Expert comment
5 min read

Tending the lily pond: Exponential growth and scenario planning

The Covid-19 pandemic has left us grappling with how to engage with exponential - as compared to linear - change. The OSPA can be adapted accordingly.

Many users of scenario planning in the pandemic have been grappling with how to best engage with exponential - as compared to linear - change.  Exponential growth (or indeed, shrinkage) refers to change where the rate of change is itself accelerated and - for time at least - unbounded. So instead of calculating change by adding two and two to get four and then adding another two to get six, one adds double the change each time so that the pattern is two plus four plus eight plus sixteen plus thirty-two and so on.  This rate can result in change feeling initially slow and incremental, then surprising when it later appears ‘suddenly’, becoming rapid and overwhelming.

For example, here in the UK from where we write, Public Health England announced on the 22 January that they were moving the risk of the virus to citizens from being very low to low, yet within 13 weeks a total of 41,000 people had died (April 22 2020 data) in the UK. 

Cognitive psychologists explain the difficulty of grasping exponential change as an ‘exponential growth bias’, where one treats this type of change as if it was linear. 

Wagenaar and Sagaria’s research suggests that we have an intuitive preference to see growth as additive and steady and not as multiplicative, where change is first felt as slow, and suddenly then as very rapid.  So we hear expressions such as ‘it spread like wildfire’ and ‘technological disruption’ (driven by Moore’s law which refers to the doubling of transistors on a computer chip and thus available computing power per chip every two years) being used to describe exponential growth.

The famous story of the king who mistook how much corn it would take to reward the inventor of chess gives a perfect example of the exponential growth bias. The inventor asked to be paid by having one corn kernel put on the first square, two on the second and so on doubling the amount for each square. The king felt this was a very humble and modest request until the calculations were done and he was shocked to learn that the total was a twenty figure number and more than all the corn that existed in the world at the time. In finance, this bias has been found to explain why people intuitively underestimate the impact of compound interest on savings and loans.

A Lily Pond photographed by Jacky Watt

The tendency to treat exponential growth as if was linear appears to be a key reason for organisations under-preparing for developments operating on such a trajectory. The bias also helps explain the initial underestimation of the speed and the severity of the pandemic, and why many find the experience so disorientating. 

Scenario planning is a well-established strategic practice for helping people navigate deep uncertainty, and undertaken well, can be deployed to help address the exponential growth bias. The experience of Covid-19 is providing many invaluable insights about conducting scenario planning to engage with deep uncertainty generated by exponential growth. Here, we offer some guidance for users of the Oxford Scenario Planning Approach (OSPA):

1. Explain to users the nature of exponential growth

Highlighting the nature of exponential growth and the human bias against it, can be helpful for people to imagine how quickly substantial change can arise.  Consider using contrasting metaphors such as a line for linear growth and the lilypond for exponential growth.  If one lily emerges on day one, doubling every day and completely covering the pond on the 48th day, the pond will only be half covered on the 47th day.   In the current context, this conversation will alert people to this type of growth when conducting subsequent scenario planning engagements.  

2. Validate disorientation

Acknowledging and experiencing the bias against exponential growth, can validate the difficulty of engaging with it properly. Build in a sharing session of how people feel (as is done in Extinction Rebellion ‘fire circle’ meetings). This can render people’s disconcerting experiences acceptable, valid, and valuable and enable deeper learning.

3. Be discerning about growth trajectories

When conducting scenario planning, be attentive to the nature of change in the phenomena you are investigating. Look for percentage increases time on time (e.g., a percentage growth in something per annum). Note positive feedback loops to see where change is amplified and novel interconnections that can drive exponential growth. Don’t dismiss what appear to be small changes. Remember the story about the lily pond! 

4. Consider how exponential change is reflected in scenario time horizons and story arcs

After researching factors to be included in the scenarios, consider their trajectory and where exponential change is a factor. Use this information to determine a pertinent time horizon for the scenarios. Similarly, when developing the scenarios, consider the pattern of exponential change i.e. slow until it hits a threshold, becomes rapid, then stalls, and decelerates to reach a final level (like the Sigmoid or S curve).

5. Use tailored techniques to communicate exponential change

To counter the bias, consider ways to explain it in scenario storylines. Use relevant analogies from history or other industries. Similarly, communicate proportions in a way that highlights exponential change patterns such as decreasing time intervals between events.

6. Prepare to act early and quickly

Actions in the early stages of exponential change can have a disproportionate impact. Delay can mean organisations become overwhelmed and the actions of its members become constrained or highly expensive. This applies to risks, opportunities and new collaborations. From the scenario work, where the potential impact of exponential change is recognised as a significant factor for the organisation, consider and prepare quick, early responses.

7. Develop relevant monitoring signals for exponential change

Ensure that signals providing advanced warning about unfolding developments in the scenarios match the identified growth trajectory of the phenomena. In the case of monitoring for exponential change, look for signals that reflect a multiplier pattern or an acceleration, and which don’t discount slow change at the start. 

It is important to remember that Covid-19 is unlikely to be the only time we experience major exponential change in our future professional lives. Another candidate is climate change as a result of the official pursuit of year on year ‘business as usual’ economic growth (a classic example of exponential growth). Thus, take the opportunity to capture your learnings from the current experience and incorporate them into your scenario planning practices.

Thanks to Dr Jerome Ravetz from the Institute for Science, Innovation and Society at the University of Oxford for his helpful comments on exponential growth. As always, we welcome comments and questions.  Please email Trudi Lang and Rafael Ramirez