Another Necessary Story.

The statistician began his evidence to Parliament. “I imagine you’re all aware of the natural or Gaussian distribution, a bell shaped curve like this”, he showed an example. They all nodded sagely. “In the present unrest where a relatively small proportion of the populous are demonstrating on the streets one might well assume, in the distribution between approval and disapproval, the disapprovers would appear on the left at the beginning of the curve,” he showed a small section of a curve filled in red, “a small proportion of those prone to extreme dissatisfaction.” The PM was heard to say,  “Exactly. I don’t know what all the fuss is about.” The statistician continued. “If say 2% of the population riot then 98% must support your policies. Vigorous nodding and vociferous approval. “I’m glad you see the power of statistical analysis. I have though here another distribution curve that compares one’s opinion with one’s decision to take action.” He held up a new diagram similar to the previous one. “On the left are the individuals who, on issues that concerns them, always take action and the right those who never take action. Let’s say 0% and 100%. Notice for this distribution the median occurs at around 2% on that scale.” “Exactly as one might expect” added one helpful member. The PM joined in, “It seems to me you’re rather stating the obvious.” “On the contrary Prime Minister. This distribution indicates that for every individual that takes action on some concern there are forty to fifty people who do not; one presumes through laziness, illness, fear, inconvenience etc. Perhaps you can begin to see the implications. The one million that took to the streets against the Iraq war in fact represented some forty million that didn’t but had the same concern, that’s over 70% of the population.” “That’s a totally unfounded assumption, it’s preposterous” retorted the PM. “Please consider this. One million took action against and exactly how many took action for? Records show as many as fifty thousand. On that same basis, that they each represented 40 to 50 people, they accounted for around 3 million. In total 53 million plus 7 million don’t knows.” “In other words over half the population have an opinion but don’t act on it. Am I right?” interjected the PM. “Exactly.” “Then what are we worrying about?” “Our third distribution (to general groans) was with regard to this. One might consider it the first differential of the previous one, the rate of change of opinion. Because the median, the mass of the people, was at 2% it’s clear that any small change in that median will affect a huge number of people. A 1% change for example would put 2 million on the streets, with many thousand prepared for violent action. It represents great volatility, the nearness of a tipping point; the very reason you called me here today. According to this statistical analysis gentlemen there will shortly be a revolution.”