The Science of Standing Ovations
https://www.coursera.org/learn/model-thinking/lecture/IdA4x/the-standing-ovation-model
We’ve all seen it before. The pianist ends with a final flourish, the orator delivers a spellbinding line, the distinguished figure appears on stage. Out of nowhere, with great force, the entire mass of the audience rises to its feet. The term “standing ovation” has been around since 1831 [1], and since then it has been an essential part of many formal events, including lectures, concerts and speeches. Participating in a standing ovation is a decision of etiquette; it’s usually a “follow-the-crowd” decision, made in an effort to avoid seeming uncultured or unknowledgeable. Although the situation may seem simple enough, the decision logic for whether to stand or sit can become quite sophisticated depending on the situation.
Scott Page of the University of Michigan analyzes this model in his online course “Model Thinking.” He notes that there are really two decisions being made: one right before the applause starts and one right after it starts. The decision before the applause starts is simple. Suppose we can assign some quantitative measure Q of how good the performance was. Each person’s Q score is different based on their subjective experiences and tastes, so there is some variation in the value of Q. Each audience member has a threshold T such that if Q > T, the show immediately deserves a standing ovation. Those who aren’t excited enough to stand wait and gauge the rest of the crowd’s reaction [2].
This second choice is more complicated as it involves the actions of the other people surrounding each individual in the audience, whose decisions in turn involve their own neighbors, and so on. We can make the decision more concrete by using game theory, treating the stand/sit decision as an instance of a simple 2×2 game. Each individual is player one and the people surrounding them (in front, to the left, to the right, and behind) are consolidated into a single player, player two.
For simplicity, this model operates under the assumption that everyone can see everyone else in the auditorium, including people behind them. Also, we assume that nobody in the crowd knows anyone else. That way, any one neighbor doesn’t influence the decision any more than the others. (Scott Page’s course, linked at the top of the page, dives into some interesting results that occur if we don’t hold these assumptions to be true.) Finally, we suppose that if the majority of an audience member’s neighbors stand, then “player two” (the single player representing the neighbors) is standing. Otherwise, “player two” is sitting.
The payoff matrix for the 2×2 game is below for an audience member and their neighbors. The audience member chooses rows and the neighbors collectively choose columns.
| Stand | Sit | |
| Stand | (5, 5) | (0, 2) |
| Sit | (2, X) | (2, 2) |
Suppose you’re an audience member. Your payoff is high if both you and your neighbors are standing – it feels great to be part of a standing ovation. If you stand while your neighbors are seated, it may be embarrassing so the payoff is low. If you sit while your neighbors are standing, your payoff is modest. If both you and your neighbors are sitting, it’s again a modest payoff.
Notice the payoff of “X” for neighbors that choose to stand while the player sits. This is because their payoff for standing depends on how many of their own neighbors are standing. The value of X has profound effects on your neighbor’s behavior, which in turn affects your own behavior:
- If many people are standing initially, this payoff X is likely to be higher since your neighbor is more likely to have standing neighbors of their own. If so, standing becomes a dominant strategy for your neighbors. Since your best response to your neighbors’ standing is standing as well, the pair (Stand, Stand) becomes a Nash equilibrium.
- If few people are standing initially, the neighbor isn’t likely to have anyone standing around them. X is low, so standing is not a dominant strategy for your neighbors. In that case, both you and your neighbor may be better off sitting instead.
Standing ovations are an example of how game strategies can propagate through the crowd. The two strategies in this case, “sit” or “stand”, spread through the network as people observe others around them. If your neighbors obtain a larger payoff than you in this game, you are likely to adopt your neighbors’ strategy (i.e. either “stand” or “remain seated”) as your own. If enough people stand at the beginning, it isn’t hard to see that the “stand” strategy percolates quickly through the audience, since standing with neighbors yields a higher payoff than sitting while neighbors are standing. Soon enough, the “standing” strategy has decidedly overtaken the “sitting” strategy, and the entire crowd is on its feet.
The next time you watch a performance and gauge the reaction at the end, think about this 2×2 game. Imagine the “standing” strategy spreading through the network as each actor makes game-theoretic decisions about the world around them. The beauty of this model – where small decisions made by individuals have large consequences on the global properties of the system – surely deserves a standing ovation of its own.
[1] “Ovation.” Dictionary.com. Dictionary.com, n.d. Web. 16 Sept. 2016. <http://www.dictionary.com/browse/ovation>.
[2] Page, Scott. “The Standing Ovation Model.” Coursera. University of Michigan, n.d. Web. 16 Sept. 2016. <https://www.coursera.org/learn/model-thinking/lecture/IdA4x/the-standing-ovation-model>.