| Copyright © 2009. National Academy of Sciences. All rights reserved. Terms of Use and Privacy Statement |
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 215
6
Meso-Level Formal Models
I
n this chapter we describe and discuss formal models of human behavior
at a level of aggregation and detail between the micro and macro levels.
Such models are often referred to as meso-level models. Typically the
models represent interactions and influences among individuals in groups
and cover both individual and group phenomena and their interactions.
These models include several voting and social decision models, social net-
work models, link analysis, and agent-based modeling (ABM). The models
have been developed in varied disciplines, including social psychology,
sociology, anthropology, economics, and computer and communications
sciences.
vOTINg AND SOCIAL DECISION MODELS
Understanding and predicting social phenomena requires good models
of individuals and groups. The behavior of a group can differ from that of
the individuals that comprise it. A science of aggregation is needed to model
the behavior and actions of collections of people. There is a need to know
how individual beliefs, goals, and skills combine on various tasks, such as
problem solving and decision making. This section covers voting models
that assume people reveal their true preferences, game theory models that
assume people vote strategically, and social psychological models that con-
sider how individual preferences might change in a group setting.
5
OCR for page 216
BEHAVIORAL MODELING AND SIMULATION
What Are voting Models?
The research and models from voting theory provide a natural place to
begin an investigation into aggregation for both pragmatic and conceptual
reasons.1 Governments, terrorist groups, and alliances all make decisions
by “voting.” Some follow formal voting rules and procedures and others
informally aggregate competing desires. Thus, our use of the term “vot-
ing” goes well beyond formal (e.g., electoral) registering of a preference to
much less formal situations in which a preference is exercised or a decision
is made with input from multiple individuals.
Conceptually, voting models are valuable for three reasons: (1) a sub-
stantial body of theory exists, (2) that theory shows no shortage of counter-
intuitive results, thus highlighting the challenges of aggregation, and (3) the
theory highlights a key point: to model groups well, one must be able to
model individuals and the interactions between them.
State of the Art in Social Decision Modeling
We first describe the basics of preference theory. We then discuss results
from social choice theory that reveal the problems created by aggregation
as well as briefly comment on game theoretic models of strategic voting.
The distinction between social choice theory and game theory hinges on
behavioral assumptions. Social choice theory assumes that people truthfully
reveal their preferences. Game theory does not. It assumes that people act
strategically, which may or may not lead them to reveal their true prefer-
ences. The game theory models also enable one to understand how and why
various institutional rules matter. We also discuss research from psychology
that addresses how choices are made in a group context.
Preference Theory
Preferences capture how much people value or desire things. They dif-
fer from choices, which are what people select. Modelers define preferences
over a set of alternatives. These alternatives can be outcomes, or they can
be policies that produce outcomes (Page, 2007). Preferences impose an
ordering over the alternatives. It is customary to write the preferences of
someone who prefers apples (A) to bananas (B) as follows: A > B. Most
modelers make two assumptions about individual preferences: that a person
can compare any two alternatives (completeness) and that a person does
not exhibit any preference cycles or internal contradictions (transitivity).
1 We might have alternatively considered models of riots or collective ecosystem mainte-
nance, but the related literature is not as deep or well thought out.
OCR for page 217
MESO-LEVEL FORMAL MODELS
If a person claimed to prefer apples (A) to bananas (B), and bananas to
coconuts (C), and then claimed to prefer coconuts to apples, one might
think that person was irrational. Formally, it would be said that the person
exhibits a preference cycle in which A > B > C, but C > A. When individual
preferences satisfy both completeness and transitivity (i.e., A > B > C and
A > C), then they are called rational.
If a person has rational preferences and if the modeler rules out indif-
ference, then that person’s preferences can be written as an ordered list from
the most to the least preferred alternative. Given a set of five alternatives,
A, B, C, D, and E, one person’s preferences might be written A > B > C >
D > E, and another person’s might be written E > D > C > B > A.
This construction does not represent strengths of preferences. One per-
son might strongly prefer A to B and strongly prefer B to C. Another person
might have the same preference ordering but strongly prefer A to B and only
weakly prefer B to C. To capture these relative strengths, one can assign pay-
offs or utilities to each alternative. Payoffs are not considered here because
comparing these utilities across people is considered a dubious practice.
Social Choice Theory
If the members of a group have identical preferences, then aggregating
those preferences is straightforward. One can think of the group as one big
individual—and for some groups that may not be a bad assumption. The
aggregation of preferences becomes problematic when the group members’
preferences are diverse. Preference diversity can be fundamental (people
want different outcomes) or instrumental (people want the same outcomes
but differ over the means to achieve them). In what follows, that distinction
is ignored, but it becomes important when thinking about linking models.
If voting models are to be linked with cognitive models, then the source of
preference diversity is important to define because information can reduce
instrumental preference diversity but has little effect on fundamental prefer-
ence diversity.
A collection of individuals with rational preferences may fail to have
rational preferences as a group. We give an example and then state a gen-
eral theorem.
In this example, three military leaders have preferences over which city
to use as a base of operations. The three candidate cities are Paris, London,
and Berlin. The leaders are denoted L1, L2, and L3. Their preferences are
as follows:
Leader L1: Paris > London > Berlin
Leader L2: London > Berlin > Paris
Leader L3: Berlin > Paris > London
OCR for page 218
BEHAVIORAL MODELING AND SIMULATION
Were these three leaders to vote on their choice between each pair of
cities, London defeats Berlin two votes to one, Berlin defeats Paris two
votes to one, and Paris defeats London two votes to one. Thus, the collec-
tive preferences exhibit a cycle. Although the collective consists of rational
individuals, the collective is not rational. In theoretical terms, the property
of rationality does not aggregate.
The possibility of a cycle is not an artifact of majority rule voting.
Kenneth Arrow proved that any rule for aggregating preference orderings
that is not a dictator produces cycles (Arrow, 1951). It requires only that
preferences are diverse, rankings between two alternatives do not depend
on a third irrelevant alternative, and rankings reflect unanimity—if every-
one prefers A to B, then so does the collective.
