Modeling gossip networks
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Abstract
THE EFFECT OF GOSSIP ON SOCIAL NETWORKS
In this project we study a simple model of the effects of gossip spread on social network structure. We define gossip as information passed between two individuals A and B about a third individual C which affects the strengths of all three relationships: it strengthens A-B and weakens B-C and A-C. We find out that if gossip occurs in simple triads, it destroys them but if gossip propagates through large dense clusters, it strengthens them. This work is novel in two respects. First, there is no theoretical work on how network structure changes when information passing through a network affects edges not in its direct path. And second, while past studies have looked at how network structure affects gossip spread, there is no work done on how gossip spread affects network structure.
The latest pdf paper is available here: File:Gossip.pdf.
Paper Draft
Introduction
Gossip is ubiquitous in human groups and has even been argued to be fundamental to human society (Dunbar 2004). Gossip usually has negative connotations: generally, no one wants to be thought of as a ‘gossip,’ and gossiping has traditionally been viewed as an indirect form of aggressiveness. However, gossip also seems to have a variety of benefits, including helping individuals learn the cultural rules of their group (Baumeister et al 2004). Dunbar (2004) even proposed that gossip is analogous to grooming in primates: it is essentially a tool to create and maintain relationships between individuals, with little importance given to the accuracy or quality of the actual information being passed.
Unlike rumors, which pertain to issues and events of public concern, gossip targets the behavior and life of a private individual. Gossip can essentially be defined as information passed from one individual (originator) to another (gossiper) about an absent third individual (victim) (Lind et al. 2007). Therefore, any analysis of gossip must occur at the level of the triad or higher (Wittek & Weilers 1998).
Closely related to the vast body of contagion literature (Dodds & Watts 2004) studying the spread of cultural fads (Bikhchandani et al. 1992), technological innovations (Bass 1969) or contagious disease (Morris 1993), previous work has explored how social structure influences the flow of gossip and which network types best promote gossip (Lind et al. 2007). Gossiping, however, could damage some relationships and strengthen others (Wittek & Weilers 1998). This suggests a flip side to the problem of the spread of gossip that has remained unaddressed. Hence, in this paper, we investigate how gossip affects the structure of the social network it flows through.
The process of an information flow molding a network has been previously studied in the context of Hebbian learning, where the simultaneous activation of neurons leads to an increase in the strength of their synaptic connection [Roozbeh, can you provide a ref here?]. A similar type of path reinforcement has also been observed in ants (Goss et al. 1989), humans (Helbing et al. 1997), and even slime molds (Nakagaki et al. 2000). Both of the above models, however, concern modification of the network only along the flow's direct path. Our contribution is to reveal how information passed along one edge can affect the strengths of other edges in the network. [Allison: this isn't quite right...in these examples where there is some sort of 'conservation' then information passed along one network edge indirectly affects the others -- e.g. because there are a finite number of ants, by choosing one path more, they are indirectly choosing the other path less. We should include this idea, but I haven't been able to come up with a good way to explain it.]
Methods
We conducted simulations on a simple network model (built in NetLogo) to understand how the spread of gossip influences social network structure. Each simulation was run for 10,000 gossip events. [add a note about convergence] We ran simulations with 48 different parameter combinations (3 network types, 2 network sizes, 2 methods of victim choice, 2 methods of originator choice, 2 methods of changing connection strength) for 10 repetitions each, for a total of 480 simulation runs.
Model
To simulate a single gossip event on a network we first choose a victim of gossip as a random node in the network. We choose one of the victim’s neighbors as the originator of the gossip (FIGURE 1a). In the first wave of a gossip event, the gossip is spread to all the mutual neighbors, now gossipers, of the victim and originator (FIGURE 1b). Each of these new gossipers then spreads the gossip to their mutual friends with the victim, in subsequent waves (FIGURE 1c). This process continues until no new individuals become gossipers.
