opinion dynamics -...
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Opinion DynamicsWeb Science (VU) (706.716)
Elisabeth Lex
ISDS, TU Graz
June 4, 2018
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Introduction
Repetition
Agent-based ModelsComplex systemsExample models
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Introduction
Opinion dynamics
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Introduction
Today
We will learn how to mathematically assess how opinions evolve in asocial networkMicroscopic interactions among individuals defined by set of rules (inline with social theories)Microscopic interactions help us understand macroscopic behavior(e.g. reaching consensus)Models for opinion dynamics: Voter Model, Sznajd model, BoundedConfidence ModelsModels for cultural dynamics: Axelrod modelModels for language dynamics: Naming GameCase study: applying naming game to understand consensus buildingin online collaboration networks
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Introduction
Opinion dynamics
Human behavior driven by opinionsOpinions play crucial role in many global challenges: financial crisis,migration, climate changeFormation of opinions is social process of collective intelligenceProcess can lead to consensus, fragmentation, polarization
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Introduction
Agent-based models and opinion dynamics
In practice, opinion dynamics often studied with agent-based modelsAgents: e.g., individuals, groups, institutions, that can featureattributes (e.g. social status)Social network: interactions between agents in which opinions areexchangedUpdate rules: agents’ behavior can lead to change in their opinionstate
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Introduction
Opinion dynamics
A typical research question would be:
How does a system evolve from an initially disordered state with multiplecompeting opinions to an ordered state (consensus, fragmentation,
polarization) and what impacts this process?
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Introduction
Opinion dynamics
We are looking for a mathematical approach to model and understandopinion dynamicsThe field of Physics provides mechanisms to quantitatively describesocial and economic processesStatistical mechanics: study phenomena where relationship betweenmicroscopic properties and macroscopic behavior plays a roleA major topic of interest in statistical mechanics (and in physics ingeneral) is the understanding of phase transitions (e.g. freezing ofwater to form ice), which requires the study of interacting models.Do you remember a model from last lecture that can be used to studyopinion dynamics?
Ising model
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Introduction
Opinion dynamics
We are looking for a mathematical approach to model and understandopinion dynamicsThe field of Physics provides mechanisms to quantitatively describesocial and economic processesStatistical mechanics: study phenomena where relationship betweenmicroscopic properties and macroscopic behavior plays a roleA major topic of interest in statistical mechanics (and in physics ingeneral) is the understanding of phase transitions (e.g. freezing ofwater to form ice), which requires the study of interacting models.Do you remember a model from last lecture that can be used to studyopinion dynamics?Ising model
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Introduction
Recap: Ising model
Models consists of spin variables 𝑠𝑖 that can take the values up (+1)or down (−1)Each spin interacts with its nearest neigbors in case of a 2 Drepresentation with its 4 neighbors) as well as with an externalmagnetic field ℎThe spins want to align with the direction of ℎ - either ferromagneticor paramagneticIf temperature is low, all spins align themselves - spontaneousmagnetizationIf temperature is increased, spontaneous magnetization is destroyed,thermal fluctuationCritical temperature 𝑇𝑐 below which spontaneous magnetization,above that, no magnetizationHow do we call that?
Phase transition
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Introduction
Recap: Ising model
Models consists of spin variables 𝑠𝑖 that can take the values up (+1)or down (−1)Each spin interacts with its nearest neigbors in case of a 2 Drepresentation with its 4 neighbors) as well as with an externalmagnetic field ℎThe spins want to align with the direction of ℎ - either ferromagneticor paramagneticIf temperature is low, all spins align themselves - spontaneousmagnetizationIf temperature is increased, spontaneous magnetization is destroyed,thermal fluctuationCritical temperature 𝑇𝑐 below which spontaneous magnetization,above that, no magnetizationHow do we call that?Phase transition
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Introduction
Ising model and opinion dynamics
Spins: binary opinionsAn individual’s opinion represented as individual spin stateConsensus: modeled as ferromagnetic ordering in the Ising model
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Introduction
Which problems do you see with that approach?
Driving forces of social dynamics are different from forces drivingdynamics of interacting particles in physical systemsCan you think of factors that govern social dynamics?Social influence, homophily, reciprocity, ...
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Introduction
Which problems do you see with that approach?
Driving forces of social dynamics are different from forces drivingdynamics of interacting particles in physical systemsCan you think of factors that govern social dynamics?
