Modeling gossip networks

Abstract

THE EFFECT OF GOSSIP ON SOCIAL NETWORKS

In this project we look at the effects of gossip spread on social network structure. We define gossip as information passed between two individuals A and B about an individual C who is not present, which has the potential to affect the strengths of all three relationships A-B, B-C, and A-C. This work is novel in two respects: first, there is no theoretical work on how network structure changes when information passing through a network has the potential to affect edges not in the 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.

Gossipers David Brooks, Milena Tsvetkova, Allison Shaw, Chang Yu, and Roozbeh Daneshvar, hard at work.

Paper Draft

Introduction

Gossip is ubiquitous in human groups and has even been argued to be fundamental to human society (Dunbar 2004). Although 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 – it seems to have a variety of benefits, including serving to help individuals learn the cultural rules of their group (Baumeister et al 2004). Dunbar (2004) even proposed that gossip is analogous to grooming in primates; essentially a tool to create and maintain relationships between individuals, with little importance given to the actual information being passed.

Schematic for the effect of gossip on strengths of relationships of individuals in the triad. Individuals are represented as nodes and the strength of their relationship is represented by the thickness of the line between them. An originator (O) spreads gossip about a victim (V) to a mutual friend, the gossiper (G). The result is a stronger relationship between the originator and gossiper, and a weaker relationship between the victim and each the originator and the gossiper.

Unlike rumors, gossip involves a single target individual, the ‘victim’ (Lind et al 2007). Gossip can essentially be defined as information passed from one individual (the ‘originator’) to another (the ‘gossiper’) about an absent third individual (the ‘victim’), and therefore any analysis of gossip must occur at the level of the triad or higher (Wittek & Weilers 1998). [ref about strengthening and weakening connections – can’t remember where i read this - Milena: It's in Wittek & Weilers 1998]

Some work done on how social structure influences the flow of gossip and which network types best promote gossip (e.g. Lind et al. 2007). We propose to do the flip side of this and see how gossip affects network structure.

Although some work done on how information passing through networks influences strength of edges it passes over (e.g. reinforcement, hebbian learning, neurons), nothing has been done on how information passed along one edge affects the strengths of other edges in the network. [more on reinforcement] [sentence on ant trails]

Methods

We conducted simulations on a simple network model (built in NetLogo) to understand how the spread of gossip influences social network structure.

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.

Schematic for how gossip spreads in a social network. a) We randomly chose a node to be the victim (V) and one of it’s neighbors to be the originator of the gossip (O). b) the originator spreads the gossip to all mutual friends with the victim, strengthening connections between all gossipers and weakening all connections between the victim and gossipers. c) This process continues until no more individuals can become gossipers.

We assume that spreading gossip results in a stronger relationship between all gossipers, and a weakened relationship between the victim and all gossipers. Allowing link weights to take values between 0 and 1, we used two functions describing this effect: quadratic (sqrt(w) increase and w^2 decrease) and hysteresis (w+0.4(1-w) increase and 0.6w decrease). [Can we call the latter "hysteresis"? I know that Roozbeh had something else in mind here, but the one we have has the hysteresis property, if I understood it correctly...] All edges were initially set to have a strength of 0.5. Furthermore, those links whose weight dropped below 0.005 were severed.

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.

Each simulation was run for 10,000 gossip events. [add a note about convergence]

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 [why? Refs?] networks. We did not consider scale-free networks since these inherently have a branching form with no triads (ref), making them incompatible with our model of gossip. [rewiring prob for small world?]

For comparison we generated small (N=50) and large (N=200) networks that were sparsely (L=6) and densely (L=12), connected [is L the right letter?].

Heterogeneity

• Also tried non-random victim choice -- picked node with the most connections (since gossip hypothesized to level social playing field (Boehm 1999)
• Tried non-random choice of originator – weakest connection with victim, since expect that wouldn’t pass gossip about close friends, benefit most by weakening already weak connection [ref]

Statistics

Looked at average node degree, average path length, clustering coefficient, degree distributions. [we didn’t really use all these in the end -- which stats were the most helpful?]

Results

	Clustering			Average Node Degree
Variable	Coef.	Std. Err.		Coef.	Std. Err.
Number of nodes	.0002*	.0001		.0014***	.0003
Spatially-clustered	.1046	.0618		.8574**	.3272
Small-world	-.0612	.0373		-.2812	.1972
Victim: degree-central	.0121	.0076		.1304**	.0401
Originator: weakest-link	-.0871***	.0075		-.3818***	.0399
Initial clustering	.6477***	.1193		-3.0686***	.6314
Constant	-.0308	.0175		5.4037***	.0928
Adj. R-squared	.9127			.7750
* p < 0.05, ** p < 0.01, *** p < 0.001
Number of observations: N = 240

Many more details here – figures? Tables?

at the very least discuss these: 1. null-gossip 2. spreading-gossip 2a. random networks 2b. spatially clustered and small-world 3. heterogeneity 3a. non-random victim choice 3b. non-random originator choice

some comment on convergence!

Gossip breaks up triads when it doesn’t spread or random network is used BUT strengthens triads when gossip spreads in spatially clustered network

A priori expect that by breaking links (note: no way to form new links) that network will become more fragmented

Discussion / Future Directions

many assumptions we make are overly simplistic and model could be easily extended to be more realistic. For example:

• value of gossip likely decreases as you move away from source [ref], so effect of gossip on relationship between gossipers likely decreases with each step away from the originator
• gossip doesn’t always have to be negative, could be positive where A tells B good things about a friend of theirs C who B doesn’t know, resulting in B making a connection with C (FIGURE 3)

Schematic for positive gossip (as opposed to negative gossip as depicted in FIGURE 1).

• Alternatively assume that if B shares with A positive gossip about C, A diverts time from her relationship with B and starts hanging out with C, so weaken A-B instead.
• if A gossips to B about C: B weakens A-B and strengths B-C

Also, more heterogeneity could be incorporated, for example:

• 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?

References

• Baumeister, RF, L Zhang, and KD 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

• 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)

• 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.

• 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):1-10.

• 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.

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

• Allison Shaw
• Chang Yu
• David Brooks
• Milena Tsvetkova
• Roozbeh Daneshvar

Tasks

• Allison/Roozbeh: create null model in NetLogo
• Milena/Roozbeh: create spreading model in NetLogo
• Milena: create NetLogo function to build different network types
• Roozbeh: come up with list of relevant network metrics and implement in NetLogo
  • degree distribution, done!
  • average path length
  • clustering coefficient
  • number 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.