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The dynamics of audience applause.

Mann RP, Faria J, Sumpter DJ, Krause J - J R Soc Interface (2013)

Bottom Line: Individuals' probability of starting clapping increased in proportion to the number of other audience members already 'infected' by this social contagion, regardless of their spatial proximity.The cessation of applause is similarly socially mediated, but is to a lesser degree controlled by the reluctance of individuals to clap too many times.We also found consistent differences between individuals in their willingness to start and stop clapping.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Uppsala University, Uppsala 75106, Sweden. rmann@math.uu.se

ABSTRACT
The study of social identity and crowd psychology looks at how and why individual people change their behaviour in response to others. Within a group, a new behaviour can emerge first in a few individuals before it spreads rapidly to all other members. A number of mathematical models have been hypothesized to describe these social contagion phenomena, but these models remain largely untested against empirical data. We used Bayesian model selection to test between various hypotheses about the spread of a simple social behaviour, applause after an academic presentation. Individuals' probability of starting clapping increased in proportion to the number of other audience members already 'infected' by this social contagion, regardless of their spatial proximity. The cessation of applause is similarly socially mediated, but is to a lesser degree controlled by the reluctance of individuals to clap too many times. We also found consistent differences between individuals in their willingness to start and stop clapping. The social contagion model arising from our analysis predicts that the time the audience spends clapping can vary considerably, even in the absence of any differences in the quality of the presentations they have heard.

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Ignoring the effect of number of claps on the probability of stopping, the clapping model can be expressed in terms of mean-field differential equations (4.4) and (4.5). The model parameters are set from the best model fit when ignoring clap number-dependent stopping (i.e. γ3 = 0), with stopping parameters adjusted from per clap values to per second values using the average clap interval of 0.28 s, yielding γ2 = 2.15 per second, γ1 = 0.0011 per second and γ2 = 0.094 per second. (a) Change of susceptible and infected individuals through time when S(0) = 0.95 and I(0) = 0.05. (b) Phase plane of susceptible versus infected. When  (indicated by the blue dotted line) clapping reaches a maximum. The red arrowed line shows the time integration from figure 5a.
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RSIF20130466F5: Ignoring the effect of number of claps on the probability of stopping, the clapping model can be expressed in terms of mean-field differential equations (4.4) and (4.5). The model parameters are set from the best model fit when ignoring clap number-dependent stopping (i.e. γ3 = 0), with stopping parameters adjusted from per clap values to per second values using the average clap interval of 0.28 s, yielding γ2 = 2.15 per second, γ1 = 0.0011 per second and γ2 = 0.094 per second. (a) Change of susceptible and infected individuals through time when S(0) = 0.95 and I(0) = 0.05. (b) Phase plane of susceptible versus infected. When  (indicated by the blue dotted line) clapping reaches a maximum. The red arrowed line shows the time integration from figure 5a.

Mentions: While an analogy to disease spread is the starting point for describing social contagion, our study reveals important differences between biological and social processes. As in the standard Susceptible, Infected and Recovered (SIR) model for the spread of a disease [21], and in contrast to models based on tipping points or quorums [22,23], clapping increases linearly with the proportion of individuals already involved in it. This linear response is similar to that seen in movement decisions in monkeys [24] and in gaze-following by humans [7]. However, unlike the SIR model, ‘recovered’ individuals (those who have stopped clapping) increase the recovery rate of those who are clapping. This is consistent with an early model by Daley & Kendall [25] of fads and fashions. Figure 5 shows a phase plane for a differential equation version of our clapping model, in which the effect of number of claps on the probability of stopping is ignored. Unlike the SIR model, clapping always spreads even when the starting rate λ2 is small. The point at which most people are infected with clapping is near to the point at which there remain very few susceptibles, similar to both the experimental results (figure 1) and the stochastic simulations (figure 3). As seen in the experimental results (figure 1), the model predicts that even before everyone has started clapping, some individuals will usually have recovered and stopped.Figure 5.


The dynamics of audience applause.

