Social Modelling Agent-Based Simulation and Complexity

SMABSC: Cognitive Agents

Cognitive models are a representation of an agent control mechanism resembling the cognitive architecture of a mind.  It can be understood as a control system (e.g. a flow graph how to react) that takes sensory inputs and produces motor outputs (Piaget, 1985).

More advanced models include adaptive memory (Anderson, 1983).

Famous models include SOaR: State Operator and Result (Laird, Newell, & Rosenbloom, 1987); BDI: Belief, Desire, and Intention (Bratman, Israel, & Pollack, 1988); PECS: Physics, Emotions, Cognitive, Social (Urban & Schmidt, 2001); ACT-R: Adaptive Control of Thought – Rational (Anderson, Matessa, & Lebiere, 1997); CLARION: Connectionist Learning with Adapative Rule Induction On-line (Sun, 2006); and Agent Zero (Epstein, 2014).

The communality of all these is summed up in this slide from the University of Michigan:

 

References

Anderson, J. R. (1983). A spreading activation theory of memory. Journal of Verbal Learning and Verbal Behavior, 22(3), 261–295.
Anderson, J. R., Matessa, M., & Lebiere, C. (1997). ACT-R: A theory of higher level cognition and its relation to visual attention. Human-Computer Interaction, 12(4), 439–462.
Bratman, M. E., Israel, D. J., & Pollack, M. E. (1988). Plans and resource‐bounded practical reasoning. Computational Intelligence, 4(3), 349–355.
Epstein, J. M. (2014). Agent_Zero: Toward neurocognitive foundations for generative social science. Princeton University Press.
Laird, J. E., Newell, A., & Rosenbloom, P. S. (1987). Soar: An architecture for general intelligence. Artificial Intelligence, 33(1), 1–64.
Piaget, J. (1985). The equilibration of cognitive structures: The central problem of intellectual development. University of Chicago Press.
Sun, R. (2006). The CLARION cognitive architecture: Extending cognitive modeling to social simulation. In Cognition and multi-agent interaction: From cognitive modeling to social simulation (pp. 79–99). Cambridge University Press.
Urban, C., & Schmidt, B. (2001). PECS–agent-based modelling of human behaviour. In Emotional and Intelligent–The Tangled Knot of Social Cognition. Presented at the AAAI Fall Symposium Series, North Falmouth, MA.

SMABSC: Disease Propagation

The SIR model was introduced as a mathematical model with differential equations (Kermack & McKendrick, 1927). The basic states are Susceptible, Infected, and Recovered.

[latex]N_i = \frac{dS}{dt}+\frac{di}{dt}+\frac{dR}{dt}[/latex]

In the SIR model, the fundamental trajectory of disease propagation could be captured, immunity was acquired after disease and the population is homogeneous.

But the SIR model has short-comings:

  • populations are not infinite and increase/decrease over time,
  • populations are spatial objects and have (voluntary) spatial interactions,
  • populations are heterogeneous, including isolated sub-populations with irregular interactions as well as significant distances.
  • populations are driven by endogenous social factors and constrained by exogenous environmental circumscription.

Additional states were introduces such as Exposed (i.e. dormant infections that does not infect others yet) and Maternal immunity (i.e. individuals that cannot be infected). The order has been rearranged such as SIS, SEIS, SIRS.

These models still did not address explicit spatial reference to population loci & transportation networks, distribution of social & medical information (temporal and spatial), mechanisms to simulate voluntary & forced quarantines, treatment options and their delivery (temporal and spatial), and characteristics of pathogens and disease vector.

Questions that needs to be answered about a model is the form of circumscription (Carneiro, 1961, 1987, 1988) (e.g. social and environmental forces), instantiation topologies (i.e. abstract or logical relationships, social networks, or space), activation schemes (e.g. random, uniform random, Poisson), and encapsulation.

References

Carneiro, R. L. (1961). Slash-and-burn cultivation among the Kuikuru and it implications for cultural development in the Amazon Basin. In J. Wilbert (Ed.), The evolution of horticultural systems in native South America, causes and consequences. “Antropológica” (pp. 47–67). Caracas, Venezuela: Editorial Sucre.
Carneiro, R. L. (1987). Further reflections on resource concentration and its role in the rise of the state. In L. Manzanilla (Ed.), Studies in the Neolithic and Urban Revolutions (pp. 245–260). Oxford, UK: Archaeopress.
Carneiro, R. L. (1988). The Circumscription Theory: Challenge and response. The American Behavioral Scientist, 31(4), 497–511.
Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 115(772).

SMADSC: Social Networks

Social networks often give structure to relations. They can be considered as abstract, mathematically, tractable and computationally instantiatable systems. Social networks have become a field of their own. It is very interdisciplinary touching mathematics (graph theory), computer science (algorithms), sociology (population group trends), psychology (individual and social behaviour), and complex network theory.

