Logistic Growth of Movements – Exponential, but with Limits

I’ve talked some about exponential growth of a social movement in Logarithmic Planning for Exponential Growth. This is the only way that a small movement can grow large enough to involve a large part of society. But the reality is a little more complicated. Let’s see what movements and organizations really do. We can use this better understanding of growth to better evaluate and improve our organizing models.

Exponential Growth Revisited

To recap, a group of 20 people growing at an exponential rate, doubling every 2 years would be at 40 people in 2 years, 80 in 4, and so on to 640 in 10 years. That’s something, but if it continues, it would reach over 20,000 in 20 years, and over 20 million people in just 40 years. But hmmm, in 70 years, it would reach twice the entire human population, and beyond that it just gets more ridiculous. Obviously we’re missing something that would stop the process before it gets to the impossible.

Here's a graph of exponential growth using the world's human population growth as an example. You can see the distinctive "hockey stick" shape, where growth looks slow until the elbow around 1900 where growth appears to explode. In reality, there is no precise mathematical point where this happens, but despite a consistent growth rate, there will be a period where things really seem to be taking off compared to some time in the past.

Hockey stick shaped exponential growth graph

Introducing Logistic Growth

In reality, any process that experiences exponential growth also has a limit, and growth doesn’t just proceed at top speed until it slams into that limit. Instead, growth slows the closer it gets to this limit. Instead of the hockey-stick shaped graph of exponential growth, a more accurate model is the S-shaped curve of logistic growth.

Logistic growth shares much of the features of exponential growth. There’s the slow but steady introduction—the curve looks flat there unless you look very closely. After that is the “elbow”—the point where things seem to explode.

But there are some new features. An anti-elbow at the top followed by rapidly stalled growth. And between the elbow and the anti-elbow, there’s an inflection point. This is where explosive exponential growth starts to slow. Growth is still fast, so you might not notice that you’re headed right for the anti-elbow and the stagnation that comes with it.

S-shaped logistic growth graph

This is of course another simplification, but it’s a useful model that matches many growth processes in movements as well as a wide range of natural physical and biological processes. Some examples are human population growth, nuclear chain reactions, and the spread of communicable disease. These are often talked about as exponential growth, but in reality they are examples of logistic growth that just appear exponential up to a point.

Limits to Growth

The most important point that logistic models add to exponential is the concept of a limit. This limit can be many things. In a physical process such as a fire, the limit is defined by the amount of fuel. Once the fuel starts to run out, the fire first slows its growth, then once the fuel is fully consumed, the fire completely stops. In an earlier post, Small Group Size Limits and Self-Reinforcing Feedback Loops, I talked about a much smaller, self-imposed limit caused by organizational structure and process for communication. There are a wide variety of possible causes for these limits.

Likewise, even the most successful movement in a city is ultimately limited by something short of the total population of the city. More likely, the organizing model or the pent-up “fuel” that drives the growth will have some built-in limits far short of this theoretical maximum. In a city of 1 million, a movement organizing for the bottom 99% won’t get many from the 1% and not everyone in the 99% will ever agree with the goals of the movement or have the ability to meaningfully get involved. A theoretical upper limit of 1 million will never be reached, but for many reasons, anything even above 100,000 would be very optimistic.

If you’ve been organizing for some time, you’ll probably be more familiar with limits far closer to 500 than 500,000. In fact, your biggest successes have probably followed logistic growth, starting small, ramping up quickly and then leveling off after mobilizing just a few dozens or hundreds of people.

This can be frustrating because organizing models and actions that had great success seem to get stuck. It’s tempting to think that the problem is a deviation from the successful model, that returning back to “what works” will bring back continued exponential growth. And that might be part of it. But more likely you’ve hit a limit of your model, and the only way forward is to adjust the model.

Another interpretation, one that can be an obstacle to organizing, is that the model is correct but the fuel isn’t there due to people or society not being “ready”. This interpretation leads to a doubling-down on the model—keep spinning faithfully until conditions change themselves somehow to provide fuel to your correct organizing model. While there is some truth to this, as mass receptivity ebbs and flows over time in ways generally beyond our control, it can be a missed opportunity as well as an irrational, conceited presumption.

We shouldn’t ignore lessons from historical struggles, but we have to continually evolve our analysis and action. An organizing model is a hypothesis, an educated guess at a way forward. We can be sure that some potential models are doomed to failure, but we can never assume that we have chosen the perfect path forward. When a model stalls, we must take this fact as new empirical evidence—reality is telling us something about our initial guess. We can choose to ignore this message, but if we stalled at dozens of people rather than tens of thousands, it’s likely we have misplaced faith in our direction and will never advance without trying something new.

Likewise, refusing to adapt misses the opportunity to experiment new models and variations. Spinning in place teaches us nothing and gets us nowhere, but adapting and experimenting lets us learn from our mistakes and tap into new possibilities for expanding our limits. Maybe we’re stuck because people in society are content and apathetic, or maybe we have failed to successfully agitate and find a powerful motivating source of anger and hope. Or maybe we have the fuel, but our model has self-limiting flaws built into it. See Small Group Size Limits and Self-Reinforcing Feedback Loops as one of many sources of potential self-limitation.

Conclusion

Regardless what you do to respond to this limit, the important thing to remember is that for any given organizing model and societal context, there will always be a limit. We can’t control the societal context, but our choice of organizing model, our structure and process, and the way we execute on the model can make the difference between a very low, self-imposed limit versus a much higher natural limit.

But logistic growth and its concept of a limit isn’t the end of the story. In practice, social movements rarely experience a flat-line limit as suggested in logistic growth. This is yet another simplification, more accurate than exponential growth as a model, but it falls apart at the end.

Next: we’ll take a closer look at what happens after the limit is reached.