Social influence, homophily, reciprocity, ...
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Introduction
Which problems do you see with that approach?
Driving forces of social dynamics are different from forces drivingdynamics of interacting particles in physical systemsCan you think of factors that govern social dynamics?Social influence, homophily, reciprocity, ...
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Opinion dynamics models
Opinion dynamics - preliminaries
Our goal: model and understand opinion dynamics in social networksWe assume that each node in the network has an opinion stateOpinion state can be discrete or continuousWe study the system’s evolution starting from an arbitrary opiniondistributionA number of models exist to study opinion dynamicsMany show the existence of a tipping point, i.e., a critical value of amodel variableSystem behaves very differently above and below the tipping pointDo you remember a dynamic model we discussed in one of ourlectures that has a tipping point?
Threshold models
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Opinion dynamics models
Opinion dynamics - preliminaries
Our goal: model and understand opinion dynamics in social networksWe assume that each node in the network has an opinion stateOpinion state can be discrete or continuousWe study the system’s evolution starting from an arbitrary opiniondistributionA number of models exist to study opinion dynamicsMany show the existence of a tipping point, i.e., a critical value of amodel variableSystem behaves very differently above and below the tipping pointDo you remember a dynamic model we discussed in one of ourlectures that has a tipping point?Threshold models
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Opinion dynamics models
Voter Model: “Tell me what to think” (Sood & Redner,2005)
Each node in the system can take one of the two typical states𝑠 = +1, −1 (binary opinions)At each time step, pick a node 𝑖 at randomThat node picks a random neighbor 𝑗 and copies the opinion of thisneighbor, i.e. 𝑠𝑖 = 𝑠𝑗In other words, nodes imitate their neighborsIn finite systems, at some point, consensus is always reached for thismodelAny ideas wrt runtime?
Time to reach consensus scales linearly with system size
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Opinion dynamics models
Voter Model: “Tell me what to think” (Sood & Redner,2005)
Each node in the system can take one of the two typical states𝑠 = +1, −1 (binary opinions)At each time step, pick a node 𝑖 at randomThat node picks a random neighbor 𝑗 and copies the opinion of thisneighbor, i.e. 𝑠𝑖 = 𝑠𝑗In other words, nodes imitate their neighborsIn finite systems, at some point, consensus is always reached for thismodelAny ideas wrt runtime?Time to reach consensus scales linearly with system size
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Opinion dynamics models
Voter Model
Simulation: https://math.berkeley.edu/~bgillesp/apps/voter
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Opinion dynamics models
Voter Model and impact of network topologies
Regular networks: the order is irrelevant in which a node and itsneighbors is selectedWhat happens in networks with heterogeneous degree distribution?
Who wins - high or low degree nodes?High degree nodes win - why?Typically, only few high degree nodes, picked rarely - change rarelyLow degree nodes picked often, adopt opinions often
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Opinion dynamics models
Voter Model and impact of network topologies
Regular networks: the order is irrelevant in which a node and itsneighbors is selectedWhat happens in networks with heterogeneous degree distribution?Who wins - high or low degree nodes?
High degree nodes win - why?Typically, only few high degree nodes, picked rarely - change rarelyLow degree nodes picked often, adopt opinions often
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Opinion dynamics models
Voter Model and impact of network topologies
Regular networks: the order is irrelevant in which a node and itsneighbors is selectedWhat happens in networks with heterogeneous degree distribution?Who wins - high or low degree nodes?High degree nodes win - why?