Arrow’s theorem does not imply that cycles are unavoidable, only that
if one wants to avoid cycles, one has to sacrifice one of the other conditions
of his claim—appoint a dictator, sacrifice unanimity, or violate indepen-
dence of irrelevant alternatives. In general, as argued by Donald Saari, pref-
erence cycles are more a function of the voting system than the voter. He
suggests that voting paradoxes arise when the voting system fails to respect
the natural cancellations of votes and so generates preference cycles (Saari,
2001). For example, one such voting system or scoring rule, the Borda rule
(Marchant, 2000), does not create cycles. Under the Borda rule with three
alternatives, a person’s top choice gets three points, her second gets two
points, and her third gets only one point. Each alternative gets a score,
making cycles impossible. Borda rule can, however, result in a tie, which
is what would occur in the example of voting over cities. A tie isn’t neces-
sarily a bad thing. It reflects equal support for each alternative. Borda rule
may thus seem to be better than majority rule, but we must keep Arrow’s
theorem in mind. Borda rule must violate one of his conditions, and, in
fact, Borda does not satisfy independence of irrelevant alternatives. In the
example above, a fourth, irrelevant city could be introduced and change the
outcome under Borda rule. The fact that by introducing irrelevant alterna-
tives someone could change the outcome argues against using Borda rule.
The debate thus moves from a discussion of the voter to a discussion of the
scoring rules (Saari, 2006).
Given that regardless of the voting rule individual agents may fail to
reach a stable aggregation, organizational and institutional structures take
on great importance. The rules for how a group makes decisions can have
large effects on outcomes. For example, if someone has the power to set
the agenda, then that person may have substantial power. Thus, even if an
organization is democratic in principle, it may not be democratic in prac-
tice, especially if one person controls the agenda.
OCR for page 219
MESO-LEVEL FORMAL MODELS
Strategic voting
In aggregating preferences, it can be assumed either that people vote
sincerely or that they vote strategically. Strategic voting occurs even in large
groups in mature democracies; people vote for candidates who they think
can win rather than the candidates whom they most prefer. Alan Gibbard
and Mark Satterthwaite have shown this incentive to misrepresent to be
universal (e.g., Satterthwaite, 1975).
Why does strategic voting further complicate matters? We have shown
that rational individual preferences need not aggregate into a rational col-
lective preference. Thus, it may not be possible to discern what a group
would decide even if one knew the preferences of every member of that
group. Given that people have incentives to misrepresent their preferences,
they wouldn’t reveal their true preferences anyway. Thus, one must discern
how people’s true preferences get mapped into their actions—in this case,
their votes. And that requires a model of individual behavior in groups.
The possibility of coalitions further complicates the analysis of vot-
ing models. Subgroups may have an incentive to form a coalition to steer
outcomes toward desired ends. This is seen in parliamentary systems, with
Israel as an example. It may not be possible to predict which coalitions will
form: politics makes strange bedfellows, and predicting those bedfellows
can be difficult.
In a group setting, social influence dynamics can muddy the picture
even further, as people may change their preferences to align with the real or
the inferred preferences of others. Concern for the preferences of others and
for one’s own standing in a group creates more indeterminacy in collective
decisions. A striking example of such social influence effects is provided by
the Abilene paradox, in which each person privately prefers X but believes
that others prefer Z. If all group members revealed their true preferences,
the group would clearly choose X. However, the desire to conform to what
is (incorrectly) perceived to be the normative opinion can lead a member
to suggest Z and others to agree (Harvey, 1974).
While this counterintuitive outcome is probably rare in practice, it
highlights the importance of realizing that social influence is not sim-
ply a matter of one person seeking to change the preference of another.
People also actively seek to align their preferences with important others.
Both computational models and empirical studies have demonstrated that
the impact of others on individual preferences tends to create uniformity
of preferences among people who are closely connected. Dynamic social
impact theory (Latané, 1996) predicts that people will change their prefer-
ences to match those of others, with the impact based on both the strength
(status) and the immediacy (social closeness) of others. The result is emerg-
ing pockets of uniform attitudes based on social network clusters. Research
OCR for page 220
0 BEHAVIORAL MODELING AND SIMULATION
on minority influence (e.g., Nemeth, 1986) also shows that the views of a
cohesive minority, when clearly and consistently stated, can also change
the opinions of majority members. Hence, knowing what the majority of
individuals prefer at time 1 may not allow one to predict confidently what
a group will choose at time 2.
Relevance, Limitations, and Future Directions for Social Decision Models
While voting models per se, especially those that compare specific vot-
ing rules like Borda and majority rule, may seem more relevant to political
science than to the situations that concern us here, the insights that can be
drawn from these models are of critical importance. Two of the main rec-
ommendations of this report are that modelers should recognize diversity of
background, activity, and preferences and that they should embrace uncer-
tainty. Nowhere does that advice ring more clearly and loudly than in under-
standing the link from individual incentives to group behavior. Moreover,
one can link diversity of background, activity, and preferences and uncer-
tainty about all three into a general insight: the more diverse the members
of a group in their general makeup (their background), their preferences,
and their actions, the more uncertain one should be about their collective
decisions and actions. For example, models that attempt to make predictions
about the attitudes and behaviors of a group of noncombatant civilians
must consider the diversity of that group in terms of the sociocultural-
ethnographic-economic background, preferences, and available actions. The
more diverse the group on any of these three dimensions, the less certain the
predictions. At a very practical level, the implication of recognizing diversity
is to make the models more complex. Another practical implication is that
model results should often be characterized in terms of how the diversity
of the population being modeled impacts the results (e.g., show entropy or
diversity indices to characterize the initial population and show how out-
comes change as the initial population varies on this metric).
Even if group models cannot be expected to make point predictions,
they can provide a way to predict sets of possible outcomes. If one has
even crude approximations of preferences, possible coalitions, and a set of
possible voting rules, he can write game theoretic or agent-based models,
and those models can provide some guidance for what might happen and,
equally important, what probably will not happen. For a recent survey of
these methods, see Kollman and Page (2006).
The ability to apply voting theory depends on data, knowledge, and
theory. For many of the problems relevant to this study, one would not have
information about individual-level preferences. And, even if one did have
access, the theory tells us that it is not possible to predict outcomes with
certainty from that data. Equally important, one may not have knowledge
OCR for page 221
MESO-LEVEL FORMAL MODELS
of the voting rules. And, as discussed above, the voting rule has a substantial
influence on the outcome. Thus, even with information about preferences,
one would also need to know something about the process of preference
aggregation in the group of interest. Finally, to apply these models, one
needs models of how people behave in groups. Are the group members
strategic? Do coalitions form, and who belongs to those coalitions?
Imagine a model that includes the actions of a terrorist organization or
of a nascent nation-state. One could make a black box assumption about
how that organization or government acts. In other words, one could treat
the group as an individual, presumably an individual who is the average of
the group members.
