Pareto’s Law

Well, Pareto never actually used 80/20 in a phrase. The term came in later when Dr. Joseph Juran attributed the 80/20 rule to Pareto. His principle was known as ‘the vital few and the trivial many’. In Pareto’s understanding, it meant 80% of the wealth is owned by 20% of the people.

This 80/20 rule applies to most parts of my life. 80% of my calls are only from 20% of people in my contact list; 80% of my Facebook messages are from 20% of my friends; 80% of blogging comes from 20% of my time. The theory suggests that we focus more on the 20% and make our time more worthwhile. However, as F. John Reh suggests, the theory is flawed. He says, helping the good become greater is, better, than helping the great become excellent.

Power laws formulate in mathematical terms the notion that a few large events carry most of the action.

Even so, it is surprising that there is a power law distribution behind every webpage. Smaller events, like webpages, coexist with larger webpages which are called nodes. In the Barabasi reading, it says that a random network is like a highway system, where the nodes are the cities and the highways are the links. In a scale-free network it is like a flight route, where the nodes have a few links, and are held together by a few highly connected hubs, which is similar to the power law distribution. According to Huberman here, he analyses several activities:
1. Distribution of pages per site follows a pareto style distribution

2. Distribution of links per site follows a pareto style distribution.

3. Number of clicks per session follows a pareto style distribution.

4. Distribution of visitors per site follows a universal power law. Pareto is omnipresent.

We would come to see that power law distributions determine structural stability, dynamic behaviour, robustness, and error and attack tolerance of real networks.

“The fact that the networks behind the Web, Hollywood, scientists, the cell, and many other complex systems all obey a power law allowed us to paraphrase Pareto and claim for the first time that perhaps there were laws behind complex networks.”

 

We now know that the discovery of hubs are a consequence of power laws. But what are the mechanisms behind it?