Typically, only few high degree nodes, picked rarely - change rarelyLow degree nodes picked often, adopt opinions often
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Opinion dynamics models
Voter Model and impact of network topologies
Regular networks: the order is irrelevant in which a node and itsneighbors is selectedWhat happens in networks with heterogeneous degree distribution?Who wins - high or low degree nodes?High degree nodes win - why?Typically, only few high degree nodes, picked rarely - change rarelyLow degree nodes picked often, adopt opinions often
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Opinion dynamics models
Variants of the Voter Model
Presence of “zealots”: individuals that do not change its opinion(“committed agents”)Constraint voter model: agents can be in three states (leftists,rightists, centrists) but interactions can only involve centrists.Extremists do not talk to each otherMajority rule model
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Opinion dynamics models
Majority rule model: Social Imitation (Galam, 2002)
In population of 𝑁 agents with binary opinions, fraction of 𝑝+ agentshas opinion +1, 𝑝− agents have opinions −1Suppose all agents can communicate (complete graph)At each iteration, group of 𝑟 agents selected as random (“discussiongroup”)Group size 𝑟 selected at each step from given distributionOdd 𝑟 - majority is in favor of either opinion, 𝑟 even: possibility of atie (𝑟/2 agents have either opinion)If tie: introduce bias so that opinion prevails in the group (e.g. +1)Inspired by social inertia: people are reluctant to accept a reform if noclear majority is in its favor (Friedman & Friedman, 1984)
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Opinion dynamics models
Majority rule model (Galam, 2002)
Assume an initial fraction of agents 𝑝+10 who have opinion +1
If 𝑝+10 > 𝑝𝑐(𝑟) where 𝑝𝑐(𝑟) is a threshold, all agents will have opinion
+1 and opinion −1 otherwiseTime to reach consensus: log N (nr of updates per agent)Odd group sizes: 𝑝𝑐(𝑟) = 1/2 due to symmetry of both opinionsFor groups with 𝑟 even: 𝑝𝑐 < 1/2, i.e., the favored opinion willeventually be the dominant one, even if it is initially shared by aminority of agents.
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Opinion dynamics models
Sznajd model: “United we stand, divided we fall”(Stauffer, 2003)
Impact a social group has on an individual increases with group size -remember the herding examples in this course!Convincing a person is easier for > 2 people than a single individual -basic principle behind Sznajd modelSznajd model relates to social validation phenomenon, extends theIsing model
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Opinion dynamics models
Sznajd model (Stauffer, 2003)
Agents occupy the sites of a linear chainBinary opinions (on (+1) and off (-1) like Ising spin variables)A pair of neighboring agents 𝑖 and 𝑖 + 1 determine the opinions oftheir two nearest neighbors 𝑖 − 1 and 𝑖 + 2 according to these rules:
if 𝑠𝑖 = 𝑠𝑡+1 then 𝑠𝑖−1 = 𝑠𝑖 = 𝑠𝑖+1 = 𝑠𝑖+2if 𝑠𝑖 ≠ 𝑠𝑡+1 then 𝑠𝑖−1 = 𝑠𝑖+1 and 𝑠𝑖+2 = 𝑠𝑖
Thus: if agents of the pair have the same opinion, they impose theiropinion on their neighbors. Social validation: If two people share thesame opinion, their neighbors will start to agree with them andchange their opinion.If they disagree, each agent imposes its opinion on the other agent’sneighbor. Discord destroys: If a block of adjacent persons disagree,their neighbors start to argue with them. Intuitively: If the given pairof people disagrees, both adopt the opinion of their other neighbor.
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Opinion dynamics models
Sznajd model (Stauffer, 2003)
Agents occupy the sites of a linear chainBinary opinions (on (+1) and off (-1) like Ising spin variables)A pair of neighboring agents 𝑖 and 𝑖 + 1 determine the opinions oftheir two nearest neighbors 𝑖 − 1 and 𝑖 + 2 according to these rules:
if 𝑠𝑖 = 𝑠𝑡+1 then 𝑠𝑖−1 = 𝑠𝑖 = 𝑠𝑖+1 = 𝑠𝑖+2if 𝑠𝑖 ≠ 𝑠𝑡+1 then 𝑠𝑖−1 = 𝑠𝑖+1 and 𝑠𝑖+2 = 𝑠𝑖
Thus: if agents of the pair have the same opinion, they impose theiropinion on their neighbors. Social validation: If two people share thesame opinion, their neighbors will start to agree with them andchange their opinion.
If they disagree, each agent imposes its opinion on the other agent’sneighbor. Discord destroys: If a block of adjacent persons disagree,their neighbors start to argue with them. Intuitively: If the given pairof people disagrees, both adopt the opinion of their other neighbor.