We assume that spreading gossip results in a stronger relationship between all gossipers, and a weakened relationship between the victim and the gossipers. Allowing link weights to take values between 0 and 1, we used two functions describing this effect:
- normalized: For increasing, w_{n+1} \leftarrow w_n + \alpha (1-w_n) and for decreasing, w_{n+1} \leftarrow \beta w_n in which \alpha < 1 and \beta < 1. In the simulations, we fixed \alpha = 0.4 and \beta = 0.6. This method has hysteresis, i.e. an increase followed by a decrease does not necessarily lead to the initial value of strength.
- quadratic: For increasing, w_{n+1} \leftarrow sqrt{w_n} and for decreasing, w_{n+1} \leftarrow {w_n}^2. Other powers can be used for extensions. In this function, gossip has a weak effect on strong ties and a strong effect on weak ties.
All edges were initially set to have a strength of 0.5. Furthermore, those links whose weight dropped below 0.005 were severed.
Algorithm #1: Basic Model 1. for each gossip event 2: set all individuals as non-gossipers 3: choose victim: pick a random individual, chosen completely randomly 4: choose originator: pick a random neighbor of victim, chosen completely randomly 5: set originator as a gossiper 6: while there are mutual neighbors of the victim and a gossiper that are non-gossipers 7: set all mutual neighbors of the victim and each gossiper as gossipers 8: end while 9: decrease the links between the victim and each gossiper 10: increase the links between all pairs of gossipers 11: end for
To test if any results we saw were due to just strengthening and weakening connections between triads of nodes, we also ran simulations on a null-gossip network, where a single gossip event only occurred within a single triad of individuals. In other words, gossip was only allowed to spread from the originator to one other individual.
Algorithm #2: Null Model 1. for each gossip event 2: set all individuals as non-gossipers 3: choose victim: pick a random individual, chosen completely randomly 4: choose originator: pick a random neighbor of victim, chosen completely randomly 5: set originator as a gossiper 6: choose one random mutual neighbor of the victim and gossiper, and set as gossiper 7: decrease the links between the victim and each gossiper 8: increase the links between the pair of gossipers 9: end for
Networks
We conducted simulations on several network types to see if the effect of gossip varied with network structure. We used random, small-world, and spatially clustered networks. These network types match observed patterns of social organization and provide sufficient variation in average path length and clustering. For the small-world networks, we used the original generative algorithm (Watts & Strogatz 1998) with a rewiring probability of 0.15. The spatially clustered networks were generated by distributing the nodes randomly in space and then letting a randomly selected node establish a link with the closest node.
For comparison, we generated small (N=50) and large (N=200) networks with an average node degree of 6.
Heterogeneity
[Is this the appropriate heading for this section? Maybe something like "Alternative Algorithms" will work better...]
In the base case, the probability of becoming a gossip victim or originator is uniform across nodes. Following theoretical arguments and previous empirical findings, we also explored two additional algorithms for starting the gossip event:
- The probability to become a victim increases with degree centrality. This algorithm models the situation where more popular people are more likely to be subjects of gossip, which is the working mechanism in the hypothesis that gossip serves to equalize the social status of individuals in a network (Boehm 1999).
Algorithm #3: Victim-Choice = Degree-Random 1. for each gossip event 2: set all individuals as non-gossipers 3: choose victim: pick a random individual, chosen based on degree -- individuals with higher degree more likely to be picked 4: choose originator: pick a random neighbor of victim, chosen completely randomly 5: set originator as a gossiper 6: while there are mutual neighbors of the victim and a gossiper that are non-gossipers 7: set all mutual neighbors of the victim and each gossiper as gossipers 8: end while 9: decrease the links between the victim and each gossiper 10: increase the links between all pairs of gossipers 11: end for
- The probability to originate gossip is 1 for the agent with the weakest connection with the victim. Here, we model the expectation that one is unlikely to pass gossip about one's close friends. Indeed, it has been found that gossip tends to weaken already weak relations (Wittek & Wielers 1998).
