# Notes on “Sociophysics, an Introduction”

These are my notes as I was reading the book, which I found to be a very good overview with good detail that didn’t get in the way of the narrative. The references are stellar. When I found an appropriate paper mentioned in the text, I’ve included it as a link, usually with an accompanying abstract.

I read the book to support the model I’m working on for my PhD on trustworthy news. I’ve been doing agent-based simulations since the ’90s when I was working on my Master’s thesis on the The Coevolution of Weapons and Aggression. I certainly feel as though it has helped update my awareness of progress in the field since that effort, back when the term sociophysics didn’t even exist.

• Chapter 2: Basic features of social systems and modelling
• Minority Opinion Spreading in Random Geometry
• Abstract: The dynamics of spreading of the minority opinion in public debates (a reform proposal, a behavior change, a military retaliation) is studied using a diffusion reaction model. People move by discrete step on a landscape of random geometry shaped by social life (offices, houses, bars, and restaurants). A perfect world is considered with no advantage to the minority. A one person-one argument principle is applied to determine locally individual mind changes. In case of equality, a collective doubt is evoked which in turn favors the Status Quo. Starting from a large in favor of the proposal initial majority, repeated random size local discussions are found to drive the majority reversal along the minority hostile view. Total opinion refusal is completed within few days. Recent national collective issues are revisited. The model may apply to rumor and fear propagation.
• Clustering coefficient (video)
```CC = 0
numNodes = 0
for(i = 0 to max)
for(j = 0 to max)
n = node(i,j)
k = n.numNeighbors()
n.setNodeCC((2*a)/(k*(k-1)))
CC += n.getNodeCC()
numNodes++
CC = CC/numNodes```
• Clustering coefficient ordering: random -> small world -> regular
• To build a scale-free network, AL Barabási, R Albert in Emergence of scaling in random networks start with a small random network and incrementally add nodes where the probability of connecting a new node with existing nodes is proportional to how many connections the current nodes have.
```network.createInitialNodes(SOME_SMALL_VALUE)
for(i = 0 to desired)
n = createNewNode()
for(j = 0 to network.numNodes)
curNode = getNode(j)
• Does node aging matter in this model?
• Null Models For Social Networks (for comparison and testing)
• Downloaded the following from the references section to my Group Polarization folder
• A bubble could be an example of a strong community [pg 17] would need to figure out a way of establishing in and out links in knowledge space
• Benchmark networks to test community detection algorithms [pg 17]. Artificially generated and the Zachary Karate club
• I appear to be working with (maybe?) class ‘C’ social networks, where links connect people indirectly [pg 19].Covered in chapter 7 – Of Flocks, Flows and Transports
• Page 25 discusses Marian Boguña et al Models of Social Networks based on Social Distance Attachment which uses the concept of social distance. A set of quantities (e.g. profession, religion, location) are used and the social distance between two individuals is the difference in the quantities.
• More state-space simulation from page 28: Spin-glass-like Dynamics of Social Networks. Digging around uncovered her thesis: Information and Entropy in Neural Networks and Interacting Systems. From the abstract:
• Like neural networks, large ensembles of similar units that interact also need a generalization of classical information-theoretic concepts. We extend the concept of Shannon entropy in a novel way, which may be relevant when we have such interacting systems, and show how it differs from Shannon entropy and other generalizations, such as Tsallis entropy.
• Mean Field Approximation – In physics and probability theory, mean field theory (MFT also known as self-consistent field theory) studies the behavior of large and complex stochastic models by studying a simpler model. Such models consider a large number of small individual components which interact with each other. The effect of all the other individuals on any given individual is approximated by a single averaged effect, thus reducing a many-body problem to a one-body problem.
• Chapter 3: Opinion formation in a society
• Voter models (binary choices, usually {0, 1})
• Injection of any noise always leads to a disordered system – Nonequilibrium spin models with Ising universal behaviour
• [page 56]: Heterogeneous bounds of confidence: meet, discuss and find consensus! – In this paper, heterogeneous bounds of confidence are studied. The surprising result is that a society of agents with two different bounds of confidence (open-minded and closed minded agents) can find consensus even when both bounds of confidence are significantly below the critical bound of confidence of a homogeneous society. I think that this may represent exploiters and explorers. Need to read.
• On [page 62], the authors discuss Phase transitions in a two-parameter model of opinion dynamics with random kinetic exchanges, which they say shows  that agent behavior is unrealistic when there is only positive influence. This could support my Anti-belief element in my model.
• On [page 66] the authors briefly discuss Opinion dynamics with confidence threshold: an alternative to the Axelrod model, where voter have continuous opinion. Clusters happen when confidence is 0 < c < 1. Interval notation (0, 1)
• An important point seems to be the number of opinions. For low numbers of discretized opinions and many agents, clustering happens. For the reverse, pretty much every agent has their own opinion. Runs at different number of opinions can show the thresholds that these these transitions happen (called precipitation?).