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Opinion dynamics models
Sznajd model (Stauffer, 2003)
Agents occupy the sites of a linear chainBinary opinions (on (+1) and off (-1) like Ising spin variables)A pair of neighboring agents 𝑖 and 𝑖 + 1 determine the opinions oftheir two nearest neighbors 𝑖 − 1 and 𝑖 + 2 according to these rules:
if 𝑠𝑖 = 𝑠𝑡+1 then 𝑠𝑖−1 = 𝑠𝑖 = 𝑠𝑖+1 = 𝑠𝑖+2if 𝑠𝑖 ≠ 𝑠𝑡+1 then 𝑠𝑖−1 = 𝑠𝑖+1 and 𝑠𝑖+2 = 𝑠𝑖
Thus: if agents of the pair have the same opinion, they impose theiropinion on their neighbors. Social validation: If two people share thesame opinion, their neighbors will start to agree with them andchange their opinion.If they disagree, each agent imposes its opinion on the other agent’sneighbor. Discord destroys: If a block of adjacent persons disagree,their neighbors start to argue with them. Intuitively: If the given pairof people disagrees, both adopt the opinion of their other neighbor.
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Opinion dynamics models
Sznajd model (Stauffer, 2003)
At start: random initial configuration, both opinions are equallydistributionOpinions are updated in random sequential orderIn 1D, we reach two steady states: either consensus (with all spins upor down, “ferromagnetic state”) or stalemateStalemate? Because: if 𝑠𝑖 6 𝑠𝑡+1 then 𝑠𝑖−1 = 𝑠𝑖+1 and 𝑠𝑖+2 = 𝑠𝑖Alternating on and off spin values unrealistic: would mean thatcomplete population uniformly change their opinions at each timestep. Unsufficient to represent behavior of a community.
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Opinion dynamics models
Sznajd model: alternative dynamics rule
Social validation unchanged but second rule modified:if 𝑠𝑖 = 𝑠𝑡+1 then 𝑠𝑖−1 = 𝑠𝑖 = 𝑠𝑖+1 = 𝑠𝑖+2if 𝑠𝑖 = −𝑠𝑡+1 then 𝑠𝑖−1 = 𝑠 and 𝑠𝑖+2 = 𝑠𝑖+1
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Opinion dynamics models
Sznajd model (Stauffer, 2003)
Model very useful to describe how opinions spread in a society as itmodels how information flows outwardApplied in politics to describe voting behavior in elections
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Opinion dynamics models
Discrete vs continuous opinions
So far, we treated opinions as discrete variableReasonable in several scenarios (pro and contra opinions)However: opinion of individuals can vary smoothly from one extremto the otherEx: political orientation is typically not restricted to extreme choicesbut to all options in betweenThis requires a different modeling framework
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Opinion dynamics models
Bounded Confidence Models
Initial state typically a population of N agents with randomly assignedopinionsOpinions can be represented by real numbers within some intervalAll agents start with different opinionsOpinion clusters may emerge in final stationary stage: consensus (oneopinion), polarization (two), fragmentation (more)In principle: all agents can interact with each other regardless of thenature of their opinionIn real life: real discussions often only if opinions of the involvedagents are sufficiently close to each otherThis is called bounded confidence
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Opinion dynamics models
Bounded Confidence Models
Basic intuition: agents adjust their opinion gradually towards opinions ofothers when distance in opinion is within their bound of confidence.
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Opinion dynamics models
Deffuant model (Deffuant et al., 2000)
Describes pattern for social interactionTwo neighboring individuals randomly meet and share their opinionson a certain topic, if the difference between their opinions is notbeyond a given threshold
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Opinion dynamics models
Deffuant model: How does it work
We consider a population of N agentsEach agent i initially has an opinion 𝑥𝑖 - opinions are chosenrandomly from the interval [0, 1]At each time step, a randomly selected agent 𝑖 interacts with one ofits neighbors 𝑗 (also chosen randomly)Both have opinions 𝑥𝑖(𝑡) and 𝑥𝑗(𝑡)If difference of opinions 𝑥𝑖(𝑡) and 𝑥𝑗(𝑡) exceeds a threshold 𝜖 - eachagent keep their original opinionIf |𝑥𝑖(𝑡) − 𝑥𝑗(𝑡)| < 𝜖, then:
𝑥𝑖(𝑡 + 1) = 𝑥𝑖(𝑡) + 𝜇[𝑥𝑗(𝑡) − 𝑥𝑖(𝑡)]𝑥𝑗(𝑡 + 1) = 𝑥𝑗(𝑡) + 𝜇[𝑥𝑖(𝑡) − 𝑥𝑗(𝑡)]where 𝜇 is the convergence parameter, lies in interval [0, 1/2]
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Opinion dynamics models
Deffuant model (Deffuant et al., 2000)
Compromise strategy: after a constructive debate, the positions ofagents get closer to each other by relative amount 𝜇If 𝜇 = 1/2, the two agents converge to the average of their opinionsbefore discussionFor any value of 𝜖�and 𝜇, the average opinion of the agents’ pair isthe same before and after the interactionIn other words: the global average opinion (1/2) of the population isan invariant of Deffuant dynamics
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Opinion dynamics models
Bounded Confidence Models
Netlogo model: Download fromhttp://ccl.northwestern.edu/netlogo/models/community/bcImplements another bounded confidence model: Hegselman and Krause(2002)
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Cultural dynamics
Culture dynamics
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Cultural dynamics
Culture dynamics
Culture: “the set of individual attributes that are subject to socialinfluence” ... “something people learn from each other” (Axelrod 1997)
Culture dynamics similar to opinion dynamicsIn opinion dynamics, opinions are considered as scalar variablesThe culture of an individual is considered as being more facetedTherefore: modeled as vector of variables, whose dynamics arecoupledTypical questions: e.g. what are the microscopic mechanisms thatdrive formation of cultural domains?Or, what is the role of diversity - will it persist or will all differenceseventually disappear in the long run?