The voting models reveal the problems with that approach. Groups do
not make choices as though they were a single individual. The natural way
to improve the model would be to make the black box transparent and to
allow for multiple characterizations of the collective decision-making pro-
cesses that produce those outcomes. This will require data, knowledge, and
models of the group of interest, but the potential payoff is large, as it will
provide a more accurate assessment of the likely distribution of behaviors
over the set of possible actions.
Finally, empirical voting studies demonstrate that humans do not act in
a strictly rational or strategic manner, hence calling into question the formal
mathematical “rational” and “strategic” voting models. Summaries of the
empirical literature point to the social rather than rational nature of vot-
ing behavior; for example, people vote primarily along ethnocultural lines
rather than according to their economic interests and display widespread
voter ignorance (Friedman, 2005). As another example, research on the
“voter participation paradox”—in which it is asked why people vote at
all, as each individual has virtually zero probability of affecting the out-
come (Converse, 1964; Green and Shapiro, 1994)— both demonstrate this
lack of rationality and suggests that there are huge variations in individual
behavior. Turnout depends on a number of social factors, including the size
of the electorate (as the size of the electorate grows, fewer voters turn out),
the closeness of the competition (the closer it is, the higher the turnout),
and the presence of an underdog (more turnout). This empirical work sug-
gests both that the formal models and simplistic game theoretic models
are inadequate and that the more detailed and nuanced behaviors possible
in agent-based models (ABMs) are better at capturing the complexities of
voting behavior.
SOCIAL NETWORK MODELS
Networks are ubiquitous, and many techniques have been developed
for analyzing, predicting, and understanding the world in terms of the set
OCR for page 222
BEHAVIORAL MODELING AND SIMULATION
of connections among entities—a network. As the focus here is on social
and behavioral modeling, we limit our discussion of network modeling
techniques to those that have been and are being used to address individual,
social, organizational, political, or cultural issues, rather than, say, gene
interaction networks or computer networks. For a review of the field of net-
work analysis, see Freeman (2004), and for the methodology, see Freeman,
White, and Romney (1991) and Wasserman and Faust (1994).
What Are Social Network Models?
Social network models view groups as consisting of a set of nodes
(the members of the group) and a set of ties that connect them, which link
together to form a network. The ties are often seen as pipes or roads along
which various kinds of traffic flow, such as informational and material
resources, as well as influences and coordination. Thus, a key aspect of net-
work modeling is concerned with predicting (and controlling) what flows
to whom at what time. Ties are also seen as providing a kind of underlying
structure or topology that has effects on the performance of the group or
individuals. A fundamental proposition of social network models is that a
node’s position in the network (in conjunction with its attributes) deter-
mines the opportunities for and constraints on action that it will encounter.
A group-level corollary of this proposition is that the network structure of a
group (together with other attributes of the group), determines the perfor-
mance or outcomes of the group. Thus, network models differ from other
models in placing less emphasis on characteristics of the nodes and more
emphasis on the structure of connections between the nodes.
Social network analysis (SNA) has received a great deal of attention
since the terrorist attacks of September 11, 2001 (Borgatti and Foster,
2003). Phrases for fighting terrorism, such as “disconnect the dots” and
“it takes a network to fight a network,” and for doing business, such as
“it’s not who you know but who or what who you know knows” and “are
you networking?” have appealed to the imagination and raised awareness
of this area. In addition, there have been successful applications of this
approach. For example, social network information was used to locate
Saddam Hussein, and several SNA tools have been used in various criminal
investigations. Social network information is used in popular social net-
working web services, like Friendster, to help students vet their dates.
Traditionally, most SNA has focused on the analysis of relatively simple
datasets involving a small number of social relations (often of just one kind)
connecting a set of persons in some kind of group at a single point in time.
Analysts in this area use computational techniques primarily to statistically
analyze these networks. This area has a long tradition, predating World War
II. It emerged from the social sciences, particularly from social psychology,
OCR for page 223
MESO-LEVEL FORMAL MODELS
anthropology, and sociology, and has now spread to organization science,
economics, physics, and computer science.
More recent work has focused on more complex networks involving
large numbers of nodes of differing types (see section on Multimode Net-
works below). For example, Carley (2003) has developed social network
metrics that take into account not only relations among individuals, but
also relations among tasks, relations among items of knowledge, assign-
ments of tasks to individuals, relations of knowledge to individuals and
other relationships.
In addition, a key research interest today is in understanding network
dynamics, both in the sense of how networks change over time (especially
in response to attacks) and in the sense of how things flow over the network
links. Carley (2003) has used multiagent models in a network context to
predict and reason about change in social and other networks.
State of the Art in Social Network Models
In this section, we lay out the key concepts of SNA, starting with a
discussion of the nature of the data and followed by an outline of the key
analytical constructs, namely cohesion, centrality, equivalence, and cluster-
ing. The section ends with a discussion of network evolution.
Nodes and Ties
The set of actors or agents that form the nodes of a network can
consist of either individuals or collectives, such as organizations, cities, or
countries. Nodes are assumed to possess characteristics that define their
goals and affect their ability to achieve and exploit their network positions.
These characteristics are modeled as a set of categorical and/or continuous
attributes.
In general, relations among nodes are modeled as dyadic 2-tuples (called
ties, links, or edges) that bind exactly two nodes to each other. Therefore,
a conversation among three people A, B, and C is typically modeled as
three separate dyadic interactions consisting of A with B, B with C, and A
with C. For the most part, the ties modeled among nodes typically belong
to a general class known as social relations. These include such things as
acquaintance (e.g., knows), kinship (e.g., brother of, father of), other social
roles (e.g., friend of, teacher of), and affective relations (e.g., likes, dislikes).
Each type of tie can be further characterized by relevant characteristics or
attributes. For example, a friendship tie can be characterized in terms of
intensity, closeness, and duration.
In addition, network modelers often represent interactions over time—
such as in-person meetings, communication, or fighting—as ties. Hence a tie
OCR for page 224
4 BEHAVIORAL MODELING AND SIMULATION
is considered to exist between two nodes if at least one interaction between
them is observed during a given period. The actual number of interactions
may be recorded as an attribute of this tie. Interactions are inherently
transitory and evanescent but are often seen as revealing the presence of
underlying social relations.