Mann RP, Faria J, Sumpter DJ, Krause J - J R Soc Interface (2013)

Ignoring the effect of number of claps on the probability of stopping, the clapping model can be expressed in terms of mean-field differential equations (4.4) and (4.5). The model parameters are set from the best model fit when ignoring clap number-dependent stopping (i.e. γ3 = 0), with stopping parameters adjusted from per clap values to per second values using the average clap interval of 0.28 s, yielding γ2 = 2.15 per second, γ1 = 0.0011 per second and γ2 = 0.094 per second. (a) Change of susceptible and infected individuals through time when S(0) = 0.95 and I(0) = 0.05. (b) Phase plane of susceptible versus infected. When  (indicated by the blue dotted line) clapping reaches a maximum. The red arrowed line shows the time integration from figure 5a.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4043176&req=5

RSIF20130466F5: Ignoring the effect of number of claps on the probability of stopping, the clapping model can be expressed in terms of mean-field differential equations (4.4) and (4.5). The model parameters are set from the best model fit when ignoring clap number-dependent stopping (i.e. γ3 = 0), with stopping parameters adjusted from per clap values to per second values using the average clap interval of 0.28 s, yielding γ2 = 2.15 per second, γ1 = 0.0011 per second and γ2 = 0.094 per second. (a) Change of susceptible and infected individuals through time when S(0) = 0.95 and I(0) = 0.05. (b) Phase plane of susceptible versus infected. When  (indicated by the blue dotted line) clapping reaches a maximum. The red arrowed line shows the time integration from figure 5a.
Mentions: While an analogy to disease spread is the starting point for describing social contagion, our study reveals important differences between biological and social processes. As in the standard Susceptible, Infected and Recovered (SIR) model for the spread of a disease [21], and in contrast to models based on tipping points or quorums [22,23], clapping increases linearly with the proportion of individuals already involved in it. This linear response is similar to that seen in movement decisions in monkeys [24] and in gaze-following by humans [7]. However, unlike the SIR model, ‘recovered’ individuals (those who have stopped clapping) increase the recovery rate of those who are clapping. This is consistent with an early model by Daley & Kendall [25] of fads and fashions. Figure 5 shows a phase plane for a differential equation version of our clapping model, in which the effect of number of claps on the probability of stopping is ignored. Unlike the SIR model, clapping always spreads even when the starting rate λ2 is small. The point at which most people are infected with clapping is near to the point at which there remain very few susceptibles, similar to both the experimental results (figure 1) and the stochastic simulations (figure 3). As seen in the experimental results (figure 1), the model predicts that even before everyone has started clapping, some individuals will usually have recovered and stopped.Figure 5.

Bottom Line: Individuals' probability of starting clapping increased in proportion to the number of other audience members already 'infected' by this social contagion, regardless of their spatial proximity.The cessation of applause is similarly socially mediated, but is to a lesser degree controlled by the reluctance of individuals to clap too many times.We also found consistent differences between individuals in their willingness to start and stop clapping.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Uppsala University, Uppsala 75106, Sweden. rmann@math.uu.se

ABSTRACT
The study of social identity and crowd psychology looks at how and why individual people change their behaviour in response to others. Within a group, a new behaviour can emerge first in a few individuals before it spreads rapidly to all other members. A number of mathematical models have been hypothesized to describe these social contagion phenomena, but these models remain largely untested against empirical data. We used Bayesian model selection to test between various hypotheses about the spread of a simple social behaviour, applause after an academic presentation. Individuals' probability of starting clapping increased in proportion to the number of other audience members already 'infected' by this social contagion, regardless of their spatial proximity. The cessation of applause is similarly socially mediated, but is to a lesser degree controlled by the reluctance of individuals to clap too many times. We also found consistent differences between individuals in their willingness to start and stop clapping. The social contagion model arising from our analysis predicts that the time the audience spends clapping can vary considerably, even in the absence of any differences in the quality of the presentations they have heard.

Show MeSH
Related in: MedlinePlus