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Cultural dynamics
Culture dynamics
Culture: “the set of individual attributes that are subject to socialinfluence” ... “something people learn from each other” (Axelrod 1997)
Culture dynamics similar to opinion dynamicsIn opinion dynamics, opinions are considered as scalar variablesThe culture of an individual is considered as being more facetedTherefore: modeled as vector of variables, whose dynamics arecoupledTypical questions: e.g. what are the microscopic mechanisms thatdrive formation of cultural domains?Or, what is the role of diversity - will it persist or will all differenceseventually disappear in the long run?
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Cultural dynamics
Axelrod model (Axelrod, 1997)
Basic intuition: people become similar through interactionIncludes two mechanisms that are believed to be fundamental whenmodeling and understanding dynamics of cultural assimilation /diversity: social influence & homophilySocial influence: tendency of individuals to become more similar whenthey interact - increases number of cultural attributes they shareHomophily: similar people tend to interact more frequently - peoplemore likely to interact with others who share many of their culturalattributes
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Cultural dynamics
Axelrod model
Example: people are more likely to talk to someone who speaks asimilar language than to someone, who speaks a dissimilar language.Through their communication their future patterns of speech tend tobecome even more similar (Axelrod, 1997)
Social scientists expected that those two factors will eventually leadto global convergence to a single cultureDo you think that this is realistic?In some cases, diversity persists regardless of self-reinforcingmechanism (more interaction means more similarity).The model proposed by Axelrod lets us study and predict that.
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Cultural dynamics
Axelrod model
Example: people are more likely to talk to someone who speaks asimilar language than to someone, who speaks a dissimilar language.Through their communication their future patterns of speech tend tobecome even more similar (Axelrod, 1997)Social scientists expected that those two factors will eventually leadto global convergence to a single cultureDo you think that this is realistic?
In some cases, diversity persists regardless of self-reinforcingmechanism (more interaction means more similarity).The model proposed by Axelrod lets us study and predict that.
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Cultural dynamics
Axelrod model
Example: people are more likely to talk to someone who speaks asimilar language than to someone, who speaks a dissimilar language.Through their communication their future patterns of speech tend tobecome even more similar (Axelrod, 1997)Social scientists expected that those two factors will eventually leadto global convergence to a single cultureDo you think that this is realistic?In some cases, diversity persists regardless of self-reinforcingmechanism (more interaction means more similarity).The model proposed by Axelrod lets us study and predict that.
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Cultural dynamics
Axelrod model - How does it work?
Individuals are located in a 𝐿𝑥𝐿 lattice of cells (could also be nodesin a network)Each cell is inhabitated by an individual who is endowed with acertain cultureThis culture is described by a list of features 𝑓 (e.g. language,religion, style of music, ...)Features are integer values 𝜎1, ..., 𝜎𝑓) that can assume 𝑞 traits𝜎𝑓 = 0, 1, ...𝑞 − 1Traits 𝑞 correspond to the number of possible traits allowed perfeatureCulture of individual 𝑖 can be represented by vector 𝑥𝑖 of 𝑓 variablesand each variable takes an integer value in the range [0, 𝑞 − 1]Intuition: model the different beliefs, attitudes and behaviors ofindividuals
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Cultural dynamics
Axelrod model - dynamics
At each time step, an individual 𝑘 is selected at random (active agent)One of 𝑘’s neighbors 𝑗 is selected at random (passive agent)𝑘 and 𝑗 interact with a probability that is equal to their culturalsimilarity 𝑛𝑘,𝑗/𝑓 where 𝑛𝑘,𝑗 corresponds to the number of culturalfeatures for which both have the same traitInteraction: active agent 𝑘 randomly selects one of the 𝑓 − 𝑛𝑘𝑟features on which both agents differ and copies the trait of thepassive agent 𝑗Thus, agent 𝑘 approaches the cultural interests of 𝑗Continues until no more cultural changes can occurWhat is the outcome?
