Dynamics of Applause: Modeling Group Phenomena ThroughAgent Interaction
Gary Lupyan ([email protected])Center for Neural Basis of Cognition
4400 5th Ave. Pittsburgh, PA 15207 USA
Ilya Rifkin ([email protected])Department of Computer Science. Cornell University
Ithaca, NY 14853 USA
Unlike many social conventions that proved to bepassing fads, applause appears to be a remarkablystable facet of human culture. Although its mani-festations have varied from the fluttering of fans ofVictorian ladies, to hearty overhead clapping and cat-calls of less “refined” concert-goers, the desire to ex-press approval through a culturally-specified displayhas been in existence for millennia. Demonstratingthe perceived importance of applause, French theaterand opera companies of the 1800s hired claques, pro-fessionals who led others in applause to secure encoresand educate audiences on the finer points of the per-formance. Using a dynamic game theory model, thepresent work looks at how applause dynamics emergefrom the interaction of individual desires. What arethe benefits that drive applause? What are the coststhat work to end it? How do the costs and benefits ofan individual interact with those of others in the au-dience? Despite some simplifying assumptions madein the present model, it offers robust predictions ofapplause in audiences of varying sizes responding toevents of varying levels of “impressiveness.” More gen-erally, this work demonstrates how a complex socialbehavior can be modeled with few assumptions andfree parameters.Procedure The benefit of applause was taken tobe the emotional benefit of expressing appreciation.This benefit was proportional to the impressivenessof the event. The costs were twofold. An em-barrassment cost was calculated based on randomly-generated “embarrassment thresholds” assigned toeach agent. This was based on the intuition that someindividuals are more easily embarrassed than othersand will hesitate to applaud unless others are alsoclapping. The embarrassment cost at a given time wasinversely proportional to the percentage of audiencemembers applauding. The second cost was the phys-ical cost of applause, which built up proportionatelyto the time spent applauding. An agent clapped whenthe desire to express their appreciation outweighed theembarrassment and physical costs, and ceased clap-ping when the costs outweighed the benefit.
A typical sequence of events in response to an eventis as follows:
1. An event of a particular impressiveness value occurs.
2. People with low embarrassment thresholds (those not easilyembarrassed) begin to applaud and lower the embarrassment costfor others in the audience.
3. If the decrease in the embarrassment cost is not enough tocause other agent to clap, the clapping quickly dies down due to anincrease in physical costs.
4. Otherwise, the decrease in embarrassment causes other agentsto begin clapping, which in turn causes a cascade of applause.
5. As the physical cost of continued applause begins to outweighthe benefit of showing one’s appreciation, individuals stop clappingraising embarrassment costs for others in the audience, eventuallycausing everyone to cease applauding.
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 10.0
0.2
0.4
0.6
0.8
1.0
Dur
atio
n of
App
laus
e(a
rbitr
ary
units
)
Pro
port
ion
Cla
ppin
g
"Impressiveness" of Event
DurationProportion
Figure 1: Effect of impressiveness on proportion ofaudience clapping and duration of applause.
Results We started out with two basic hypothe-ses: Applause starts quicker than it ends. If an ap-plauder is not joined by others, they typically stopclapping. These hypotheses come from observationsof audiences; the first is also supported by analysis ofdigitized recordings of actual applause. Both hypothe-ses were accurately supported by the model. Themodel furthermore made predictions regarding effectsof event impressiveness and audience size on applausedynamics. Events of low impressiveness predictablyresult in few individuals clapping for a short time. Be-yond a certain ”impressiveness threshold,” virtuallyeveryone starts applauding. Further increases in im-pressiveness yield longer applause times of the wholeaudience (see Fig. 1). The effect of audience size ismore subtle. For events of high impressiveness, audi-ence size proved to have no effect—everyone applaudsin all audiences. For events of lower impressiveness,however, smaller groups behaved more erratically, oc-casionally breaking out into universal applause, whileat other times not breaking the 50% mark. These pre-dictions have all been confirmed through observationof applauding audiences.
1378