Interactions, such as conversations, provide the mechanism by which
things flow through social relations, as when an actor transmits informa-
tion to a friend through communication or when a person infects another
with a disease via personal contact. Thus flows represent a third category
of tie that a network modeler can choose to model. Typical flows of interest
have been information, ideas, infections, material goods (such as guns and
money), and such intangibles as energy and motivation. These are often
referred to by network analysts as “tokens.”
Multimode Networks
When a categorical variable exists that distinguishes between different
types of nodes, and, in addition, ties exist only between nodes of different
types (and not within types), the resulting networks are referred as k-node
networks or, in graph theory, as k-partite graphs, where k refers to the
number of distinct types of nodes. These kinds of data typically arise in the
context of recording affiliations between individuals and groups or events.
For example, Davis, Gardner, and Gardner (1941) recorded which women
attended which social events in a given season. Ties exist between women
and events, but not among women and not among events. Similarly, it is
common to record for each person in a group the organizations to which
they belong(ed). And in organizational analysis, one can collect the number
of hours that each person worked on various tasks or projects.
Multinode networks can be analyzed directly or converted into simple
1-node networks by deriving co-occurrence indices. For example, a 2-node
women-by-events network can be converted into a 1-node women-by-
women network in which a tie between each pair of women is characterized
by the number of events they attended in common.
With multiple nodes, it is possible to represent the system as a whole
as a meta-matrix (Carley, 2003). The meta-matrix is a conceptual device
for identifying the set of networks within and among nodes of multiple
classes. For example, given the three classes of nodes—people, knowledge,
and activities—the set of subnetworks possible is shown in Table 6-1. The
second key concept is the entity ontology—for network analysis, this is the
set of categories that defines the node classes and the link classes among the
nodes used in a particular study. The table illustrates a particular ontology;
other ontologies are needed for other applications.
OCR for page 225
5
MESO-LEVEL FORMAL MODELS
TABLE 6-1 Illustrative Meta-Matrix
People Knowledge Activities
People Social network Knowledge network Activity network
Knowledge Information network Needs network
Activities Precedence network
Cohesion Models
A fundamental concept in network modeling is cohesion. Cohesion
refers to the connectedness or structural integrity of a network, and it
is often interpreted in terms of the network’s potential for coordinating
among its members or exploiting knowledge that is distributed across the
network.
One aspect of network cohesion is density, which refers to the propor-
tion of pairs of nodes that have a direct tie (i.e., are not dependent on an
intermediary). A high density implies that, on average, each node is directly
connected with many others. If the ties represent something like trust rela-
tions, this indicates a group in which information can flow quite freely.
Another aspect of cohesion is the average path distance, also known as
characteristic path length. Path distance refers to the number of links in the
shortest path between two nodes. A network with low average distance is
one in which the lengths of the shortest paths between pairs of nodes are
quite small, so that things flowing through the network can reach any or all
nodes comparatively quickly. In the case of viruses or other infections, this
is a measure of the vulnerability of the network to disease. In the case of
the spread of best practices, it can be seen as a determinant of the potential
performance of a continuously adapting system.
Centrality Models
A frequent analytical strategy in network modeling has been the iden-
tification of key players who are disproportionately important due to their
structural position in the network (Borgatti and Everett, 2006). The struc-
tural importance of a node in a network is conceptualized as its centrality.
One way to think about centrality is in terms of a node’s direct or indirect
contribution to the cohesion or structural integrity of the network. For
example, degree centrality is defined as the number of ties that a node has.
If the total number of ties in the network is a measure of the cohesion of the
network, then clearly degree centrality can be seen as each node’s “share”
of the total cohesion. In this sense, the centrality measure implies a model
of the sources of cohesion.
OCR for page 250
50 BEHAVIORAL MODELING AND SIMULATION
chains. For example, pattern discovery techniques can be used to derive
equations from historical data that can then be used in ABMs to evolve
future systems. ABM techniques can be used to evaluate courses of action
and to suggest areas for further data collection. Combining these techniques
will enable new types of problems to be solved; for example, combining
social network metrics with pattern discovery techniques is the key to build-
ing an understanding of how networks grow and evolve.
This is not to suggest that the military should move to large integrated
behavioral models—quite the contrary. What is needed is increased inter-
operability of the tools. The development of ABM CLs and the explosion
of network analytic tools are putting social behavioral modeling into the
hands of the masses. Moreover, these trends are leading to the development
of many small, single-purpose tools. This should be taken advantage of by
encouraging interoperability (this is also discussed further in Chapter 8).
It is important to note that it would not be feasible to require all tools
to be written in a single language or to require the use of a single frame-
work; rather, the solution needs to enable the integration of models not
only from diverse domains but also in diverse languages. Multiple models,
visualization tools, and the like should be available to address diverse prob-
lems, but in such a way that data (real and virtual) can be shared easily
among the various tools.
There are a variety of things needed to support such interoperability.
Standards for the interchange of relational data need to be developed.
Behavioral modeling tools need to be web enabled, and XML input-output
(IO) languages need to be developed. A uniform vocabulary for describ-
ing relational data also needs to be developed; this is particularly critical
because the tools and metrics are coming out of at least 20 different scientific
fields.8
For defense and intelligence applications, common platforms and data
sharing standards need to be explored and developed so that tools written
in the unclassified realm can be rapidly moved, without complete redesign,
to the classified realm. Enabling interoperability and providing a platform
and common ontologies for these tools will enable novel problems to be
more rapidly addressed by regrouping existing models. It will also enable
various subject matter experts to interact through the interaction of their
models. In turn, this will enable a broader approach to problems, reduce
the likelihood of biased solutions, and facilitate rapid development and
deployment.
8 These fields include anthropology, sociology, psychology, organization science, marketing,
physics, electrical engineering, geology, ecology, economics, biology, bioinformatics, health
services, forensics, artificial intelligence, robotics, computer science, mathematics, statistics,
information systems, medicine, civil engineering, communication, and rhetoric.
OCR for page 251
5
MESO-LEVEL FORMAL MODELS
Current tools are either very data-greedy or become more valuable as
they are linked to real data. However, there is a dearth of relevant data
currently available in clean preprocessed form. Thus, to reduce the time
analysts spend on data collection and to increase the time they spend on
analysis, automated and semiautomated tools for data gathering, cleaning,
and sharing are needed. Such tools should include natural language process-
ing tools for extracting relational data from audio and text sources, “web-
scraping” tools, automatic ontology generators, and visual interpretation
tools to extract network data from photographs and visual images.