Each pair of neigbors has either identical cultures or completelydifferent culturesParameters 𝑓 and 𝑞 influence probability with with system evolves toonly one cultural region or to several multicultural regions
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Cultural dynamics
Axelrod model - dynamics
At each time step, an individual 𝑘 is selected at random (active agent)One of 𝑘’s neighbors 𝑗 is selected at random (passive agent)𝑘 and 𝑗 interact with a probability that is equal to their culturalsimilarity 𝑛𝑘,𝑗/𝑓 where 𝑛𝑘,𝑗 corresponds to the number of culturalfeatures for which both have the same traitInteraction: active agent 𝑘 randomly selects one of the 𝑓 − 𝑛𝑘𝑟features on which both agents differ and copies the trait of thepassive agent 𝑗Thus, agent 𝑘 approaches the cultural interests of 𝑗Continues until no more cultural changes can occurWhat is the outcome?Each pair of neigbors has either identical cultures or completelydifferent culturesParameters 𝑓 and 𝑞 influence probability with with system evolves toonly one cultural region or to several multicultural regions
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Cultural dynamics
What does that mean?
Dynamics of Axelrod’s model tend to increase similarity of interactingindividualsHowever: interaction is more likely for neighbors who share manytraits (ergo, who have higher homophily)No interaction when no trait is the sameThis gives two stable configurations for pairs of neighbors: either theyare exactly the same and thus belong to the same cultural regionOr, they are completely different
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Cultural dynamics
Axelrod Model
Netlogo Simulation: download Axelrod model fromhttp://ccl.northwestern.edu/netlogo/models/community/Axelrod%20-%20Network
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Language dynamics
Language dynamics
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Language dynamics
Language dynamics
“Open minded individuals”Focus on processes related to emergence, change, evolution,interaction and extinction of languagesSociobiological approach: evolution is the main responsible both forthe origin and the emergence of natural language in humans. Modelsbased on natural selectionSemiotic dynamics approach: language as evolving system. Newwords and grammatical constructions may be invented, new meaningsmay arise, the relation between language and meaning may shift,..
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Language dynamics
Naming Game model
Originally main focus on the formation of vocabularies, i.e., a set ofmappings between words and meanings (e.g. for physical objects)Each agent develops its own vocabulary in a random, private fashinHowever, agents must align their vocabulariesAchieved by successive conversation between a certain number ofagents, who exchange meanings - cooperation through communicationResult: globally shared vocabulary (ideally!) as consequence of localadjustments of individual word-meaning associations
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Language dynamics
Minimal Naming Game (Dall’Asta et al (2006)
We assume a population of N agentGoal: agents aim to bootstrap a common name for a given object ona fully connected networkEach agent has an inventory of word-object associations it knowsInitially, inventories of all agents are emptyAt each time step, 2 agents are randomly selected and one is assignedthe role of speaker and the other is listenerRules of interaction: speaker transmits word to listener. If listenerdoes not have the word in its inventory, it is added. If word isinventory of both agents, they agree on the word and delete all otherwords from the inventory.Thus: Naming Game describes agreement dynamics in a system
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Language dynamics
Naming Game variant: binary agreement model
Number of possible words restricted to 2 (A or B)Goal: study two competing opinionsEach noide can be either in one of the two competing states A and Bor in an intermediate state ABDifference to voter model: individuals have some inertia to changetheir state (some internal belief)Impact on dynamics: time to reach consensus scales logarithmicallywith system size
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Language dynamics
Naming Game to study opinion formation (Baronchelli etal., 2007)
Additional parameter 𝛽 to mimick an irresolute attitude of agents inmaking decisionsProbability to model the negotiation process that, in a successfulinteraction, both the speaker and the hearer update their memorieserasing all opinions except the one involved in the interaction
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Language dynamics
Naming Game: Impact of social status, network structure,user similarity (Hasani-Mavriqi et al., 2018)