Algorithm #4: Originator-Choice = Weakest-Link 1. for each gossip event 2: set all individuals as non-gossipers 3: choose victim: pick a random individual, chosen completely randomly 4: choose originator: pick neighbor of victim with the weakest connection to victim 5: set originator as a gossiper 6: while there are mutual neighbors of the victim and a gossiper that are non-gossipers 7: set all mutual neighbors of the victim and each gossiper as gossipers 8: end while 9: decrease the links between the victim and each gossiper 10: increase the links between all pairs of gossipers 11: end for
Statistics
For the analysis of the simulation results, we concentrated on the average node degree and the clustering coefficient of the network after convergence. To measure the network clustering, we first estimate the local clustering of each node (how close the node's neighbors are to being a complete graph) and then average across all nodes (Watts & Strogatz 1998).
Analysis
Results
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In our model, although gossip both weakens and strengthens links, weak links break but no new links are created. Hence, a priori, we expect that gossip will decrease the network’s clustering and average node degree.
The negative effect of gossip on clustering is most extreme in the null model: when gossip does not spread but occurs randomly in triads, the simulations quickly converge to networks with zero clustering, regardless of the properties of the initial network, the link-change function or the rules for selecting a gossip victim and a gossip originator. Furthermore, triads are unstable also when gossip spreads in networks with small initial clustering. For example, the average clustering coefficient after convergence in all 160 runs with random networks is effectively zero (mean = 0.0048, std. dev. = 0.0076). These results confirm the analytical prediction that gossip breaks triads.
Nevertheless, in networks with sufficient initial clustering, the spread of gossip can have exactly the opposite effect – it can make certain triads more stable. When gossip originates in and spreads throughout a dense cluster, it strengthens more ties than those that it weakens. For example, in a complete network of five agents, gossip weakens only four relations (between the victim and each of the gossipers), while it strengthens six (among all gossipers). Hence, although over the long run gossip destroys weakly triangulated links (i.e. “bridges”), it makes the links in dense clusters maximally strong. The result is a more fragmented and cliquish network (Figure 4).
When we account for initial clustering, the effect of gossip does not appear to differ among network types (Table 1). We only find that gossip tends to destroy links and weaken clustering to a lesser degree in large networks. Furthermore, when the gossip originator is the victim’s weakest link, average degree and clustering are lower compared to the case when the originator is randomly chosen from the victim’s links. This is so because, as elaborated in the analysis, under this rule weaker links become more likely to be severed.
Discussion / Future Directions
In this paper, we studied a general model of the effect of gossip on social structure. We concentrated on “negative” gossip, which we defined as an exchange of information that strengthens the relationships between those who gossip but weakens the tie between any gossiper and the gossip victim. We found that while gossip tends to dissolve isolated friendship triads, it strengthens them when they are embedded in dense clusters. Hence, gossip destroys clustering in weakly clustered networks and increases cliquishness in networks with already high clustering.
Many of the assumptions we made in our model are overly simplistic. Nevertheless, the model could be easily extended to be more realistic. For example, gossip does not always have to be negative. Gossip could be positive and conductive to forming new relationships (FIGURE 3). Furthermore, if O shares with G positive gossip about V, G may decide to divert time from her relationship with O and start hanging out with V. This “time conservation” principle implies a reverse mechanism where gossip weakens the relationship between the gossipers and strengthens the relationship between each gossiper and the gossip target. Alternatively, this very effect could also occur when somebody who has lost credibility starts maligning a third actor, i.e. when negative gossip goes wrong.
The effect of gossip could differ not only in direction but also in strength. It is reasonable to assume that the credibility of gossip decreases as you move away from its source. Consequently, a more realistic model would have the effect of gossip on the relationship between the gossipers decreasing with each step away from the originator.
Future developments of the model should also incorporate more heterogeneity among the agents. Some individuals are more likely to originate gossip or to pass it along. People tend to exhibit conformist behavior because they pursue the fundamental sense of belonging to a group, as well as social approval from its members. Thus, being the one person in a network who doesn't gossip might lead to social isolation (McAndrew 2008). However, individuals succumb to peer pressure to different degree. Introducing individual variation in the tendency to originate or repeat gossip to the simulation model would lead to more realistic predictions about the effect of gossip on social structure.
[I tried to include some of the ideas above but I'm not sure how to include the references.]