Appropriate subtools for node identification, entity extraction, thesau-
rus creation, and other functions are also needed. The development and
availability of these tools in an interoperable environment are critical for
providing masses of data that can be used for model tuning and validation.
Moreover, these tools reduce time spent on data collection and thereby
free the analysts’ time for analysis. More rapid data collection would also
mean the availability of more datasets for doing meta-analyses, thereby
enabling improvements in the theoretical foundations of the field and in
the understanding of social behaviors. Finally, these tools are essential for
providing the wealth of data needed by social behavioral models to make
reasonable forecasts or to provide reasonably accurate analyses of situa-
tions and organizations.
Improved speed for many of the algorithms could be provided by
computer architectures designed for relational data or by the use of special
integrated circuits with embedded versions of the less scalable algorithms.
Note this would enable a speed savings beyond that afforded by the use
of current vector technology. Such technology would facilitate faster pro-
cessing and enable more real-time solutions, particularly for large-scale
networks.
To reduce the “art” aspect of interpretation in this field, a living archive
of collected network data is needed, replete with information on metrics
for the nodes in each dataset. Such an archive could be used to set context
information. For example, such information could be used to evaluate
whether the density of particular networks is exceptionally high or low
or to identify exceptional values of connectedness of individuals. Such an
archive would facilitate meta-analysis and comparative analysis. This is
critical for improving the theoretical foundations of the field as well as for
the understanding of social behavior.
Forecasting and Possibility Analysis
Of the models described here, those that have shown the most promise
in terms of forecasting are the voting models, the dynamic network models
(that combine agent-based technology and meta-matrix of relations), and
OCR for page 252
5 BEHAVIORAL MODELING AND SIMULATION
the social influence models. These models have had limited success in
forecasting voting outcomes, changes in beliefs and attitudes at the macro
level, and identifying emergent new leaders. For other modeling techniques,
including the ABM and system dynamic techniques for complexity model-
ing, the models are best at providing insight into the space of possibilities,
that is, demonstrating what possible futures might exist and their relative
likelihood. However, for these models to provide an adequate map of the
possibilities (a reasonable response surface), the models need to be run a
vast number of times under diverse scenarios; hence, as is discussed in the
next section, there is a need for placing these models in a data farming
environment.
One question that arises is: How can these models be made more pre-
dictive? This topic, in and of itself, is quite complex and a full treatment is
beyond the scope of this study. However, several factors are worth noting.
As more of these models are placed in data farming environments, statistical
tools are developed for mining the vast data so generated, and repositories
of meta-matrices are developed and shared with scientists for testing and
validating, one can expect that many of these models will become more
reliable in their forecasts. However, there will still be many classes of social
phenomena for which prediction, of the form used in engineering and
physics, will simply not be possible due to the lack of stationarity in the
underlying social processes, the paucity of data, and the lack of continuity
in key variables.
A second question often arises regarding the concern that, if the models
are truly predictive, the mere act of making a prediction public will cause
actors to change their behaviors and so alter the outcome. While this issue
is addressed in other sections of this report, several key factors directly
related to the nature of the models described here are worth mentioning.
For most of the models described here, other than the simple voting models,
making the models transparent to the public (so that others can infer the
predictions) or making the predictions themselves public is not likely to
invalidate the predictions. There are three basic reasons for this: lack of
temporal forecasting, level of specificity, and hyper-confluence. Temporal
forecasting tends to be weak and predictions are often vague in terms of
when something will occur; rather than point predictions, most predictions
are of the form “A will likely occur after B” or “at some time in the future
more than two weeks but less than two years from now.” Most models
produce rather general results, such as that a state will fail, civil violence
is likely to erupt, or corruption will increase, rather than the more specific
“the state will fail due to a regime change where General X takes over” or
“civil violence will take the form of riots in these five cities” or “corruption
will increase the most in the area of infrastructure development in county
X.” Finally, most models generate a prediction due to hyper-confluence,
OCR for page 253
5
MESO-LEVEL FORMAL MODELS
that is, the strongest predictions are those for which there are a large num-
ber of interconnected causes that weave together in complex ways. But
single actors can best counter a specific event that is likely to occur at a
specific time with only one or two actions or activities. Even with sufficient
research funding, improved theory, and available data to overcome the
issues of vague temporal forecasting and lack of specificity; the problem of
hyper-confluence will remain. That is one of the key reasons why social and
behavioral models need to be driven by the science of the possible, rather
than the traditional science of point predictions involved in traditional
physical science and engineering models.
Data Farming
ABMs designed for applied settings need to be placed in data farming
environments. These environments need to be augmented with special-
purpose tools for running massive virtual experiments. These tools should
enable improved visualization and analysis and facilitate the development
of semiautomated response surface generators. Current data farming tools
often are cumbersome to use, require code modification of the ABM, and
are limited by the processor speed and storage capabilities of the machines
that they run on.
In order for ABM frameworks to run routinely in data farming environ-
ments, more flexible environments need to be developed and made easily
available to researchers. Moreover, ABM frameworks need to be developed
with wrappers,9 so that they can be placed in these environments. Standard-
ized IO formats need to be developed. By routinely placing ABM frame-
works in a data farming environment, a better understanding of the space
of possibilities predicted by the frameworks will be derived. This will enable
ABM frameworks to better support policy and decision making.
Currently, when ABM frameworks are used to inform policy and criti-
cal decisions, they are typically run only a few times in carefully controlled
computational experiments. While this approach enables the analyst to
explore more possibilities more systematically than not using a simulation,
it still leaves open the possibility that errors might be made if the results are
generalized beyond the scope of the experiment. By placing ABM frame-
works in a data farming environment, the number of computational experi-
ments conducted, the space of possibilities examined, and the scope of
9 “Awrapper is a software layer used to change the interface of a component or to give
new properties, such as fault tolerance or security, to the interaction between components.
Software wrappers are often used to glue existing subsystems into a larger system with new
properties and functions. The wrappers know the protocols needed to make the subsystems
work together, even if they were not originally designed for a common purpose” (Webber,
1997, p. 1).
OCR for page 254
54 BEHAVIORAL MODELING AND SIMULATION
analyzed conditions can be expanded, often by several orders of magnitude,
thus providing a stronger basis for decision making. Furthermore, once an
ABM framework has been validated, the response surface equivalent can
be used as a “rapid” model in training situations in which the users do not
have time to wait for an ABM experiment to finish running.
