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Volatility of Weak Ties Co-evolution of Selection and Influence in - - PowerPoint PPT Presentation
Volatility of Weak Ties Co-evolution of Selection and Influence in - - PowerPoint PPT Presentation
Volatility of Weak Ties Co-evolution of Selection and Influence in Social Networks Fang-Yi Yu Volatility of Weak Ties Co-evolution of Selection and Influence in Social Networks Jie Gao, Grant Schoenebeck, Fang-Yi Yu Co-evolution of Selection
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VOLATILITY OF WEAK TIES
Co-evolution of Selection and Influence in Social Networks
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An Experiment by Granovetter [1970]
- Weak Ties and Changing Jobs
Tie strength Frequency Found jobs friend 1/week 16.7% acquaintance 1/year 55.6% stranger less 27.8%
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Volatility of Weak Ties
Changing Jobs
- bring fresh information to a social
group Bubble Filters
- unfriending disproportionately affect
weak ties as compared to strong ties.
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Outline
- Model
– Opinion formation: Influence and Selection – Network: Strong and Weak Ties
- Simulation Results
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Opinion Formation
- Influence
- Selection
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Influence
- Influence
– agents changing their opinions to match their neighbors
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Influence
- Influence
– agents changing their opinions to match their neighbors
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Influence
- Influence
– agents changing their opinions to match their neighbors
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Influence 𝒈𝒋𝒐𝒈
- Influence
– agents changing their opinions to match their neighbors – 𝜓𝑢+1 𝑤 = 1 w.p. 𝑔
𝑗𝑜𝑔 𝑆𝑢(𝑤)
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Influence 𝒈𝒋𝒐𝒈
0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Voter Majority 3-Majority
- Influence
– agents changing their opinions to match their neighbors – 𝜓𝑢+1 𝑤 = 1 w.p. 𝑔
𝑗𝑜𝑔 𝑆𝑢(𝑤)
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Selection
- Influence
– agents changing their opinions to match their neighbors
- Selection
– agents re-wiring to connect to new agents when the existing neighbor has a different opinion
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Selection
- Influence
– agents changing their opinions to match their neighbors
- Selection
– agents re-wiring to connect to new agents when the existing neighbor has a different opinion
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Selection
- Influence
– agents changing their opinions to match their neighbors
- Selection
– agents re-wiring to connect to new agents when the existing neighbor has a different opinion
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Co-evolution of Selection and Influence
- Influence
– agents changing their opinions to match their neighbors – bring new information through weak ties
Network Opinion
Influence Selection
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Co-evolution of Selection and Influence
- Influence
– agents changing their opinions to match their neighbors – bring new information through weak ties
- Selection, 𝑞𝑡𝑓𝑚
– agents re-wiring to connect to new agents when the existing neighbor has a different opinion – unfriend weak ties
Network Opinion
Influence Selection
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Model of Network 𝑯𝟏 = (𝑾, 𝑭𝑻, 𝑭𝑿)
- Strong ties 𝐹𝑇
– grid edge – Not affected by selection
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Model of Network 𝑯𝟏 = (𝑾, 𝑭𝑻, 𝑭𝑿)