• On [page 69] there is a brief mention of a model with a vector of opinions, which sounds a lot like my ‘belief’ being a set of statements. The title looks good too: Different topologies for a herding model of opinion (abstract below)
• Understanding how new opinions spread through a community or how consensus emerges in noisy environments can have a significant impact in our comprehension of the social relations among individuals. In this work a new model for the dynamics of opinion formation is introduced. The model is based on a non-linear interaction between opinion vectors of agents plus a stochastic variable to account for the effect of noise in the way the agents communicate. The presented dynamics is able to generate rich dynamical patterns of interacting groups or clusters of agents with the same opinion without a leader or centralized control. Our results show that by increasing the intensity of noise, the system goes from consensus to a disordered state. Depending on the number of competing opinions and the details of the network of interactions, the system displays a first or a second order transition. We compare the behavior of different topologies of interactions: 1d chains, annealed and complex networks.
• Citing documents include this nice overview from Cell: Herding in humans. And citing this are a few others that might be worth looking at:
• Cultural Dynamics
• Chapter 4: Social choices and popularity – skimmed, not appropriate
• Chapter 5: Crowd-avoiding dynamical phenomena – skimmed, not appropriate
• Chapter 6: Social phenomena on complex networks
• Loops of nodes behave differently from trees. what to do about that? I think loops drive the echo chamber process? It is, after all, feedback..
• There is also a ‘freezing’ issue, where a stable state is reached where two cliques containing different states are lightly connected, but not enough that the neighbors in one clique can be convinced to change their opinion [Fig. 6.2, pg 135]
• Residual Energy: The difference between the actual energy and the known energy of the perfectly-ordered ground state (full consensus).
• Dynamical Processes on Complex Networks. Got the Kindle edition so now I can search! Interesting section: 10.6 Coevolution of opinions and network
• Similar chapter in this book – Social Phenomena on coevolutionary networks [pg 166]. One of the interesting things here is the use of the iterated prisoner’s dilemma. On a network, the agents typically calculate and aggregate payoff and imitate the strategy of the neighbor with the best payoff. In the coevolutionary model, an agent can cut off the link to a defector with a probability. This seems a bit like polarization, where the group severs ties with entities with sufficiently divergent views (and individuals leave when the group becomes too extreme)
• Coevolution of agents and networks: Opinion spreading and community disconnection Abstract: We study a stochastic model for the coevolution of a process of opinion formation in a population of agents and the network which underlies their interaction. Interaction links can break when agents fail to reach an opinion agreement. The structure of the network and the distribution of opinions over the population evolve towards a state where the population is divided into disconnected communities whose agents share the same opinion. The statistical properties of this final state vary considerably as the model parameters are changed. Community sizes and their internal connectivity are the quantities used to characterize such variations.
• Opinion and community formation in coevolving networks (Gerardo Iñiguez González)
• Abstract: In human societies opinion formation is mediated by social interactions, consequently taking place on a network of relationships and at the same time influencing the structure of the network and its evolution. To investigate this coevolution of opinions and social interaction structure we develop a dynamic agent-based network model, by taking into account short range interactions like discussions between individuals, long range interactions like a sense for overall mood modulated by the attitudes of individuals, and external field corresponding to outside influence. Moreover, individual biases can be naturally taken into account. In addition the model includes the opinion dependent link-rewiring scheme to describe network topology coevolution with a slower time scale than that of the opinion formation. With this model comprehensive numerical simulations and mean field calculations have been carried out and they show the importance of the separation between fast and slow time scales resulting in the network to organize as well-connected small communities of agents with the same opinion.
• Citing paper: Effects of deception in social networks (Gerardo Iñiguez González)<— Important???
• Abstract: Honesty plays a crucial role in any situation where organisms exchange information or resources. Dishonesty can thus be expected to have damaging effects on social coherence if agents cannot trust the information or goods they receive. However, a distinction is often drawn between prosocial lies (‘white’ lies) and antisocial lying (i.e. deception for personal gain), with the former being considered much less destructive than the latter. We use an agent-based model to show that antisocial lying causes social networks to become increasingly fragmented. Antisocial dishonesty thus places strong constraints on the size and cohesion of social communities, providing a major hurdle that organisms have to overcome (e.g. by evolving counter-deception strategies) in order to evolve large, socially cohesive communities. In contrast, white lies can prove to be beneficial in smoothing the flow of interactions and facilitating a larger, more integrated network. Our results demonstrate that these group-level effects can arise as emergent properties of interactions at the dyadic level. The balance between prosocial and antisocial lies may set constraints on the structure of social networks, and hence the shape of society as a whole.
• Section 6.5: Is it really a small world? Searching post Milgram