Cross-Disciplinary Initiatives
Another avenue that may promote major breakthroughs is the linkage
of ABM social behavioral modeling to gaming environments, particularly
online multiplayer games such as Everquest and America’s Army (see Chap-
ter 7). Research initiatives that explore the link of ABM social behavioral
modeling to gaming tools may be valuable. Possible research areas include
using agent-based modeling to explore the realism of the social behaviors
exhibited in gaming models; using it to provide flexible opponents or to
make the apparent number of game players larger and so force players to
think about group scale issues; and using agent-based modeling to track and
analyze game behaviors using dynamic network analysis techniques. Key
benefits here would be improved training tools and visual what-if scenario
evaluation.
As previously noted, additional ABM development needs to be done in
a number of areas. These include attachment of ABM frameworks to data
streams, improved ABM visualization, metric ABM robustness studies, and
so on. Moving ahead in these areas will require linking social networks to
other types of data, such as location and event information, and linking
diffusion theory to other forms of theory, such as action and cultural theory.
This will require the funding of both basic and applied research. It will also
require an increased recognition for, and acceptance of, applied social sci-
ence research in universities.
Currently there are a number of funded research efforts in the areas
of cultural modeling, geospatial link analysis, and adversarial modeling,
all of which are supporting work along these lines. A key to much of this
work is that it combines dynamic network analysis with geospatial rea-
soning or anthropological data-gathering techniques. Much of this work
is applied, directed at providing usable systems in several years. This is a
positive development, particularly when such modeling efforts are based on
strong empirical and theoretical foundations. However, there is still a huge
amount of basic research to be done in such areas as the development of an
ontology for tasks, a unified model of culture, or even a shared definition
of culture. Relatively little research funding is being directed to the basic
research questions in this area.
The key here is not simply to invest in the social sciences but to invest
in the mathematical and computational social sciences to engender the
OCR for page 255
55
MESO-LEVEL FORMAL MODELS
development of work that will support defense needs. The benefit will be an
improved understanding of basic social and cultural phenomena. Another
benefit will be a decrease in the development of misleading models that
appear to be social but that are not theoretically or empirically sound.
At the same time, most of the research community, particularly in the
social sciences, is not focusing on strongly applied problems. The mere idea
of hard deliverables, while accepted as common practice in engineering
and computer science, is contrary to the basic culture of most social sci-
ence departments. Thus, while there is a strong need for quantitative social
science modeling on defense issues, there is a dearth of social scientists
involved in and trained to do applied work.
Building Expertise
The lack of highly trained professionals is a key difficulty in this area.
Universities need to expand their undergraduate social science curricula
to include more of the mathematical and computational social sciences.
In particular, undergraduate courses should be routinely taught that cover
SNA and agent-based modeling, and that permit the mastery of ABM
programming tools. Universities need to encourage and facilitate applied
research. New curricula are needed that have an engineering style but
that are focused on social and policy applications. Master’s programs that
combine social and computational science need to be developed. Military
universities, such as West Point and the Naval Postgraduate School, should
also offer social network courses and possibly ABM courses, particularly
those for evolving networks, and they should integrate dynamic network
measures of shared situation awareness, leadership, and power into the
standard curriculum.
The development of these curricula and degree programs is vital to
the nation’s intellectual strength in order to remain at the forefront in this
area. The clear benefit of these programs will be a stronger workforce
of computational social analysts capable of developing and using social
behavioral models.
Analysts engaging in ABM but trained in computer science, engineer-
ing, or physics should work in teams with social scientists to avoid duplicat-
ing work already done or making commonsense assumptions about social
processes that have no empirical bases. Corporations need to provide time
and resources for selected personnel to become jointly trained in computer
and social science, either by increasing the number of personnel sent to
master’s programs, bringing in relevant faculty to teach short courses, or
engaging in more joint research with universities as equal partners (in which
the university provides the missing skill, social or computational). The key
advantage of teaming is that it will enable improved model development
OCR for page 256
5 BEHAVIORAL MODELING AND SIMULATION
and will serve as a stop-gap until more computational social analysts are
trained.
Expected Outcomes
Across the board, success in the activities outlined above would facili-
tate the rapid development and deployment of agent-based modeling. The
advantage is that it enables systematic reasoning about various courses of
action in a wide range of complex environments. More courses of action
could be evaluated in less time and more systematically than is done with
conventional table-top war-gaming or current non-computer-assisted analy-
sis of relational data. The dynamic social network and ABM tools outlined
above reduce the time spent on data processing and increase time spent
on analysis and interpretation. They would facilitate what-if analysis and
could ultimately support near-real-time what-if analysis in the field. This
would be a valuable force multiplier.
In summary, the activities listed above would increase the maturity
of the modeling field, improve scientific theory, facilitate rapid linking of
computational models to empirical data, particularly network data in a
unified reasoning framework to solve novel problems, and encourage new
discoveries. These activities would also promote the development of a new
science that combines computation and society, just as the previous join-
ing of computer science, design, and psychology led to the new science of
human-computer interaction.
REFERENCES
Arrow, K.J. (1951). Social choice and individual values. Hoboken, NJ: John Wiley & Sons.
Arthur, W.B. (2006). Out-of equilibrium economics and agent-based modeling. In L. Tesfatsion
and K.L. Judd (Eds.), Handbook of computational economics, volume : Agent-based
computational economics. Amsterdam, The Netherlands: Holland/Elsevier.
Axelrod, R. (1997). Advancing the art of simulation in the social sciences. In R. Conte, R.
Hegselmann, and P. Terna (Eds.), Simulating social phenomena (pp. 21–40). Berlin:
Springer.
Borgatti, S.P., and Everett, M.G. (1992). Notions of position in social network analysis.
Sociological Methodology, , 1–35.
Borgatti, S.P., and Everett, M.G. (2006). A graph-theoretic framework for classifying centrality
measures. Social Networks, (4), 466–484.
Borgatti, S.P., and Foster, P. (2003). The network paradigm in organizational research: A
review and typology. Journal of Management, (6), 991–1013.
Borgatti, S.P., Everett, M.G., and Shirey, P. (1990). LS sets, lambda sets and other cohesive
subsets. Social Networks, (4), 337–357.
Breiman, L. (2001). Statistical modeling—The two cultures. Statistical Science, , 199–231.
Brenner, T. (2006). Agent-learning representation: Advice on modeling economic learning. In
L. Tesfatsion and K.L. Judd (Eds.), Handbook of computational economics, volume :
Agent-based computational economics. Amsterdam, The Netherlands: Holland/Elsevier.
