Opinion Dynamics of Skeptical Agents Read-Through

Opinion Dynamics of Skeptical Agentsby A. Tsang and K. Larson

Paper Read-ThroughM2 Yu Matsuzawa

Title and publication notes

• Opinion Dynamics of Skeptical Agents– Alan Tsang and Kate Larson• Univ. of Waterloo, Canada

– AAMAS2014 (Proc. of the 13th International Conference on Autonomous Agents and Multiagent Systems, pp. 277-284), May 2014

Opinion Dynamics of Skeptical Agents 2

Shared Interest

• Opinion Dynamics– Gradated (continuous) opinions in this paper• Cf. Discrete opinions

• Cognitive Bias: Motivated cognition– Leads subjects to skewed/irrational conclusion


Motivated Cognition

• Evaluation based on/affected by:– Compatibility with the subject’s own beliefs– Profitability to the subject

• 「自分にとって都合のいいように解釈する」

• In a case of opinion convergence/debate:– Opinion/Evidence of the competitor diverges away

-> Less & less persuasive – “It must be flawed!”Opinion Dynamics of Skeptical Agents 4

Skepticism

• Key component of this research• Disbelief/Refusal against incompatible opinion

due to motivated cognition->Skepticism (Antonym: Trust)

• Summary: Opinion dynamics in networks of agents with Skepticism/Trust mechanism


Opinion Dynamics Model

• Agents are embedded in undirected graphs• Each agent has an opinion • Influenced by neighbors (direct neighbor)

• For each neighbor , an agent maintains Trust value – Represents weight of influence to from



• Def. Trust function :– (Gaussian kernel)– Used in Trusts updating– Bandwidth parameter represents empathy• Higher means the population is more willing to be

persuaded by different opinion



• Opinion update function:– (Weighted average)– represents inertia of own opinion

• Trust update function:

– represent learning rate• Higher the is, faster the trust/distrust appear



• Opinions updated, then Trusts updated in each iteration steps

• Majority of agents are initialized randomly• The remainder represent extremists– Initialized to – Extremists’ opinions and trusts are NOT updated


Graph Models

• Classic BA model• Homophily model based on ER random graph

• BA model– Explanation snipped– Parameter represents the number of edges every

new vertices have


Graph models

• Homophily model based on ER random graph– In Erdos-Renyi random graph, every possible edge

has probability to be activated– In this model, activation probability of possible

edge between and is:• where

– If opinions of aligned with ’s, highly probable they are connected

– Similar opinion, likely to be connected -> Homophily


Trust initialization

1. Uniform trust model– , for every existing and – , where represents ’s degree

2. Degree based trust model– , thus

3. Kernel based trust model– ,


Experimental designs

• Two experiments:– Ability of extremists to influence the moderate

people• 1-pole model• BA model

– Conditions for opinions of the moderate people to stratify and stabilize at multiple levels• 2-pole model• BA and Homophily model



• 200 agents• In the first set of experiments:– 10% of agents are extremists– Fixed to (1-extremists) -> 1-pole model

• In the second set:– 10% are 0-extremists, 10% are 1-extremists

-> 2-pole model



– Changing did not affect results qualitatively• Termination condition:– No opinions changed by more than – Iterations reached maximum number • Rarely reached in practice

• Results are averaged over 25 replicated trials


First Experiment

• Investigation of the effect of extremists• Measure: The mean opinion of the moderates

at the end of each experiments– If completely unaffected -> hover around 0.5– If completely affected -> near 1.0


Influence of Extremists

• Evolution of Opinions over the course of the experiment– Darker -> More

– Initially, the moderates converges to a common opinion, regardless of how close to the pole

– After that the consensus gradually drifts to the pole


Effect of Empathy

• Mean Opinions at Convergence (uniform trust)

– Effect of empathy and BA parameter – Increasing has expected effect to polarization– Increasing has no qualitative effect


Second Experiment

• Introducing 2-pole mode• Measure: The mean of absolute differences of

each agents’ opinion from 0.5 at convergence– If completely unaffected -> 0– If completely affected -> 0.5


Type of convergence in 2-pole mode

• Deffuant’s characterization (2006)

• Type I: Moderate• Type II: Polarized to one side• Type III: Split in two pole• Type IV: Fragmentation


Polarization in 2-pole mode

• Mean polarization at convergence (degree trust)

– Basic traits are the same as the first experiment– Impact of extremists mitigated on highly connected graph– Type I or II convergence


Effect of initialization

• So far the moderate population are initialized uniformly at random

• Can initially divided population produce separation(Type III) or fragmentation(IV)?

• Test with initialization

– http://www2.ipcku.kansai-u.ac.jp/~aki/pdf/beta1.htm


Divided initialization

• Evolution of opinions from

– Surprisingly, the result unchanged– Even agents initialized to the opposite pole drawn to

the converged poleOpinion Dynamics of Skeptical Agents 23

Conditions for stratification

• There appear to be two main factors for Type III(separation)/IV(fragmentation) to occur->stratification (層を形成すること )

• Initial Trust– Too much trusts are given to different opinions

• Homophily in graph structure


Kernel trust and Homophily model

• Evolution of opinions from

– Ends in Type IV convergence (fragmentation)


Kernel trust and Homophily model

• Mean polarization at convergence

– Under , stratification occurs and polarization decreases

– Higher empathy actually contributes to stratify


Discussion

• Hypothesis: High empathy agents are affected by extremists of both poles-> Preventing convergence to a single pole?

• Why the population can drift to consensus or poles even if they are initially divided?– Approximation of influence showed:

Unpolarized moderates can serve as bridge on which influence will flow, starting an avalanche


Conclusion

• Introduction of robust Opinion Dynamics model

• Combination of skepticism (Kernel trust) and Homophily graph are the condition of opinion stratification


Evaluation

• Modeling and Simulation centric research– Normal in AAMAS?– There is analytical approximation in discussion

-> Only shows the mechanism of influence-flow within the model

– Not mentioning validity of the model itself, according to real data


Evaluation

• Grand goal is unclear– Condition of opinion stratification

(which is kind of unclear word as well,i.e. diversification apart from extreme value?)

– Should be given more precisely? – And early


Evaluation

• Related work and orientation of the research is splendid– Can learn the methodology• Research lately published paper from the targeted

conference well (in this case AAMAS)• Find some backbone research to stand upon


Inspiration

• Can we use some of the idea in this paper?– Introducing cognitive bias into the model– Initialization by Beta distribution– Homophily graph model• Easily construct innately-clustered network• Possibly there is more common model for this?


Science

Opinion Dynamics of Skeptical Agents Read-Through