• In the introduction to this section [page 168], the authors say a very interesting thing: “Although the network may have the small world property, searches are usually done locally: the individual may not know the global structure of the network that would help them find the shortest path to the target node“. I think that they are talking about social networks explicitly here, but the same concept applies to an information network. This is a network description of the information horizon problem. You can’t find what you can’t see, at least in a broad outline.
• Also this: “Searching can regarded as a learning process; repeating the search several times can avoid infinite loops and lead to better solutions
• 6.5.8 Funneling properties.
• The funneling capability of a node can be defined as the fraction of successful dynamic paths through it when the target is fixed and the source is varied. Two thoughts: First, this seems to be a measurement of centrality. Second, Large, vague nodes are needed for ‘laundering’ information into misinformation or conspiracy theory.
• Consider four agents. Who have characteristics that can vary between (0, 1).
• Agent 1 has two color intensities: R=0.1, G= 0.7
• Agent 2 has one color and two note volumes R=0.3, A=0.2, F=0.6
• Agent 3 also has one color and two note volumes B=0.4, D=1, E=0.2
• Agent 4 has three notes A=0.3, D=0.4, E=0.5
• Let’s assume that funneling is not required if agents share a color or note. This means that A4 can get to A1 through A2, but A3 has to get to A1 via A4 and then A2. In a matrix this looks like
R G B A D E F
Agent1 0.1 0.7
Agent2 0.3 0.2 0.6
Agent3 0.4 1.0 0.2
Agent4 0.3 0.4 0.5
• But if we add the hypernyms Color and Notes, we can get funneling. I am summing the color and notes to give a sense of the agent’s ‘projection’ into the larger, more general space. I think the ‘size’ of the funnels are the number of items that go in them times the range of each item. So Color would have a range of (0, 3) and Notes would have a range of (0, 4), since I’m not including B, C, and G here:
R G B A D E F Color Notes
Agent1 0.1 0.7 0.8
Agent2 0.3 0.2 0.6 0.3 0.8
Agent3 0.4 1.0 0.2 0.4 1.2
Agent4 0.3 0.4 0.5 1.2
• Now agents 2 and 3 can get to each other through either Color or note in two hops, and the Agents 1 and 4 can reach each other by going through each of the funnels.
• There should be a cost in using a funnel though. You loose the information about which color or which note. Intuitively, a series of steps with non-funnel links should be somehow more specific than the same number of steps through a funnel.
• Practical uses would be a way to detect poorly reasoned conclusions, as long as the beginning and end of the train of thought could be identified.
• Knowing a network by walking on it: emergence of scaling (Alexei Vázquez) Looks like an interesting guy with a wide range of publications.
• Chapter 7:  of flocks, flows and transports [page 179]
• Boids (Flocks, herds and schools: A distributed behavioral modelCraig Reynolds):
• Try to avoid collisions with other boids (repulsion)
• Attempt to match velocity with neighboring boids
• attempt to stay close to nearby boids
• If the collision avoidance is taken out and the number of dimensions increased, then this could be the model. Rather than the flock converging around a position, look at the distances between the individuals using DBSCAN and cluster.
• Density and noise need to be independent variables and saved on runs. This would also be true in information space. You can have high organization in high density, low noise states. Thinking about that, this also implies one of the emergent properties of an information bubble is the low noise. Even though the environment may be very noisy, the bubble isn’t.
• As with the other social models, individuals can have weight. That way the flock can have leaders and followers. (See Misinformed leaders lose influence over pigeon flocks to inform the model)
• Also, I like the idea of a social network being built from belief proximity, which raises the cost for switching to another flock, even if they are nearby. It could be that once a social network forms that anti-belief repulsion starts to play a role.
• Another component to include would be a Levy Flight (truncated?). That could account for cases where a leader makes a big jump and then the crowd follows with some ejection for those who can’t/won’t keep up.
• Power law distribution of weight and max step size in the creation of the population
• Thomas Schelling (Another Herbert Simon type) Segregation Model
• Phase diagram of a Schelling segregation model (L Gauvin, J Vannimenus, JP Nadal – The European Physical Journal B, 2009). I’m beginning to think that the model could be a combination of a flocking and segregation model. That could be really interesting. I also seem to get nothing when I do a Scholar search on “flocking and segregation agent simulation
• Satisfaction criteria – when the number of unlike agents is less than a fixed proportion F. As F gets larger there is an abrupt transition to a segregated state.
• Definition of segregation coefficient – the weighted average (normalized) of all cluster sizes averaged over all configurations. When only two clusters survive, n(c) = N/2
• Migration in a small world: A network approach to modeling immigration processes (B Fotouhi, MG Rabbat – Communication, Control, and Computing, 2012 – ieeexplore.ieee.org)
• Chapter 8: Endnote [page 202]
• Frustration in Complexity (2008 – Philippe Binder)- The common thread between all complex systems may not be cooperation but rather the irresolvable coexistence of opposing tendencies.
• Definition of consensus in an opinion model – the emergence of long-range order.
• Looking for phase changes from heterogeneous to homogeneous or clustered states is important. Finding what parameters are causal and the values is considered a publishable result. Canonical types of transitions, such as the percolation threshold are discussed in the appendices.

