on Richardson,
Andersen, Maxwell, & Stewart’s (1994) work to build an expanded theoretical model of decision
maker to study certain problems, like the diffusion of insurgent tactics. The elaborated theory
includes various components of decisionmaking in the social world, including perception, mental
models, judgment, salience, and social influence. In addition to the theory, there is the
description of a small prototype model that is based on social influence models, can be expanded
to include the other theoretical dynamics, and can link with an external data set for subscripted
simulation.
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