- Strong ties 𝐹𝑇
– grid edge – Not affected by selection
- Weak ties 𝐹𝑋
– random edge – affected by selection
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Model of Network 𝑯𝟏 = (𝑾, 𝑭𝑻, 𝑭𝑿)
- Strong ties 𝐹𝑇
– grid edge – Not affected by selection
- Weak ties 𝐹𝑋
– random edge – affected by selection
- Strength of strong ties, 𝑟𝑡𝑢𝑠𝑝𝑜
– Relative frequency of communication through strong ties
𝑆𝑢 𝑤 = 𝑟𝑡𝑢𝑠𝑝𝑜 1 4 + 1 − 𝑟𝑡𝑢𝑠𝑝𝑜 4 6
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Sel-Inf 𝑯𝟏, 𝒈𝒋𝒐𝒈, 𝒒𝒕𝒇𝒎𝒇𝒅𝒖, 𝒓𝒕𝒖𝒔𝒑𝒐𝒉
- Dynamic over binary opinion 𝜓𝑢
– Agent 𝑤 has a random opinion 𝜓𝑢(𝑤)~{0.1} – At round 𝑢 + 1, a random node 𝑤 is picked
- Selection w.p. 𝑞𝑡𝑓𝑚𝑓𝑑𝑢
– Pick an incident weak tie (𝑤, 𝑣) and rewire if 𝜓𝑢(𝑤) ≠ 𝜓𝑢(𝑣)
- Influence w.p. 1 − 𝑞𝑡𝑓𝑚𝑓𝑑𝑢
– 𝑆𝑇
𝑢(𝑤)/𝑆𝑋 𝑢 (𝑤)fraction of opinion 1 in
strong/weak neighborhood of 𝑤 – Update to 1 w.p. 𝑔
𝑗𝑜𝑔 𝑆𝑢(𝑤)
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Sel-Inf 𝑯𝟏, 𝒈𝒋𝒐𝒈, 𝒒𝒕𝒇𝒎𝒇𝒅𝒖, 𝒓𝒕𝒖𝒔𝒑𝒐𝒉
- Dynamic over binary opinion 𝜓𝑢
– Agent 𝑤 has a random opinion 𝜓𝑢(𝑤)~{0.1} – At round 𝑢 + 1, a random node 𝑤 is picked
- Selection w.p. 𝑞𝑡𝑓𝑚𝑓𝑑𝑢
– Pick an incident weak tie (𝑤, 𝑣) and rewire if 𝜓𝑢(𝑤) ≠ 𝜓𝑢(𝑣)
- Influence w.p. 1 − 𝑞𝑡𝑓𝑚𝑓𝑑𝑢
– 𝑆𝑇
𝑢(𝑤)/𝑆𝑋 𝑢 (𝑤)fraction of opinion 1 in
strong/weak neighborhood of 𝑤 – Update to 1 w.p. 𝑔
𝑗𝑜𝑔 𝑆𝑢(𝑤)
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Sel-Inf 𝑯𝟏, 𝒈𝒋𝒐𝒈, 𝒒𝒕𝒇𝒎𝒇𝒅𝒖, 𝒓𝒕𝒖𝒔𝒑𝒐𝒉
- Dynamic over binary opinion 𝜓𝑢
– Agent 𝑤 has a random opinion 𝜓𝑢(𝑤)~{0.1} – At round 𝑢 + 1, a random node 𝑤 is picked
- Selection w.p. 𝑞𝑡𝑓𝑚𝑓𝑑𝑢
– Pick an incident weak tie (𝑤, 𝑣) and rewire if 𝜓𝑢(𝑤) ≠ 𝜓𝑢(𝑣)
- Influence w.p. 1 − 𝑞𝑡𝑓𝑚𝑓𝑑𝑢
– 𝑆𝑇
𝑢(𝑤)/𝑆𝑋 𝑢 (𝑤)fraction of opinion 1 in
strong/weak neighborhood of 𝑤 – Update to 1 w.p. 𝑔
𝑗𝑜𝑔 𝑆𝑢(𝑤)
𝑆𝑢 𝑤 = 𝑟𝑡𝑢𝑠𝑝𝑜 1 4 + 1 − 𝑟𝑡𝑢𝑠𝑝𝑜 4 6
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Sel-Inf 𝑯𝟏, 𝒈𝒋𝒐𝒈, 𝒒𝒕𝒇𝒎𝒇𝒅𝒖, 𝒓𝒕𝒖𝒔𝒑𝒐𝒉
- Dynamic over binary opinion 𝜓𝑢
– Agent 𝑤 has a random opinion 𝜓𝑢(𝑤)~{0.1} – At round 𝑢 + 1, a random node 𝑤 is picked
- Selection w.p. 𝑞𝑡𝑓𝑚𝑓𝑑𝑢
– Pick an incident weak tie (𝑤, 𝑣) and rewire if 𝜓𝑢(𝑤) ≠ 𝜓𝑢(𝑣)
- Influence w.p. 1 − 𝑞𝑡𝑓𝑚𝑓𝑑𝑢
– 𝑆𝑇
𝑢(𝑤)/𝑆𝑋 𝑢 (𝑤)fraction of opinion 1 in
strong/weak neighborhood of 𝑤 – Update to 1 w.p. 𝑔
𝑗𝑜𝑔 𝑆𝑢(𝑤)
Influence through weak ties Influence through strong ties Selection on weak ties None Small 𝑟𝑡𝑢𝑠𝑝𝑜 Strong 𝑟𝑡𝑢𝑠𝑝𝑜 Small 𝑞𝑡𝑓𝑚𝑓𝑑𝑢 Large 𝑞𝑡𝑓𝑚𝑓𝑑𝑢
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Outline
- Model
– Opinion formation: Influence and Selection – Network: Strong and Weak Ties
- Simulation Results
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Consensus Time of Voter Model
Influence through weak ties Influence through strong ties Selection on weak ties
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Consensus Time of Iterative Majority
Influence through weak ties Influence through strong ties Selection on weak ties
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Consensus Time
Voter model 13-majority Majority
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Low selection->Spread
Voter model 13-majority Majority
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High Selection->Bubble Filter
Voter model 13-majority Majority
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Strong Ties
Voter model 13-majority Majority
Stuck Slow Fast
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Fast, Slow, and Stuck
Consensus Time Number of Switches
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Take-home Message
- In influence dynamics, the strength of weak ties is to get new
information and fresh ideas into the comfort zone created by strong ties.
- In selection dynamics, the role of strong ties and weak ties, in