The "infection" of Gossip

Background

Gossip spread by word-of-mouth is a quick way to disseminate information in small communities such as small towns, workplaces, and schools. It typically starts with a single individual who shares this information with a few others who share it with others, thus, leading to its rapid growth.

Our model aims to represent the spread of gossip in various situations by focusing on some key aspects of gossip spread, including how likely individuals are to believe the gossip once they hear it (gullibility), the number of people in the community (density), and amount of time that passes before people make up their final opinion (duration) as well as the number of times they must have heard the gossip when making their final opinion (gossip frequency). This model also integrates the Complex Contagion Theory (Centola & Macy, 2007) and the Marketing Rule of Seven (“The marketing rule of 7”, n.d.) by allowing the agents to decide whether or not they accept and spread gossip depends on the number of times they have heard it themselves.

Model setup

Each agent within the model represents a single person in the population, depicted by the shape of a human. These agents are able to move freely throughout the plot in order to spread the gossip. There are four possible states an individual can be in, each represented by a different color – (1) never heard the gossip (represented by green), (2) heard the gossip, have not yet decided to permanently believe it, but believes it temporarily and is currently spreading it (red), (3) heard the gossip and has decided permanently that its false (gray), and (4) heard the gossip and has permanently decided that its true (blue). The initial setup of the model is depicted in the figure below -

Running the model

The agents can move freely and randomly throughout the model, interacting with each other to spread the gossip which models verbal, person-to-person communication. Once they interact with each other, their colors change based on the state of gossip spreading they are currently in. After a given time (duration), the gossip spreader will make a permanent decision on whether to accept the gossip as fact/truth or to deny it and assume it is false. For example, the figure below shows the final status of the gossip in a population where almost everyone believes that it's false (and is gray) and the rest never come to hear the gossip (green) -

This mainly occurs because for the population depicted above, the individuals only needed to have heard the gossip 4 times before making their final decision of believing that the rumor was true. And with the given model paramenters, that was quite likely to happen, thereby resulting in widespread rumor. Now, in contrast to this, below we have a population where the gossip mostly dies out -

Overall, we found that gullibility only has a large influence on how much the gossip is accepted permanently when gossip frequency (number of times one must hear the gossip to permanently believe it’s true) is low. With a low gossip frequency, low gullibility induces about half of the population to permanently believe the gossip, while high gullibility induces almost unanimous permanent belief that it is true. On the contrary, high gossip frequency nullifies virtually all of gullibility’s possible influence. It does not matter how much what the gullibility level is, if gossip frequency is high, the population would not believe in the gossip permanently. These results are depicted in the figure below. The y-axis refers to the total percentage of the population who permanently believed in the gossip at the end of the model's run.

Finally, the density of the population impacted the speed with which gossip spread as well as the likelihood that agents believed it. A smaller population (essentially, low population density) was far less likely to spread it compared to a large population. Small populations were also more likely to deem the gossip false despite the alteration of other parameters. Setting the duration short, the gossip is usually permanently deemed false as well as does not spread much.

References

Afassinou, K. (2014). Analysis of the impact of education rate on the rumor spreading mechanism. Physica A: Statistical Mechanics and Its Applications, 414, 43-52.

Campbell E., & Salathe´ M. (2013). Complex social contagion makes networks more vulnerable to disease outbreaks. Scientific reports, 3. Retrieved from https://doi.org/10.1038/srep01905

Centola, D., & Macy, M. (2007). Complex Contagions and the weakness of long ties 1. American Journal of Sociology, 113(3), 702-734.

Mønsted, B., Sapieżyński, P., Ferrara, E., & Lehmann, S. (2017). Evidence of complex contagion of information in social media: An experiment using Twitter bots. PLoS ONE, 12(9), 1–12. https://doi-org.www2.lib.ku.edu/10.1371/journal.pone.0184148

The marketing rule of 7, and why it's still relevant in B2B. (n.d.). Retrieved May 4, 2020, from https://www.b2bmarketing.net/en/resources/blog/marketing-rule-7-and-why-its-still-relevant-b2b

Zhao, Laijun, Cui, Hongxin, Qiu, Xiaoyan, Wang, Xiaoli, & Wang, Jiajia. (2013). SIR rumor spreading model in the new media age. Physica A: Statistical Mechanics and Its Applications, 392(4), 995-1003.

Zhao, Laijun, Qiu, Xiaoyan, Wang, Xiaoli, & Wang, Jiajia. (2013). Rumor spreading model considering forgetting and remembering mechanisms in inhomogeneous networks. Physica A: Statistical Mechanics and Its Applications, 392(4), 987-994.