OCR for page 257
5
MESO-LEVEL FORMAL MODELS
Butts, C.T., and Carley, K.M. (in press). Structural change and homeostasis in organizations:
A decision-theoretic approach. Journal of Mathematical Sociology.
Carley, K.M. (2003). Dynamic network analysis. In National Research Council, Dynamic
social network modeling and analysis: Workshop summary and papers (pp. 133–145).
R. Breiger, K.M. Carley, and P. Pattison (Eds.), Committee on Human Factors. Board on
Behavioral, Cognitive, and Sensory Sciences, Division of Behavioral and Social Sciences
and Education. Washington, DC: The National Academies Press.
Carley, K.M. (2004). Estimating vulnerabilities in large covert networks using multilevel data.
In Proceedings of the NAACSOS 004 Conference, Pittsburgh, PA. Available: http://
www.casos.cs.cmu.edu/events/conferences/2004/2004_proceedings/Carley,Kathleen.doc
[accessed Feb. 2008].
Carley, K.M., and Newell, A. (1994). The nature of the social agent. Journal of Mathematical
Sociology, (4), 221–262.
Carley, K.M., Columbus, D., DeReno, M., Reminga, J., and Moon, I.-C. (2007). ORA user’s
guide. (Report No. CMU-ISRI-07-115). Carnegie Mellon University School of Computer
Science, Institute for Software Research.
Chen, H., and Lynch, K.J. (1992). Automatic construction of networks of concepts character-
izing document databases. IEEE Transactions on Systems, Man, and Cybernetics, (5),
885–902.
Clark, A. (1997). Being there: Putting brain, body, and world together again. Cambridge,
MA: MIT Press.
Converse, P.E. (1964). The nature of belief systems in mass publics. In D.E. Apter (Ed.),
Ideology and discontent (pp. 206–261). London, England: Free Press of Glencoe.
Davis, A., Gardner, B.B., and Gardner, M.R. (1941). Deep south: A social anthropological
study of caste and class. Chicago, IL: University of Chicago Press.
de Toqueville, A. (1835). Democracy in America. London, England: Saunders and Otley.
Dibble, C. (2006). Computational laboratories for spatial agent-based models. In L. Tesfatsion,
and K.L. Judd (Eds.), Handbook of computational economics, volume : Agent-based
computational economics. Amsterdam, The Netherlands: Holland/Elsevier.
Festinger, L. (1957). A theory of cognitive dissonance. Palo Alto, CA: Stanford University
Press.
Franklin, S. (1995). Artificial minds. Cambridge, MA: MIT Press.
Freeman, L. (2004). The development of social network analysis: A study in the sociology of
science. Vancouver, British Columbia: Empirical Press.
Freeman, L.C., White, D.R., and Romney, A.K. (Eds.). (1991). Research methods in social
network analysis (revised edition). Piscataway, NJ: Transaction Press.
Friedman, J. (2005). Popper, Weber, and Hayek: The epistemology and politics of ignorance.
Critical Review, (1–2). Available: http://www.criticalreview.com/2004/pdfs/ignorance_
article.pdf [accessed March 2008].
Gardner, M. (1970). The fantastic combinations of John Conway’s new solitaire game “Life.”
Scientific American, , 120–123.
Getoor, L., and C. Diehl (2005). Link mining: A survey. SIGKDD Explorations, 7(2). Avail-
able: http://www.cs.umd.edu/~getoor/Publications/getoor-kddexp05.pdf [accessed April
2008].
Getoor, L., Friedman, N., Koller, D., and Taskar, B. (2001). Probabilistic models of relational
structure. In Proceedings of the International Conference on Machine Learning. Avail-
able: http://www.cs.umd.edu/~getoor/Publications/jmlr02.pdf [accessed April 2008].
Getoor, L., Friedman, N., Koller, D., and Taskar, B. (2002). Learning probabilistic models
of link structure. Journal of Machine Learning Research, , 679–707. Available: http://
www.jmlr.org/papers/volume3/getoor02a/getoor02a.pdf [accessed Feb. 2008].
OCR for page 258
5 BEHAVIORAL MODELING AND SIMULATION
Gibbard, A. (1973). Manipulation of voting schemes: A general result. Econometrica, 4(4),
587–601.
Gintis, H. (2000). Game theory evolving: A problem-centered introduction to modeling
strategic interaction. Princeton, NJ: Princeton University Press.
Gladwell, M. (2000). The tipping point: How little things can make a big difference. Boston,
MA: Little, Brown, and Company.
Goldberg, H.G., and Senator, T.E. (1998). Restructuring databases for knowledge discovery
by consolidation and link formation. In Proceedings of the st International Conference
on Knowledge Discovery and Data Mining, Quebec, Montreal. Available: http://citeseer.
ist.psu.edu/cache/papers/cs/3649/http:zSzzSzeksl-www.cs.umass.eduzSzailazSzgoldberg-
senator.pdf/goldberg95restructuring.pdf [accessed Feb. 2008].
Goldberg, H.G., and Wong, R.W.H. (1998). Restructuring transactional data from link
analysis in the FinCEN AI system. In Proceedings of the AAAI Fall Symposium
on Artificial Intelligence and Link Analysis. Available: http://kdl.cs.umass.edu/events/
aila1998/goldberg-wong.pdf [accessed April 2008].
Green, D., and Shapiro, I. (1994). Pathologies of rational choice theory. New Haven, CT:
Yale University Press.
Harvey, J.B. (1974). The Abilene paradox and other meditations on management. Organiza-
tional Dynamics, (1).
Hauck, R.V., Atabakhsh, H., Ongvasith, P., Gupta, H., and Chen, H. (2002). COPLINK
concept space: An application for criminal intelligence analysis. IEEE Computer Digital
Government Special Issue, 5(3), 30–37.
Heider, F. (1988). The notebooks: Balance theory, volume 4. New York: Springer Verlag.
Jensen, D., and Neville, J. (2002). Linkage and autocorrelation cause feature selection bias
in relational learning. In Proceedings of the Nineteenth International Conference on
Machine Learning (pp. 259–266), Sydney, Australia. Available: http://citeseer.ist.psu.edu/
cache/papers/cs/30391/http:zSzzSzkdl.cs.umass.eduzSzpaperszSzjensen-neville-icml2002.
pdf/jensen02linkage.pdf [accessed Feb. 2008].
Kollman, K., and Page, S.E. (2006). Computational methods and models of politics. In L.
