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Simulation of

Stance Perturbation

Peter Carragher�Lynnette Hui Xian Ng

Kathleen M. Carley

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SNA x ABM: Exogenous vs Endogenous

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Will, M., J. Groeneveld, K. Frank, and B. Muller. 2020, Feb.. “Combining social network analysis and agent-based modelling to explore dynamics of human interaction: A review”. Socio-Environmental Systems Modelling 2:16325.

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Stance flipping & Tipping Points

Endogenous & exogenous features are equally important in predicting pro/ anti vaccine stance flips on Twitter [1]
SI process is vulnerable to manipulative actors.

Empirical: 25% confederates for tipping point in language adoption [3]
Simulation: 2-4% confederates for tipping point in social networks [2]

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1 Ng, L. H. X., and K. M. Carley. 2022. “Pro or Anti? a Social Influence Model of Online Stance Flipping”. IEEE Transactions on Network Science and Engineering:1–18

2 Centola, D., J. Becker, D. Brackbill, and A. Baronchelli. 2018, June. “Experimental evidence for tipping points in social convention”. Science 360(6393):1116–1119

3 Ross, B., L. Pilz, B. Cabrera, F. Brachten, G. Neubaum, and S. Stieglitz. 2019, July. “Are social bots a real threat? An agent-based model of the spiral of silence to analyse the impact of manipulative actors in social networks”. European Journal of Information Systems 28(4):394–412

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Term Definitions

Stance y: pro/ anti (1.0, -1.0)
Susceptibility A: how ‘open-minded’ is the agent?
Influence W: how much an agent effects its neighbors stances

Perturbation: an agents attempt to ‘nudge’ stances
Confederates: agents that are perturbing the network
Tipping Point: % confederates required to change consensus

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Co-evolutionary SI Model

Stance update¹:

Influence update²:

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Friedkin, N. E., and E. C. Johnsen. 1990. “Social influence and opinions”. Journal of Mathematical Sociology
Macy, M. W., J. A. Kitts, A. Flache, and S. Benard. 2003. “Polarization in dynamic networks: A Hopfield model of emergent structure”. Dynamic Social Network Modeling and Analysis

Stance update (exogenously imposed network): agents adjust their stance to match their ego-networks (agents with influence over them)

Influence update (endogenously emerging network): update their influence weights based on the homophily principle

When stance rate >> influence rate:

‘we always change our stance to agree with our friends’
the simulation converges quickly as defined by the influence network topology

When influence rate >> stance rate:

‘we break & form friendships based on homophily’
agents adjust their influence based on stance homophily first and foremost
influence stance tradeoff (exploration / exploitation tradeoff)

Goal of (conversion) confederate is to perturb network stance w/o loss of influence

Graph shows an example of an agent trying to perturb network while maintaining influence

To perturb the network towards -1, they lower their stance
This lowers affects their homophily, negatively affecting the influence update rule in future timesteps
To rebuild their influence, they raise their stance incrementally to align with non-confederate nodes

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Methodology: Stable Polarized State

Construct scale-free network
Agent selection strategy
Perturbation Strategy
Run till stance convergence

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Perturbation Strategies

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Conservative:

Conversion:

Cascade:

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Virtual Experiments Setup

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Items	Range	Value	Number
Independent
N agents	Natural number	10, 15, 20, 25	4
% confederates	[0, 100]	0, 5, 10, 15, 20, 25, 30, 35, 40	5
Agent selection strategy	[0, 2]	random, influence, susceptibility	3
Perturbation strategy	[0, 2]	conserve, convert, cascade	3
Dependent
Mean Influence	Nx1 Vector (real)
Mean stance at final timestep	[-1.0, 1.0]	[-1, 1]	R
# timesteps till convergence	Natural number	[50, 1000]
Control
Influence update rate	[0,1.0]	0.01 (Hopfield)	1
Stance update rate	[0, 1.0]	0.001	1
Susceptibility	Nx1 Vector (real)	gaussian(0.1, 0.1)	N

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Influential agents are better confederates

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Optimal confederates target local ego-networks

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Network construction explains mean stance

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Minority stance ‘tipping points’ around 25%

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Limitation in Validation

We cannot intentionally perturb real social networks
Stance determination requires data collection + prediction
Similarity of scale-free networks to real networks
Confederates can only control their stance (cannot ‘friend’ others)
Stance & influence update rates are:

instantaneous (temporal / ‘lagging’ relations are not modeled)
constant (vs GLIE based RL policies)

Single topic, continuous stances

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Future Work

Formalize wisdom of crowds & tipping points as 2 extremes of conditional probability spectrum parameterized by social influence

Wisdom of crowds -> independence
Tipping points -> conditional independence via influence network

Explore impact of lagging social influence effects on stance
Do dynamics change when confederate agents saturate environment?

Higher suspicion, lower trust, lower susceptibility
“Lemons market”

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Recovery from Stable Polarized State

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Recovery from Stable Polarized State

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References

Centola, D., J. Becker, D. Brackbill, and A. Baronchelli. 2018, June. “Experimental evidence for tipping points in social convention”. Science 360(6393):1116–1119.
Friedkin, N. E., and E. C. Johnsen. 1990. “Social influence and opinions”. Journal of Mathematical Sociology 15(3-4):193–206. Publisher: Taylor & Francis.
Macy, M. W., J. A. Kitts, A. Flache, and S. Benard. 2003. “Polarization in dynamic networks: A Hopfield model of emergent structure”. Dynamic Social Network Modeling and Analysis:162–173. Washington DC: National Academies Press.
Ng, L. H. X., and K. M. Carley. 2022. “Pro or Anti? a Social Influence Model of Online Stance Flipping”. IEEE Transactions on Network Science and Engineering:1–18.
Ross, B., L. Pilz, B. Cabrera, F. Brachten, G. Neubaum, and S. Stieglitz. 2019, July. “Are social bots a real threat? An agent-based model of the spiral of silence to analyse the impact of manipulative actors in social networks”. European
Journal of Information Systems 28(4):394–412. Will, M., J. Groeneveld, K. Frank, and B. Muller. 2020, Feb.. “Combining social network analysis and agent-based modellingto explore dynamics of human interaction: A review”. Socio-Environmental Systems Modelling 2:16325.

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Research Questions

Under what conditions is stance convergence non-trivial?
How does the stance - influence update ratio affect convergence?

How do perturbations affect the average stance?
What is the minimal perturbation required to change consensus?
How can confederates perturb the network without losing influence?

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Hypotheses

Agent selection strategy: targeting influential agents' is better than targeting ‘extremist’ or low susceptibility agents.
Perturbation strategy:

nudging is better than extremism
targeting ego-networks beats targeting the mean

Tipping points for the minority stance may be artificially induced by well targeted perturbations.

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Validation

Theoretical validity: ~25% mean tipping point agrees w/ literature

2-4% tipping points exist but are rare

Pattern validity: stylized facts from known phenomena

stance of users in the network converge via social conformity
influential agents are the best confederates

Process validity: coordinated inauthentic behaviour, influence ops

real-world scenarios where confederates perturb the stance of the network

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Validation

Several stylized facts that can be used to determine known phenomena
Product of the simulation dynamics: stance of users in the network eventually come to an equilibrium because users achieve social conformity with each other
For scale-free networks, agents with a higher out-degree tend to be more influential. By taking a weighted sum of agent out-degree and initial stances, we should see a correlation with mean stance at the final timestep

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