In our own work, we found that social status can speed up consensusbuilding in the Naming GameWe found that in assortative networks, consensus is always reachedWe found that user similarity and social status are opposing forceswith respect to consensus
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Language dynamics
Naming Game: Impact of social status, network structure,user similarity (Hasani-Mavriqi et al., 2018)
Study online collaboration systems and consensus building in thosesystems: StackExchange, Reddit, Wikipedia,..RQ: Which factors govern consensus building in online collaborationsystems?Factors social status, network structure, user similarityApproach: Adapting Naming Game to account for those factors
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Language dynamics
Naming Game: Impact of social status, network structure,user similarity (Hasani-Mavriqi et al., 2018)
Study online collaboration systems and consensus building in thosesystems: StackExchange, Reddit, Wikipedia,..RQ: Which factors govern consensus building in online collaborationsystems?Factors social status, network structure, user similarityApproach: Adapting Naming Game to account for those factors
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Language dynamics
Adapting Naming Game
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Language dynamics
Probabilistic Meeting Rule: Social Status
Idea: Social status how interactions turn into meetingsMeeting rule to decide whether meeting takes place
𝑝𝑠𝑙 = 𝑚𝑖𝑛(1, 𝑒𝛽(𝑠𝑠−𝑠𝑙) (1)
where 𝑠𝑠 is the social status of the speaker and 𝑠𝑙 of the listener and𝛽 is a stratification factor
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Language dynamics
The emergence of social classes
Egalitarian society: any agent can exchange opinions regardless ofstatus (𝛽 = 0)Ranked society: we can model any situation inbetween the extremecases (e.g. opinions likely flow from high status agents to low statusagents) (𝛽 >>)Stratified society: opinion flow in only one direction from higherstatus agents to lower status agents (𝛽 >)
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Language dynamics
StackExchange
Reputation scores as proxy for social statusSocial status correlates with node degree
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Language dynamics
Naming Game
Initialize agents‘ inventories with opinions at randomCreate meeting sequences: pairs of agents selected at random, definenr of interactions (iterations)Calculate different values for 𝛽Report averaged simulation results per beta
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Language dynamics
Naming Game: Impact of Social Status
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Language dynamics
Findings
Weakly stratified societies – fastest consensusCompletely stratified societies – no consensusSpecial setting for each network – optimal social status influence
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Language dynamics
The role of network structure
Hubs are key to reaching consensusExternal interventions facilitate consensus building in dissortativenetworks (where dissimilar agents are more likely connected)Any idea why?
More details can be found here:https://computationalsocialnetworks.springeropen.com/articles/10.1186/s40649-018-0050-1
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Language dynamics
Summary
Opinion dynamicsCultural dynamicsLanguage dynamics
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Language dynamics
Take away
We can model complex social processes about opinion formation andconsensus building using mathematical approaches and models (mostlyfrom physics). Simplified models help us understand complex humanbehavior in online systems.
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Language dynamics
References
Baronchelli et al. (2007) The role of topology on the dynamics of theNaming Game https://link.springer.com/article/10.1140%2Fepjst%2Fe2007-00092-0Castellano et al. (2009) Statistical physics of social dynamics:https://arxiv.org/pdf/0710.3256.pdfDall’Asta et al (2006) Nonequilibrium dynamics of language games oncomplex networks http://www.cpt.univ-mrs.fr/~barrat/pre74.pdfDeffuant et al. (2002) Mixing beliefs among interacting agents https://www.worldscientific.com/doi/abs/10.1142/S0219525900000078
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Language dynamics
References
Hasani-Mavriqi et al. (2018) Consensus dynamics in online collaborationsystems https://computationalsocialnetworks.springeropen.com/articles/10.1186/s40649-018-0050-1Hegselmann and Krause (2002) Opinion dynamics and boundedconfidence: models, analysis and simulationhttp://jasss.soc.surrey.ac.uk/5/3/2.htmlXia et al. (2013) Opinion Dynamics: A Multidisciplinary Review andPerspective on Future Researchhttps://www.igi-global.com/article/international-journal-knowledge-systems-science/61135
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Language dynamics
Thanks for your attention - Questions?
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