- In the heterogeneity model, we add conformity behavior to nodes. Conformity behavior happens to everyone when a person pursues the fundamental sense of belongingness or social approval from groups. A person tends to follow the majority behavior in a group because he is eager to be admitted and accepted. Even it means to go against his original perceptions. Study shows that individuals with a high need for social approval will distort their judgments of objectively determinable stimuli in response to perceived group pressure more frequently(Strickland, Bonnie R.; Crowne, Douglas P.1962). In this model, the probability of a node to become an originator depends on the Tendancy_to_Originate_Gossip which is a slider in the interface.
- Also we consider how peer pressure from gossiping group pushes a node to be a gossiper. According to Solomon Asch, that social influences shape every person's practices, judgments and beliefs is a truism to which anyone will readily assent(Solomon Asch.1955). It means a node will join in the gossiping group to be a gossiper under the group pressure although he initially doesn’t want to be.
References
- Bass, Frank M. 1969. A New Product Growth for Model Consumer Durables. Management Science 15(5):215-227.
- Baumeister, R.F., L. Zhang, and K.D. Vohs. 2004. Gossip as Cultural Learning. Review of General Psychology 8:111-121.
- not as relevant, but suggests that gossip helps individuals learn cultural rules of their group
- Bikhchandani, Sushil, David Hirshleifer, and Ivo Welch. 1992. A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades. Journal of Political Economy 100(5):992-1026.
- Boehm, Christopher. 1999. Hierarchy in the Forest: The Evolution of Egalitarian Behavior. Harvard University Press.
- gossip as leveling mechanism for neutralizing dominance tendency of others (cited in McAndrew 2008)
- Dodds, Peter S., and Duncan J. Watts. 2004.Universal Behavior in a Generalized Model of Contagion. Physical Review Letters 92, 218701.
- Dunbar, R.I.M. 2004. Gossip in Evolutionary Perspective. Review of General Psychology 8(2):100–110.
- Gossip is not about information but about creating and maintaining relationships (analogous to grooming among primates). Gossip also serves to control free-riders.
- Goss, S., Aron, S., Deneubourg, J. L. & Pasteels, J. M. 1989. Self-organized shortcuts in the Argentine ant. Naturwissenschaften. 76: 79-581.
- path choice in ants
- Helbing, D., Keltsch, J. & Molnar, P. 1997. Modelling the evolution of human trail systems. Nature. 388: 47-50.
- path choice in humans
- Lind, Pedro G., Luciano R. da Silva, José S. Andrade Jr., and Hans J. Herrmann. 2007a. Spreading Gossip in Social Networks. Physical Review E 76, 036117.
- Morris, Martina. 1993. Epidemiology and Social Networks: Modeling Structured Diffusion. Sociological Methods and Research 22(1):99-126.
- Nakagaki, T., Yamada, H. & Tóth, Á. 2000. Intelligence: Maze-solving by an amoeboid organism. Nature. 407: 470.
- path choice in slime molds
- Watts, Duncan J., and Steven Strogatz. 1998. Collective Dynamics of 'Small-World' Networks. Nature 393(6684):440-443.
- Wittek, Rafael, and Rudi Wielers. 1998. Gossip in Organizations. Computational & Mathematical Organization Theory 4(2):189–204.
- Gossip strengthens the relationship between ego and alter and weakens an already weak relationship between the two and a third actor.
- Strickland, Bonnie R.; Crowne, Douglas P. 1962. Conformity under conditions of simulated group pressure as a function of the need for social approval. Journal of Social Psychology,Vol 58(1), 1962, 171-181.
- Solomon Asch. 1955.Opinions and Social Pressure.
More Info / To Include
Extensions/Variants
SIMPLE:
- in model2: if A gossips to five secondary individuals (B1,B2,...) about C, does A-C increase 5x over?
ALTERNATIVE GOSSIP RULES:
- how do networks resulting from positive vs negative gossip differ?
- * (a priori expect that positive gossip will result in the network becoming more connected)
- combined gossip types: pass both positive and negative gossip through network, vary % positive
- let all links (friendships) grow over time according to some function. gossip events change link location on curve (negative moves down, positive moves up).
