Opinion Dynamics of Skeptical Agents
by A. Tsang and K. Larson
Paper Read-Through
M2 Yu Matsuzawa
Title and publication notes
• Opinion Dynamics of Skeptical Agents
– Alan Tsang and Kate Larson
• Univ. of Waterloo, Canad...
Shared Interest
• Opinion Dynamics
– Gradated (continuous) opinions in this paper
• Cf. Discrete opinions
• Cognitive Bias...
Motivated Cognition
• Evaluation based on/affected by:
– Compatibility with the subject’s own beliefs
– Profitability to t...
Skepticism
• Key component of this research
• Disbelief/Refusal against incompatible opinion
due to motivated cognition
->...
Opinion Dynamics Model
• Agents are embedded in undirected graphs
• Each agent 𝑖 has an opinion 𝑥𝑖 ∈ 0,1
• Influenced by n...
Opinion Dynamics Model
• Def. Trust function 𝑇:
– 𝑇 𝑥, 𝑥′ = exp −
𝑥−𝑥′ 2
ℎ
(Gaussian kernel)
– Used in Trusts 𝑤𝑖,𝑗 updatin...
Opinion Dynamics Model
• Opinion update function:
– 𝑥𝑖 ←
𝑤 𝑖,𝑖 𝑥 𝑖+∑𝑤 𝑖,𝑗 𝑥 𝑗
𝑤 𝑖,𝑖+∑𝑤 𝑖,𝑗
(Weighted average)
– 𝑤𝑖,𝑖 repre...
Opinion Dynamics Model
• Opinions updated, then Trusts updated in
each iteration steps
• Majority of agents are initialize...
Graph Models
• Classic BA model
• Homophily model based on ER random graph
• BA model
– Explanation snipped
– Parameter 𝑚 ...
Graph models
• Homophily model based on ER random graph
– In Erdos-Renyi random graph, every possible edge
has probability...
Trust initialization
1. Uniform trust model
– 𝑤𝑖,𝑗 = 1, for every existing 𝑖 and 𝑗
– 𝑤𝑖,𝑖 = 𝑑𝑖, where 𝑑𝑖 represents 𝑖’s de...
Experimental designs
• Two experiments:
– Ability of extremists to influence the moderate
people
• 1-pole model
• BA model...
Experimental designs
• 200 agents
• In the first set of experiments:
– 10% of agents are extremists
– Fixed to 𝑥𝑖 = 1 (1-e...
Experimental designs
• 𝑟 = 1.5
– Changing 𝑟 did not affect results qualitatively
• Termination condition:
– No opinions ch...
First Experiment
• Investigation of the effect of extremists
• Measure: The mean opinion of the moderates
at the end of ea...
Influence of Extremists
• Evolution of Opinions over the course of the
experiment
– Darker -> More
– Initially, the modera...
Effect of Empathy
• Mean Opinions at Convergence (uniform trust)
– Effect of empathy ℎ and BA parameter 𝑚
– Increasing ℎ h...
Second Experiment
• Introducing 2-pole mode
• Measure: The mean of absolute differences of
each agents’ opinion from 0.5 a...
Type of convergence in 2-pole mode
• Deffuant’s characterization (2006)
• Type I: Moderate
• Type II: Polarized to one sid...
Polarization in 2-pole mode
• Mean polarization at convergence (degree trust)
– Basic traits are the same as the first exp...
Effect of initialization
• So far the moderate population are initialized
uniformly at random
• Can initially divided popu...
Divided initialization
• Evolution of opinions from 𝐵𝑒𝑡𝑎(0.5,0.5)
– Surprisingly, the result unchanged
– Even agents initi...
Conditions for stratification
• There appear to be two main factors for Type
III(separation)/IV(fragmentation) to occur
->...
Kernel trust and Homophily model
• Evolution of opinions from 𝐵𝑒𝑡𝑎(0.5,0.5)
– Ends in Type IV convergence (fragmentation)
...
Kernel trust and Homophily model
• Mean polarization at convergence
– Under ℎ > 0.3, stratification occurs and
polarizatio...
