Thresholds and abrupt social change

Publish Date: 
Sun, 03/20/2011 - 20:00

How does large-scale social change sometimes happen abruptly without a clear cause? One day thousands of people take over the streets and refuse to leave until their demands are met. 20th century leadership-based models for social movements appear to be inadequate to explain how people are doing it this year.

One way to look at this is using a threshold model.

Suppose everyone has a threshold for participation - one person will join in if 60 percent of the people do, while another person is ready to go once only 10 percent are willing. Some people are willing no matter what – we can say their threshold is zero or less – and some people will probably never do it, and we can say their threshold is larger than 100%. In the first figure here, we imagine a hypothetical community where people are generally favorable toward participating. The left side of the figure shows how many people have the various threshold levels: the most common is 45% and half the people have thresholds smaller than 45%.


Figure: (Left side)
Thresholds for participation: average 45%, standard deviation 35%.
(Right side)
The outcome: a cascade of increasing participation, until most of the community is involved.

The right side of the figure shows how to work out what will happen in this community. Above each number is the number of people whose threshold is that value or less. From this curve we can see that, first of all, if nobody expects anyone else to do anything, there is about 10 percent of the community who will show up on the street anyway. We see this by looking at the value above the number 0 – it's about 10 percent. But then by looking at the value above 10 percent we see that when there is 10 percent participation, about 14 percent of the community finds that their threshold for participation is satisfied. And when 14 percent participate, that satisfies about 19 percent of the people's thresholds. And so on.

This scenario is based on a classic paper by sociologist Mark Granovetter: Threshold Models of Collective Behavior, American Journal of Sociology, 1978. Granovetter uses the example of a potential riot situation where a crowd of angry people have gathered in the street, and might or might not become actively confrontational. If one or two people throw bottles, maybe a lot of people will join in and the crowd will erupt, but under slightly different conditions the crowd might remain passive.

The figure above describes a crowd that will erupt. First 10 percent of the crowd will start off the action on their own initiative; then another 4 percent will join in once they see that so many others are doing it; then another 5 percent will join once the riot has grown that much larger; and in this way, more and more people will join in until very nearly everyone is involved. The stopping point is at the blue dot in the upper right where the curve crosses the diagonal dotted line. That is at about 90 percent because in this example, if that many people are expected to come out, that's also the number who will come out in response. (The diagonal dotted line is where the number participating is equal to the number who will respond.) The 90% number is self-consistent, and that is what is needed for the cascade to stop.

Now consider another, slightly different community, sketched in the next figure.


Figure: (Left side)
Thresholds for participation: average 45%, standard deviation 25%.
(Right side)
The outcome: widespread participation is possible, but a community starting at zero will get stuck at a low level of participation.

In this example, like the previous one, 45% is the most common threshold and half the people are even more ready to participate with thresholds less than 45%. But the people are less diverse in their attitudes: there are fewer people with very low or very high thresholds.

On the right side we see a curve very similar to the one we saw before, but with a crucial difference: it crosses the diagonal at the bottom left as well as at the upper right.

In this community, some people will start off the change on their own, and others will join as they see that they have enough company; but they will stop at about 5 percent and nobody else will join in. When 5 percent of the people participate, that satisfies the threshold for participation for that 5 percent and not for anyone else. Lots of people would join in if the turnout were large enough, and in fact participation would rise all the way to about 99 percent, but the community doesn't get to that point because there aren't enough people with very low thresholds. (Extra credit question: why isn't the other crossing at about 37% also a possible outcome?)

This model is clearly simpler than reality, and the differences might matter a lot. These models can fail to match reality any time people are influenced more by their acquaintances than by strangers, or if people predict how many others will participate by some means other than direct, accurate observation, if they are partially guided by some kind of random chance, or if people's thresholds change quickly and often.

Also this idea of thresholds is pretty abstract, and it's not clear whether people's thresholds for a certain behavior could ever be measured, and whether a particular prediction about thresholds could be verified or falsified. In the case of a riot or a national uprising, we would imagine people's thresholds for participation would be influenced by their political beliefs, their opinions of the other people expected to participate, their schedules and free time, their assessment of what the action might accomplish, their personal investment in the outcome, the actions of the police, the weather, the presence or absence of international media, and many other things. In the case of a possible change in social norms, such as historical resistance to footbinding in China, rejection of female genital cutting in Africa, or public support for unions or opposition to nuclear power in the US, the array of factors contributing to individuals' thresholds for participation are surely just as multifarious.

Whether they might be implicit in the idea of thresholds, there are a large number of things that this description leaves out that are important in discussing any kind of social change: the role of the police, and in some cases the army; changing economic opportunities and expectations; the media (traditional and online); the role of organizations in planning actions and turning people out; people's material conditions; race, caste, gender, and class divisions, to name a few.

But even with all these caveats, a model that presents a caricatured, schematic representation of a real situation can do very useful work. It can offer new ways of thinking about the situation. It can suggest useful questions, it can expose novel hypotheses about the situation that can be tested in other ways, and it can help us to discover new, creative ways of acting. This threshold model offers a simplified, short-term, tactical view of a social change situation, and may suggest an inspiring idea, or a way of asking questions that might lead to something useful.

The two threshold model examples in this post suggest three scenarios for abrupt social change:

1. The thing that happens in the first figure. Someone initiates a demonstration, or adoption of some new behavior, and people successively become willing to join in, until ultimately most of the community has joined.

2. A community that is like the second figure, with very little adoption, and then for some reason a number of people's thresholds become lower (they become more willing to make the change or join the demonstration), so that it becomes like the first figure, and the rest of the community gets drawn into adopting the behavior. As the figures show, the very low participation scenario can change to the very high participation scenario with only a very small, subtle change in the actual preferences of the individuals in the community – compare the left sides of the two. They look almost alike.

3. A community that is like the second figure, with lots of people who would adopt the change if they expected enough other people to do it, but they aren't adopting it because they don't think there are enough people to satisfy their thresholds. Then someone finds a way to convince people that lots of other people feel the same way, and then they all become willing to do it. Maybe this is the role of the celebrated Facebook pages that gathered thousands of subscribers before the uprisings in Egypt?

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