Tesfatsion and K.L. Judd (Eds.), Handbook of computational economics, volume :
Agent-based computational economics. Amsterdam, The Netherlands: Holland/Elsevier.
Kubica, J., Moore, A., Schneider, J., and Yang, Y. (2002). Stochastic link and group detec-
tion. In Proceedings of the Eighteenth National Conference on Artificial Intelligence
(pp. 798–804), Menlo Park, CA: AAAI Press/MIT Press. Available: http://www.cs.cmu.
edu/~schneide/AAAI02_GDA.pdf [accessed April 2008].
Kubica, J., Moore, A., and Schneider, J. (2003). Tractable group detection on large link data-
sets. In X. Wu, A. Tuzhilin, and J. Shavlik (Eds.), The Third IEEE International Confer-
ence on Data Mining (pp. 573–576). Washington, DC: IEEE Computer Society.
Latané, B. (1996). Dynamic social impact: The creation of culture by communication. Journal
of Communication, 4, 13–25.
Lee, R. (1998). Automatic information extraction from documents: A tool for intelligence and
law enforcement analysts. In Proceedings of the AAAI Fall Symposium on Artificial Intel-
ligence and Link Analysis (pp. 63–67). Available: http://citeseer.ist.psu.edu/cache/papers/
cs/15373/http:zSzzSzeksl-www.cs.umass.eduzSzailazSzlee.pdf/richard98automatic.pdf
[accessed Feb. 2008].
Marchant, T. (2000). Does the Borda rule provide more than a ranking? Social Choice and
Welfare, (3), 381–391.
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon, U. (2002).
Network motifs: Simple building blocks of complex networks. Science, (5594),
824–827.
OCR for page 259
5
MESO-LEVEL FORMAL MODELS
Moon, I.-C., and Carley, K.M. (2007). Modeling and simulation of terrorist networks in social
and geospatial dimensions. IEEE Intelligent Systems, Special Issue on Social Computing,
(5), 40–49.
National Research Council. (2003). Dynamic social network modeling and analysis: Workshop
summary and papers. R. Breiger, K. Carley, and P. Pattison (Eds.), Committee on Human
Factors. Board on Behavioral, Cognitive, and Sensory Sciences, Division of Behavioral
and Social Sciences and Education. Washington, DC: The National Academies Press.
Nemeth, C.J. (1986). Differential contributions of majority and minority influence. Psycho-
logical Review, (1), 23–32.
Page, S.E. (2007). The difference: How the power of diversity creates better groups, firms,
schools, and societies. Princeton, NJ: Princeton University Press.
Page, S.E. (2008). Agent-based models. In L. Blume and S. Durlauf (Eds.), The new Palgrave
dictionary of economics, second edition. Hampshire, England: Palgrave Macmillan Ltd.
Popp, R., Kaisler, S.H., Allen, D., Cioffi-Revilla, C., Carley, K.M., Azam, M., Russell, A.,
Choucri, N., and Kugler, J. (2006). Assessing nation-state instability and failure. Paper
presented at the Aerospace Conference IEEE 2006, March, Big Sky, MT. Available:
http://ieeexplore.ieee.org/iel5/11012/34697/01656054.pdf?tp=&isnumber=&arnumber
=1656054 [accessed April 2008].
Saari, D.G. (2001). Decisions and elections: Explaining the unexpected. Cambridge, England:
Cambridge University Press.
Saari, D.G. (2006). Which is better, the Condorcet or Borda winner? Social Choice and
Welfare, (1), 107.
Satterthwaite, M. (1975). Strategy-proofness and Arrow’s conditions: Existence and cor-
respondence theorems for voting procedures and social welfare functions. Journal of
Economic Theory, 0, 187–217.
Schelling, T.C. (1978). Micromotives and macrobehavior. New York: W. W. Norton.
Snijders, T. (2001). The statistical evaluation of social network dynamics. In M. Sobel and
M. Becker (Eds.), Social methodology dynamics (pp. 361–395). Boston and London:
Basil Blackwell.
Taskar, B., Abbeel, P., and Koller, D. (2002). Discriminative probabilistics models for rela-
tional data. Paper presented at the 18th International Conference on Uncertainty in
Artificial Intelligence. Available: http://www.biostat.wisc.edu/~page/rmn.pdf [accessed
Feb. 2008].
Taskar, B., Wong, M.F., and Koller, D. (2003). Learning on the test data: Leveraging
“unseen” features. Paper presented at the 20th International Conference on Machine
Learning, August, Washington, DC. Available: http://ai.stanford.edu/~koller/Papers/
Taskar+al:ICML03.pdf [accessed Feb. 2008].
Tesfatsion, L. (1997). A trade network game with endogenous partner selection. In H. Amman,
B. Rustem, and A.B. Whinston (Eds.), Computational approaches to economic problems
(pp. 249–269). Dordrecht, The Netherlands: Kluwer Academic.
Tsvetovat, M., Reminga, J., and Carley, K.M. (2004). DYNETML: Interchange format for
rich social network data. (CASOS Technical Report #CMU-ISRI-04-105). Pittsburgh,
PA: Carnegie Mellon University, School of Computer Science, Institute for Software
Research International.
Vriend, N. (2006). ACE models of edogenous interactions. In L. Tesfatsion and K.L. Judd
(Eds.), Handbook of computational economics, volume : Agent-based computational
economics. Amsterdam, The Netherlands: Holland/Elsevier.
Wasserman, S., and Faust, K. (1994). Social network analysis: Methods and applications. New
York: Cambridge University Press.
OCR for page 260
0 BEHAVIORAL MODELING AND SIMULATION
Webber, F. (1997). Software wrappers to support nonstop computing. Paper presented at the
20th National Information Systems Security Conference, October, Baltimore, MD. Avail-
able: http://csrc.nist.gov/nissc/1997/proceedings/730.pdf [accessed Feb. 2008].
Wilhite, A.W. (2006). Economic activity on fixed networks. In L. Tesfatsion and K.L. Judd
(Eds.), Handbook of computational economics, volume : Agent-based computational
economics. Amsterdam, The Netherlands: Holland/Elsevier.
Young, H.P. (2006). Social dynamics: Theory and applications. In L. Tesfatsion and K.L. Judd
(Eds.), Handbook of computational economics, volume : Agent-based computational
economics. Amsterdam, The Netherlands: Holland/Elsevier.
Zeggelink, E. (1994). Dynamics of structure: An individual oriented approach. Social Net-
works, (4), 295–333.