HETEROGENEITY:
- individual variation: tendency to gossip, gossip target, impact of gossip
- individual behavior: individuals can choose to pass on the gossip, ignore it, or reject the gossiper and sever the connection
- How do individual properties (e.g. range of social circle, poverty, wealth, the information itself, or geographic location) speed up or slow down the spread of gossip?
- Can individuals influence their location in a network (e.g. increase centrality) by changing their gossiping frequency?
Predictions
- (ref?): gossiping leads to segmentation of a network where small well-connected clusters form. (A fully-connected network will turn into a small-world network with gossip.)
- (Boehm 1999, as cited in McAndrew 2008): gossip leads to equalization of social status of individuals in a network, using sum of all edges as proxy for social status. (A network where individuals have uneven social status will even out with gossip.)
- (McAndrew 2008): being the one person in a network who doesn't gossip will lead to social isolation
- (McAndrew 2008): being the person who always spreads gossip will lead to a reputation as untrustworthy
Relevant Literature
- Burt, Ronald S. 2001. Bandwidth and Echo: Trust, Information, and Gossip in Social Networks. In Networks and Markets, Alessandra Casella and James E. Rauch, eds. Russell Sage Foundation.
- Social dynamics at play in the spread of gossip: biases in the selection of trusted third parties (one draws a sample of information consistent with one’s predisposition), the reinforcement of opinions in dyads due to an etiquette mechanism, the exaggeration of information in triads due to echo effects.
- Lind, Pedro G., Luciano R. da Silva, José S. Andrade Jr., and Hans J. Herrmann. 2006. How Gossip Propagates.
- Lind, Pedro G., Luciano R. da Silva, José S. Andrade Jr., and Hans J. Herrmann. 2007b. The Spread of Gossip in American Schools. EPL 78(68005):1-5.
- McAndrew, Frank T. 2008. The Science of Gossip: Why We Can't Stop Ourselves. Scientific American Mind.
Participation
Members
Files
Meetings
5 August 6:30pm (GMT-4)
meeting:
- Chang and David have run some more simulations which Milena has analyzed and put into the results table on the wiki
- we had a long discussion of Milena's results table -- I think we finally understand it all now!
- it doesn't seem worth discussing the results from the null model in detail since these seem to always tend towards zero
- we decided that most of the remaining work is in working on the writing and some analysis (analytical and graphical) of data, we probably won't run any more simulations
- we divvied up tasks and decided to meet next week, same day but 1/2 hour later
for next time:
- Roozbeh:
- work more on analysis section (based on that probability of choosing a Victim is proportional to the degree and that probability of choosing an Originator is proportional (or absolute?) to the weakness os the link to the victim)
keep manuscript up to date- Add analysis section to the wiki
Update the pictures of the paper using PowerPoint pictures
- Dave:
- write description of heterogeneity model
- help edit manuscript
- Chang:
- write description of heterogeneity model
- Milena:
- work on writing -- intro/methods/results
- check null model results (does it always decay to zero?)
- post/email results to all
- Allison:
write up generic algorithms- redo clustering analysis for new results
post ppt of figures on wiki
12 August 7pm (GMT-4)
meeting:
- Where's Dave?
- When the NetLogo code was updated to run multiple replicates, the output for the clustering graphs wasn't updated...this has been updated now, and we have decided to run more replicates in order to make clustering graphs (see the wiki results section for these graphs with a single replicate).
- We decided to include heterogeneity discussion in both the methods and discussion sections. Heterogeneity that we actually analyzed goes in the results, non-analyzed heterogeneity goes in the discussion.
- We decided to meet at the same time next week.
- Both Milena and Roozbeh are traveling on Aug 27th, so we will be done with the paper by Aug 26th!
for next time:
- Roozbeh:
- work more on analysis section (based on that probability of choosing a Victim is proportional to the degree and that probability of choosing an Originator is proportional (or absolute?) to the weakness os the link to the victim)
- Check availability of uploading equations on the wiki (and contact John Paul in case needed)
- Add analysis section to the wiki (from previous week)
- Dave:
- write description of heterogeneity model
- help edit manuscript
- Chang:
- run simulations
- Milena:
- work on writing -- intro/methods/results
- add more references
- Allison:
update NetLogo code and send out again- redo clustering analysis for new results
get ant trail reference
19 August 7pm (GMT-4)
meeting: for next time:
Tasks
Allison/Roozbeh: create null model in NetLogoMilena/Roozbeh: create spreading model in NetLogoMilena: create NetLogo function to build different network typesRoozbeh: come up with list of relevant network metrics and implement in NetLogodegree distribution, done!average path lengthclustering coefficientnumber of clusters, done!