Interpersonal contact caused social networks to emerge. It can be understood as a descriptor for social trends (Cioffi-Revilla, 2013) . The basic elements are Nodes (units of observation), Edges (relationships), and Aggregations (Dyads, Triads, Clique, Clusters, etc.). More advanced elements are Descriptive Properties (e.g. centrality measures).

A network can also be seen as an abstract topology and “social glue”. Agents can move around the network, by jumping from node to node, either there is a connecting edge or in general. Alternatively, nodes can be mapped onto agents, either by allowing agents to move around a raster or along the edges.

A network trades off regularity and complexity, relative size and relative complexity as well as network complexity and network connectivity.

Social Network Analysis

Social Network Analysis (SNA) is based on a machine-readable representation of a social network, i.e. an adjacency matrix. While there is no “best measure” to describe a node or edge, there are several useful descriptive properties.

Bridging and spanning nodes can be identified. Also,cliques and clusters can be identified which gives a relative density of the network. Lastly, measures  of relative Connectedness and Centrality are often used (see this post).

Social Psychology

Instead of observing the network as a whole. It can be analysed from the node perspective. Nodes can be grouped into a “self” (ego) or “other (alter). The “self”‘s purpose  is “self-motivated” action relative to their role and their subjective network knowledge. If nodes are “other” then their function is that of an arbiter or reactive agent. In this view, edges represent social connectivity in the network. They represent evidence of physical, informational, and or some other material or non-material transfer or contact between nodes. Typically, the edges suggest some social binding between individuals and/or groups of nodes. Finally, an edge often connotes implicit temporal properties. Dyads are any two connected nodes in the network, whereas triads are any three connected nodes, whereas cliques are larger. Simmelian ties are strong, bidirectional social bindings.

SMADSC: Introduction

Complex systems are the core topic of  Social Modelling, Agent-Based Simulation, and Complexity. Complex systems usually emerge as an artefact of interaction. The output of a complex system follows the Power Law and may have a regime or phase changes, known as tipping points. Emergent properties and scale-free organisation are a typical feature of complex systems. It would it be possible to analyse top-down, but is best studied bottom-up.

In general, a social system is analysed by creating a mental model of it, deriving hypotheses regarding endogenous and exogenous forces that drive it and finally instantiating an agend-based model (ABM) in code that is simulated in silicio.

Recommended reading for the week is Chapter 9 in Complex adaptive
systems: An introduction to computational models of social life (Miller & Page, 2009) and Chapter 8 in Introduction to computational
social science: principles and applications (Cioffi-Revilla, 2013).

Agent-based Models (ABM)

Usually, an object-oriented software system that instantiates a model of living systems of social entities. Agent-based models go beyond numerical analysis, rather they observe emergent behaviour. Broad paradigms that influence ABMs are cellular automata, big data, social networks, and generative models. Concepts will be emergence, bottom-up computation micro-level rules lead to macro-level behaviours. There are two main dominant characteristics of ABMs:

  1.  A positive representation attempts to closely recreate or capture the abstract or detailed essence  of a prototype system.
  2. A normative representation provides input control for exogenous steering of internal feedback loops.

Generative ABMs are useful in three general cases:

  1. Modelling historical systems, that cannot be revisited
  2. Long-lived systems, that span a longer time than can be observed
  3. Unethical, illegal, unsafe or unlikely environmental  settings or exogenous  stimuli to the system

The Game of Life (Conway, 1970)

A game with two states {dead, alive} and the rules:

Each cell checks the Life State of itself and those of the cells in its local neighbourhood at a Moore distance of 1. If alive then display a pixel if dead do not. If this cell has less than two neighbours alive or more than three neighbours alive then, set this cell dead. If there are exactly three alive neighbours, set Life State alive. Randomized activation of cells continues “forever.”

It uses the concepts of cellular automata and either Moore or von Neumann distance as well as distance-neighbourhoods.

Other famous ABMs are Flocking (Reynolds, 1987), Swarming (Bonabeau & Meyer, 2001), Residential Segregation (Schelling, 1969), Residential Segregation using vector-based GIS (Crooks, 2010)

References

Bonabeau, E., & Meyer, C. (2001). Swarm intelligence. Harvard Business Review, 79(5), 106–114.
Cioffi-Revilla, C. (2013). Introduction to computational social science: principles and applications. Springer Science & Business Media.
Conway, J. (1970). The game of life. Scientific American, 223(4), 4.
Crooks, A. T. (2010). Constructing and implementing an agent-based model of residential segregation through vector GIS. International Journal of Geographical Information Science, 24(5), 661–675.
Miller, J. H., & Page, S. E. (2009). Complex adaptive systems: An introduction to computational models of social life. Princeton University Press.
Reynolds, C. W. (1987). Flocks, herds and schools: A distributed behavioral model. ACM SIGGRAPH Computer Graphics, 21(4), 25–34.
Schelling, T. C. (1969). Models of segregation. The American Economic Review, 59(2), 488–493.