Discussion
• Hypothesis: High empathy agents are affected
by extremists of both poles
-> Preventing convergence to a singl...
Conclusion
• Introduction of robust Opinion Dynamics
model
• Combination of skepticism (Kernel trust) and
Homophily graph ...
Evaluation
• Modeling and Simulation centric research
– Normal in AAMAS?
– There is analytical approximation in discussion...
Evaluation
• Grand goal is unclear
– Condition of opinion stratification
(which is kind of unclear word as well,
i.e. dive...
Evaluation
• Related work and orientation of the research
is splendid
– Can learn the methodology
• Research lately publis...
Inspiration
• Can we use some of the idea in this paper?
– Introducing cognitive bias into the model
– Initialization by B...
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Opinion Dynamics of Skeptical Agents Read-Through

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Read-through of AAMAS 2014 paper "Opinion Dynamics of Skeptical Agents" by A. Tsang and K. Larson

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Opinion Dynamics of Skeptical Agents Read-Through

  1. 1. Opinion Dynamics of Skeptical Agents by A. Tsang and K. Larson Paper Read-Through M2 Yu Matsuzawa
  2. 2. 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
  3. 3. Shared Interest • Opinion Dynamics – Gradated (continuous) opinions in this paper • Cf. Discrete opinions • Cognitive Bias: Motivated cognition – Leads subjects to skewed/irrational conclusion Opinion Dynamics of Skeptical Agents 3
  4. 4. 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
  5. 5. 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 of Skeptical Agents 5
  6. 6. Opinion Dynamics Model • Agents are embedded in undirected graphs • Each agent 𝑖 has an opinion 𝑥𝑖 ∈ 0,1 • Influenced by neighbors (direct neighbor) • For each neighbor 𝑗, an agent 𝑖 maintains Trust value 𝑤𝑖,𝑗 – Represents weight of influence to 𝑖 from 𝑗 Opinion Dynamics of Skeptical Agents 6
  7. 7. Opinion Dynamics Model • Def. Trust function 𝑇: – 𝑇 𝑥, 𝑥′ = exp − 𝑥−𝑥′ 2 ℎ (Gaussian kernel) – Used in Trusts 𝑤𝑖,𝑗 updating – Bandwidth parameter ℎ represents empathy • Higher ℎ means the population is more willing to be persuaded by different opinion Opinion Dynamics of Skeptical Agents 7
  8. 8. Opinion Dynamics Model • Opinion update function: – 𝑥𝑖 ← 𝑤 𝑖,𝑖 𝑥 𝑖+∑𝑤 𝑖,𝑗 𝑥 𝑗 𝑤 𝑖,𝑖+∑𝑤 𝑖,𝑗 (Weighted average) – 𝑤𝑖,𝑖 represents inertia of own opinion • Trust update function: – 𝑤𝑖,𝑗 ← 𝑤 𝑖,𝑗+𝑟𝑇(𝑥 𝑖,𝑥 𝑗) 1+𝑟 – 𝑟 represent learning rate • Higher the 𝑟 is, faster the trust/distrust appear Opinion Dynamics of Skeptical Agents 8
  9. 9. Opinion Dynamics Model • Opinions updated, then Trusts updated in each iteration steps • Majority of agents are initialized randomly • The remainder represent extremists – Initialized to 𝑥𝑖 = 0 𝑜𝑟 1 – Extremists’ opinions and trusts are NOT updated Opinion Dynamics of Skeptical Agents 9
  10. 10. Graph Models • Classic BA model • Homophily model based on ER random graph • BA model – Explanation snipped – Parameter 𝑚 represents the number of edges every new vertices have Opinion Dynamics of Skeptical Agents 10
  11. 11. Graph models • Homophily model based on ER random graph – In Erdos-Renyi random graph, every possible edge has probability 𝑝 to be activated – In this model, activation probability of possible edge between 𝑖 and 𝑗 is: • 1 − 𝑑 𝑝, where 𝑑 = 𝑥𝑖 − 𝑥𝑗 – If opinions of 𝑖 aligned with 𝑗’s, highly probable they are connected – Similar opinion, likely to be connected -> Homophily Opinion Dynamics of Skeptical Agents 11
