Fisher and Pry put forth “A Simple Substitution Model of Technological Change” in 1971 (Technological Forecasting and Social Change, 3, 75-88).

(The paper is not publicly available, for free, at the time I wrote this post.)

It could be useful in explaining the gap left behind by Bass, and the downsides of all the charts I showed Monday.

I like this paper.

Here’s the first paragraph:

“For people who attempt to forecast the future, there is a continuing need for simple models that describe the course of unfolding events. Each such model should be based upon easily understood assumptions that are not available for unconscious or invisible tampering by the forecaster in his efforts to make the future what he wants it to be. The model should be easy to apply to a wide variety of circumstances, and should be easy to interpret. It is our purpose to describe such a model and, by way of example, to apply it to a few illustrative forecasts.” (p. 75)

The model is based on three assumptions:

  • “Many technological advances can be considered as competitive substitution of one method of satisfying a need for another.
  • “If a substitution has progressed as far as a few percent, it will proceed to completion.”
  • “The fractional rate of fractional substitution of the new for old is proportional to the remaining amount of the old left to be substitution.”

That third assumption has a special call out to a special form of Pearl’s Law, “The Biology of Population Growth”, 1925).

By saying that I like the paper, I’m not saying that the model is valid in all circumstances. All models are imperfect. They’re merely projections of reality onto a simplified plane.

A few questions:

  • Can you see problems in the assumptions?
  • Can you understand why they made such assumptions?
  • How would you change the assumptions?
  • What consequences would your adjustments have?
  • Would your updated model be better at predicting the future?

I leave the debate about ‘substitution’ versus ‘complimentary’ social platforms for another time.


I’m Christopher Berry.
I tweet about analytics @cjpberry
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