- create NetLogo function to implement different gossip spreading rules
- read/gather literature
- generate predictions for model results
Roozbeh: Come up with a function for increasing and decreasing weights of connections. If the type of the function does not impact the dynamics of the network, we can keep it as simple as possible. (This part is done. Now we have two increase and decrease functions for changing the weights and we just need to use them in every code. About consistency of opposite actions (increase and decrease), I did not spend more time on it as I thought that it is not a priority now).- Chang: brainstorm how to incorporate heterogeneity into the network (implementation/predictions)
Chang Yu:some ideas :)
- follower tendency: This follower tendency happens to everyone. A person's behavior is affected by a group behavior when he wants to be admitted and accepted.And he will follow the majority behavior in this group. So when a listener(initail node) becomes to a gossiper, we can make it depend on gossiper-percentage of this node's neighbors. If a% of my neighbors are gossiping, I will be a gossiper.
- contact frequency: It's a counter in the model and can remember the frequency of linking between me and other nodes respectively.When an originator or gossiper wants to share, he doesn't tell a random or every reachable neighbor. He picks the most frequent neighbor.So do others.
- keep being a listener: meaning you just don't create or spread a gossip. I'm thinking whether this situation will affect this node's friend circle. Will it weaken his link strength or decrease the contact frequency with other nodes?
Original Discussion
It could be neat to develop a model of gossip networks. If you define gossip as information passed between 2 individuals (call them A and B) about a third party (C), then the act of gossiping has the potential to change the status/connection strength of all parties involved (e.g. maybe strength A-B, and weaken A-C and B-C bonds). Essentially passing information along a path in the network changes the value of BOTH edges in the direct pathway as well as other edges in the network. These are just preliminary ideas, but perhaps we could model how gossip tendency/frequency influences the structure of a network. Also, is it possible for individuals to influence their location in a network (e.g. increase centrality) by changing their gossiping frequency? (Although this is potentially a complicated rather than complex model idea...) Let me know what you guys think! Allison Shaw
- Milena Tsvetkova: This is a very interesting idea from sociological point of view. The effect of networks on the spread of gossip is well understood: some of the social dynamics at play include biases in the selection of trusted third parties (one draws a sample of information consistent with one’s predisposition), the reinforcement of opinions in dyads due to an etiquette mechanism, the exaggeration of information in triads due to echo effects. However, I am not aware of any studies that investigate how the spread of gossip affects network structure. My work is on the coevolution of behavior and social networks so we should talk!
- XOXO Chang Yu:Interesting! Gossip is not always bad. If we can model its spreading mechanism, it could help especially when you want to spread information unofficially. I get some inspirations from Tom’s last lecture on Friday. In the gossip network, what kind of properties of these agents can speed up or reduce information spread, the range of social circle, poverty, wealth, the information itself, or even the locations of houses in a community? I think we may model the different spreading results under different properties.
David Brooks: I agree that this concept of Gossip Networks is a generic for the analysis of several potential problems. I would like to talk to you about your intended direction and methods.
Gustavo Lacerda: sounds like some interesting dynamics, but how are you going to get data?
- Milena Tsvetkova: This article may be a good starting point for a first discussion: it suggest that gossip is a mechanism for bonding social groups. Should we try and schedule a brainstorming session?
Allison Shaw: Let's meet tomorrow (Thursday) around lunchtime (maybe 1pm after we've eaten?) to discuss this project in more depth -- anyone is welcome to join in!
Roozbeh Daneshvar: I'd like to join this team. It's good that we are doing a research with the same theme (Contagion in Networks). I can share the results from the heterogeneous network research group.