  12. 12. Trust initialization 1. Uniform trust model – 𝑤𝑖,𝑗 = 1, for every existing 𝑖 and 𝑗 – 𝑤𝑖,𝑖 = 𝑑𝑖, where 𝑑𝑖 represents 𝑖’s degree 2. Degree based trust model – 𝑤𝑖,𝑗 = 𝑑𝑗/𝑑𝑖 , thus 𝑤𝑖,𝑖 = 1 3. Kernel based trust model – 𝑤𝑖,𝑗 = 𝑇(𝑥𝑖, 𝑥𝑗), 𝑤𝑖,𝑖 = 1 Opinion Dynamics of Skeptical Agents 12
  13. 13. 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 Opinion Dynamics of Skeptical Agents 13
  14. 14. Experimental designs • 200 agents • In the first set of experiments: – 10% of agents are extremists – Fixed to 𝑥𝑖 = 1 (1-extremists) -> 1-pole model • In the second set: – 10% are 0-extremists, 10% are 1-extremists -> 2-pole model Opinion Dynamics of Skeptical Agents 14
  15. 15. Experimental designs • 𝑟 = 1.5 – Changing 𝑟 did not affect results qualitatively • Termination condition: – No opinions changed by more than 𝜖 = 0.001 – Iterations reached maximum number 𝑡max = 500 • Rarely reached in practice • Results are averaged over 25 replicated trials Opinion Dynamics of Skeptical Agents 15
  16. 16. 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 Opinion Dynamics of Skeptical Agents 16
  17. 17. 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 Opinion Dynamics of Skeptical Agents 17
  18. 18. Effect of Empathy • Mean Opinions at Convergence (uniform trust) – Effect of empathy ℎ and BA parameter 𝑚 – Increasing ℎ has expected effect to polarization – Increasing 𝑚 has no qualitative effect Opinion Dynamics of Skeptical Agents 18
  19. 19. 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 Opinion Dynamics of Skeptical Agents 19
  20. 20. 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 Opinion Dynamics of Skeptical Agents 20
  21. 21. 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 Opinion Dynamics of Skeptical Agents 21
  22. 22. 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 𝐵𝑒𝑡𝑎 0.5,0.5 initialization – http://www2.ipcku.kansai-u.ac.jp/~aki/pdf/beta1.htm Opinion Dynamics of Skeptical Agents 22
  23. 23. Divided initialization • Evolution of opinions from 𝐵𝑒𝑡𝑎(0.5,0.5) – Surprisingly, the result unchanged – Even agents initialized to the opposite pole drawn to the converged pole Opinion Dynamics of Skeptical Agents 23
  24. 24. 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 Opinion Dynamics of Skeptical Agents 24
  25. 25. Kernel trust and Homophily model • Evolution of opinions from 𝐵𝑒𝑡𝑎(0.5,0.5) – Ends in Type IV convergence (fragmentation) Opinion Dynamics of Skeptical Agents 25
  26. 26. Kernel trust and Homophily model • Mean polarization at convergence – Under ℎ > 0.3, stratification occurs and polarization decreases – Higher empathy actually contributes to stratify Opinion Dynamics of Skeptical Agents 26
  27. 27. 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 Opinion Dynamics of Skeptical Agents 27
  28. 28. Conclusion • Introduction of robust Opinion Dynamics model • Combination of skepticism (Kernel trust) and Homophily graph are the condition of opinion stratification Opinion Dynamics of Skeptical Agents 28
  29. 29. 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 Opinion Dynamics of Skeptical Agents 29
  30. 30. 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 Opinion Dynamics of Skeptical Agents 30
  31. 31. 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 Opinion Dynamics of Skeptical Agents 31
  32. 32. 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? Opinion Dynamics of Skeptical Agents 32

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