The diffusion of iPhones as a learning process

All theoretical and empirical diffusion studies agree that an innovation diffuses along a S-shaped trajectory. Indeed, the S-shaped pattern of diffusion appears to be a basic anthropologic phenomenon.

This observation dates as far back as 1895 when the French sociologist Gabriel Tarde first described the process of social change by an imitative “group-think” mechanism and a S-shaped pattern.1 In 1983 Everett Rogers, developed a more complete four stage model of the innovation decision process consisting of: (1) knowledge, (2) persuasion, (3) decision and implementation, and (4) confirmation.

Consequently, Rogers divided the population of potential adopters according to their adoption date and categorized them in terms of their standard deviation from the mean adoption date. He presented extensive empirical evidence to suggest a symmetric bell shaped curve for the distribution of adopters over time. This curve matches in shape the first derivative of the logistic growth and substitution curve as shown below. 

In the graph above I applied the Rogers adopter characterization to the data we have on the adoption of smartphones in the US. The latest data covering September is included.

The fact that smartphones in the US follow the theory is exciting, but what can we conclude about the adoption of specific platforms? There has been quite a bit of turnover in the leadership of the market in the first half of the time frame given. You can see this more clearly in the following fractional market share transformation.

Note that, with the exception of the iPhone, if each platform is studied individually, it would not follow a logistic (i.e. linear) pattern even though, as a whole, the technology does.

This then is the big puzzle: while we might be able to predict how smartphones will diffuse into society, we can’t seem to predict how any single firm will fare. This means that an investor cannot make a credible “bet” on the technology2. If they choose a single company as proxy, chances are they will lose. If they bet on a basket of companies then, again, chances are they will lose. There is usually one unforeseeably clear winner.

Before we get further into the question of picking winners or predicting the future division of share among rivals, we should understand the underlying causes for this pattern of adoption.

Rogers concluded that the learning behavior of individuals is the underlying cause of the symmetry of the diffusion process.

At the beginning, when an individual is confronted with a new (learning) situation they make many mistakes. These mistakes are gradually reduced (by learning) over time because more and more information is received and acts as a stimulus. The gain in learning per trial is proportional to the product of the amount already learned and the amount remaining to be learned before the limit of learning is reached.

Arnulf Grübler3 explains:

This is exactly equivalent to the F(1-F) transformation of the logistic curve. It should be emphasized that these properties of the learning process were found in real learning situations and are confirmed by a large number of laboratory and field experiments. Thus each adoption of an innovation in a social system is equivalent to a learning trial by an individual. Thus, the symmetric diffusion pattern results from the way messages about an innovation are emitted and processed by social learning.

So these observers of the process assign learning behavior as the cause for adoption of a technology. Can the learning behavior be applied to individual platforms? It’s tempting.

The hypothesis would go as follows: adopters are not only processing messages about the new technology but they are also trying different platforms as they enter and as they upgrade their phones. If we see platform choice as a learning process then if one platform has a natural advantage, it settles into a dominant position as users “learn” of its advantage. Conversely, if no platform has an advantage then platform “churn” repeats as rivals gain/lose positions of leverage in the market.

The pattern shown so far seems to point to Apple’s iPhone having a logistic pattern indicating that it might be benefiting from a learning pattern. The alternative platforms may simply be jockeying for temporary advantage.

It’s an interesting hypothesis. To be developed further we need to answer what any learnable advantage might be. I suspect it has to do with the ability to solve unmet and unarticulated needs. In other words, that the winning product solves a set of “jobs to be done” which are difficult to pin down and are perceived rather than defined.

1. Tarde was probably influenced by mathematician Pierre François Verhulst who first published the logistic function in 1845 [↩]
2. Indeed investors often get burned when new technologies emerge. While the technology booms, individual firms supplying it often fail. See the history of transportation, communication, computing and energy. [↩]
3. The Rise and Fall of Infrastructures, Physica-Verlag 1990 [↩]