Forest fires and influence

Pic courtesy matchstick

Finally had time on the long journey west yesterday morning to read the Duncan Watts paper featured here on Friday. Think I understand what he's doing.

First the paper is based on a series of simulations which aim to test some of our most common assumptions about how influence spreads through a population. The maths - though not simple - is not deliberately obscure and even I managed to follow it through, albeit slowly.

Second, what Duncan et al suggest is that our 'common sense assumption' that some individuals are much more influential than others doesn't seem to work in the real world of mass behaviour. Or rather, their influence is rather less than we'd imagine.

"In our models, influentials have a greater than average chance of triggering this critical mass, when it exists, but only modestly greater, and usually not even proportional to the number of people they influence directly"

Third, he flips the thinking round. What matters not is who is particularly influential but rather who is particularly susceptible to being influenced.

This he captures in the memorable image of forest fires:

"Some forest fires, for example, are many times larger than average; yet
no-one would claim that the size of a forest fire can be in any way attributed to the
exceptional properties of the spark that ignited it, or the size of the tree that was the first
to burn. Major forest fires require a conspiracy of wind, temperature, low humidity, and
combustible fuel that extends over large tracts of land. Just as for large cascades in social
influence networks, when the right global combination of conditions exists, any spark
will do; and when it does not, none will suffice"

Fourth, he starts to explain why we might want to see the influentials as being more important than they really are:

"anytime some notable social change is recognized, whether it be a
grassroots cultural fad, a successful marketing campaign, or a dramatic drop in crime
rates, it is tempting to trace the phenomenon to the individuals who “started it,” and
conclude that their actions or behavior “caused” the events that subsequently took place.

Indeed, because the outcome is already known, it is always possible to construct what
looks like a causal story by picking out some of the defining details of the individuals in
question—even when success is completely random...it is tempting to assert that these individuals must have been special in some way—otherwise, how could the striking event that we now know happened have come to pass? Just because the outcome is striking, however, does not on its own imply that there is
anything correspondingly special about the characteristics of the individuals involved or that their participation was either a necessary or sufficient condition for a change of the kind that occurred to have taken place"

Download the paper for yourself here. I think it's a 'keeper'.