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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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Simulation results. The plot shows the median proportion of individuals in the audience who have started clapping (black line), stopped clapping (red line) and are currently clapping (green line), aggregated over 10 000 simulations. Results are shown for (a) the optimal linear contagion model and (b) an alternative quadratic contagion model. For the starting and stopping proportions, the shaded area represents the interquartile range, illustrating the variation across simulations. The simulation has three behavioural states: susceptible (S is the proportion of individuals in this state); clapping (I) and recovered (R). The time taken to go from susceptible to clapping is exponentially distributed with rate constant λ2(I + R). After the nth clap an individual will either recover (stop clapping) with probability γ2R + γ3n/nmax or wait a time distributed N(0.28 s, 0.09 s) (matched to observed clap intervals). This process continues until all individuals have recovered.
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RSIF20130466F3: Simulation results. The plot shows the median proportion of individuals in the audience who have started clapping (black line), stopped clapping (red line) and are currently clapping (green line), aggregated over 10 000 simulations. Results are shown for (a) the optimal linear contagion model and (b) an alternative quadratic contagion model. For the starting and stopping proportions, the shaded area represents the interquartile range, illustrating the variation across simulations. The simulation has three behavioural states: susceptible (S is the proportion of individuals in this state); clapping (I) and recovered (R). The time taken to go from susceptible to clapping is exponentially distributed with rate constant λ2(I + R). After the nth clap an individual will either recover (stop clapping) with probability γ2R + γ3n/nmax or wait a time distributed N(0.28 s, 0.09 s) (matched to observed clap intervals). This process continues until all individuals have recovered.

Mentions: Rules of interaction between individuals in groups that are inferred from fine scale measurements of individual behaviour should be confirmed by demonstrating their ability to reproduce group level effects [15–17]. To further investigate the dynamics of applause, we implemented a simulation model based on the combination of the most probable starting and most probable stopping models (see §4). This model reproduces the type of dynamics seen in the experiment (figure 3a). In particular, the model accurately reproduces the form of the sigmoidal starting and stopping patterns seen in the data and the approximately symmetric growth of decay of the infection. To test our hypothesis that clapping contagion is a linear process, we also performed simulations of a model with a quadratic infection term (M3 in the starting models), using the best-fit parameters for that model (λ3 = 4.0 per second). The results of these simulations (figure 3b) show that such a model is inconsistent with the large-scale pattern of infection seen in the data (figure 1). In particular, infection occurs too rapidly, and there is a sustained period where all individuals are clapping, whereas in the data and in the linear simulations some individuals typically stop clapping before the whole audience is infected.Figure 3.


The dynamics of audience applause.

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

Simulation results. The plot shows the median proportion of individuals in the audience who have started clapping (black line), stopped clapping (red line) and are currently clapping (green line), aggregated over 10 000 simulations. Results are shown for (a) the optimal linear contagion model and (b) an alternative quadratic contagion model. For the starting and stopping proportions, the shaded area represents the interquartile range, illustrating the variation across simulations. The simulation has three behavioural states: susceptible (S is the proportion of individuals in this state); clapping (I) and recovered (R). The time taken to go from susceptible to clapping is exponentially distributed with rate constant λ2(I + R). After the nth clap an individual will either recover (stop clapping) with probability γ2R + γ3n/nmax or wait a time distributed N(0.28 s, 0.09 s) (matched to observed clap intervals). This process continues until all individuals have recovered.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4043176&req=5

RSIF20130466F3: Simulation results. The plot shows the median proportion of individuals in the audience who have started clapping (black line), stopped clapping (red line) and are currently clapping (green line), aggregated over 10 000 simulations. Results are shown for (a) the optimal linear contagion model and (b) an alternative quadratic contagion model. For the starting and stopping proportions, the shaded area represents the interquartile range, illustrating the variation across simulations. The simulation has three behavioural states: susceptible (S is the proportion of individuals in this state); clapping (I) and recovered (R). The time taken to go from susceptible to clapping is exponentially distributed with rate constant λ2(I + R). After the nth clap an individual will either recover (stop clapping) with probability γ2R + γ3n/nmax or wait a time distributed N(0.28 s, 0.09 s) (matched to observed clap intervals). This process continues until all individuals have recovered.
Mentions: Rules of interaction between individuals in groups that are inferred from fine scale measurements of individual behaviour should be confirmed by demonstrating their ability to reproduce group level effects [15–17]. To further investigate the dynamics of applause, we implemented a simulation model based on the combination of the most probable starting and most probable stopping models (see §4). This model reproduces the type of dynamics seen in the experiment (figure 3a). In particular, the model accurately reproduces the form of the sigmoidal starting and stopping patterns seen in the data and the approximately symmetric growth of decay of the infection. To test our hypothesis that clapping contagion is a linear process, we also performed simulations of a model with a quadratic infection term (M3 in the starting models), using the best-fit parameters for that model (λ3 = 4.0 per second). The results of these simulations (figure 3b) show that such a model is inconsistent with the large-scale pattern of infection seen in the data (figure 1). In particular, infection occurs too rapidly, and there is a sustained period where all individuals are clapping, whereas in the data and in the linear simulations some individuals typically stop clapping before the whole audience is infected.Figure 3.

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