# Trustworthy News Model Assumptions

Modifications

• 12.13.16: Initial post
• 12:16:16: Added reference to proposal and explicitly discussed explorer and exploiter types.

A web version of my Google Docs dissertation proposal is here. Blame them for the formatting issues. The section this is building on is Section 5.3.1. A standalone description of this task is here.

The first part of my dissertation work is to develop an agent-based simulation that exhibits information bubble/antibubble behavior. Using Sen and Chakrabarti’s Sociophysics as my guide, I’m working up the specifics of the model. My framework is an application (JavaFX, because that’s what I’m using at work these days). It’s basically an empty framework with a trivial model that allows clustering based on similar attributes such as color:

Going forward, I need to clarify and defend the model, so I’m going to be listing the components here.

Agent assumptions

• Agents get their information from global sources (news media). They have equal access, but visibility is restricted
• Agents are Explorers or Exploiters (Which may be made up of Confirmers and Avoiders)
• Agents have ‘budgets’ that they can allocate
• Finding sources has a cost. Sources from the social network has a lower cost to access
• Keeping a source is cheaper than getting a new one
• For explorers, the cost of getting a new source is lower than an exploiter.
• The ‘belief’ as a set of ‘statements’ appears to be valid
• The collection of statements and the associated values create a position in an n-dimensional hilbert space of information. Position and velocity should be calculable.
• Start at one dimension to reproduce prior opinion models

Network assumptions

• There are two items that we are looking for.
• The first is the network configuration over time. What nodes do agents connect to for their information.
• The second is the content of that information. For that, we’ll probably need some dimensionality reduction, such as NMF (look for a post on implementing this later). This is where we look for echo chambers of information, as opposed to the agents participating in them
• Adjustable to include scale-free, small world, and null configurations
• What about loops? Feedback could be interesting, since a small group that is semi-isolated could form into a very loud bubble that could lower the cost of finding information. So a notion of volume might be needed that emerges from a set of agreeing agents. This could be attraction, though I think I like an economic approach more?
• There is also a ‘freezing’ issue, where a stable state is reached where two cliques containing different states are lightly connected, but not enough that the neighbors in one clique can be convinced to change their opinion [Fig. 6.2, pg 135]

Measures

• Residual Energy: The difference between the actual energy and the known energy of the perfectly-ordered ground state (full consensus).
• Deviation from null network.
• Clustering as per community detection (Girard et. al)

Implementation details

• Able to be run multiple times with the same configuration but different seed
• Outputs to… something. MySql or Excel probably
• Visualization using t-SNE? Description plus Java implementation is here: https://lvdmaaten.github.io/tsne/

More to come as the model fleshes out.