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How the numbers grow

We will have a closer look at social dynamics - we will discuss different ways in which processes may unfold and what changes are obsered over time.
In this video, will look at one of the most important features of dynamic processes at how they unfold. What changes are observed in time? So we’ll be thinking about dynamics. We will start with our previous examples from Fruit County. Let’s say we’re investigating the process of joining a protest. We’ll be looking at the way the number of protesters grows over time. Specifically, we will assume that people observe each other and join or don’t. The ones already protesting in Grapevine, we could observe how at the start there were two initiators. This was day one. On the next day, one person joined them. Day three, one more person. Day four, three more protesters. Day five, one more.
And then on day six, the process stopped, or we’d rather say it’s stabilised. Nothing changes from this day onwards. We could draw it on a chart. First, we have two persons. Then next one joins. Then another one and some more. And then we can see a straight line, nothing changes anymore. What we can also see here is that there was quite a jump between day three and day four. The number of protesters almost doubled at that point. Let’s see how it would look like in another network if everyone had exactly two friends, and there was one initiator. Two persons joined on day two. The same happens on day three and day four. And, again, let’s see a chart for that.
What we can see is a very neat line growing by the same number every day until there are no more people to join obviously. This is a linear process. We observe the same change every day. In real life, we rarely deal with social processes that behave this way. Let’s go back to Grapevine. The numbers here didn’t grow the same each day, as they did in the circular network. There was a clear jump in there. And the process came to an abrupt halt. The process is non-linear. It means that the changes are different at different moments in time. At some points, there is a small change. At some points, large change. And at some point, no change at all.
Social processes may, in fact, grow in various ways. They can have a quick start and then the numbers grow more slowly, or they can have jobs here and there. For example, whenever a popular person joins in and a lot of people follow. During COVID-19 pandemic, the term exponential gained popularity. In the processes that grow exponentially, what we can see is that the numbers don’t grow very fast in the beginning, but they grow much, much faster with time when studying social dynamics. It’s important to pay attention to the way the numbers grow and to remember that what we should be expecting is usually far from a neat straight line.

In this video, we will have a closer look at social dynamics. We will discuss different ways in which processes may unfold and what changes are observed over time.

One small remark is needed here: in the type of threshold model we’ve been using, those numbers can only grow as there is no mechanism that would allow villagers to leave the protest. Once they’re in, they’re always in. This is why the process can only stabilise at one point and nothing changes anymore. Obviously, with social processes, it’s more complicated than that.

For example, we could assume that protesters get tired after 3 days of protesting and go back home. With this type of behaviour (on top of the fact that we should be expecting non-linearity), we could have many more ways that the process could end in. It could stabilise at one point and then die out. Or some people would join in at the same time others would get tired and we could observe ‘waves’. With more complicated processes we may also expect more variants of end results.

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People, Networks and Neighbours: Understanding Social Dynamics

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