The Decline Effect

The Decline Effect offers a radically new perspective on
how the world works. In field after field, there are ‘orphan’ laws,
some a century old, that contradict the classical idea of independent
events. These ad hoc observations turn out to obey a universal
principle. To put it simply, rare events and extreme values tend to
slowly become rarer. As a system grows larger, or older, or both, such
events and values take up a smaller proportion of the whole.

This single principle explains failing customer loyalty, crumbling political
stability, less infectious epidemics, eroding participation in
religion and politics, and the age-old mystery of success on the
battlefield.

For example, as a church grows in numbers, its members become less  committed. Whether we measure that commitment in terms of regular attendance, or financial donations, or responses to surveys indicating subjective commitment, the result is the same. We can plot the average tithes for churches with 1,000 members, and compare that number to average tithes for churches with 10,000, or 100,000.  What we see is not just a decline, but a consistent scale-invariant decline. The percentage drop as we go from 1,000 to 10,000 is the same as we go from 10,000 to 100,000. Each tenfold gain in total numbers cuts average participation by half. Thus a very large church has a far less loyal, less interested membership than a small one. The differences between them are predictable.

When we look at participation in other human endeavors we find the same curve waiting. A large pool of voters is less likely to form a strong consensus in favor of one candidate than a small one. A large army fights more slowly, so that the casualties inflicted per hour or per battle fall by half for a power-of-10 increase in numbers. A large audience for an Internet video is half as likely to post a comment once it has gotten ten times as large. And so on.

These findings overturn long-held beliefs about classical
probability, randomness, and spontaneous order, in favor of the
increasingly popular Bayesian maximum entropy framework.

The book is written in a layman-friendly style with a minimum of equations and more than 200 graphs and illustrations, covering a huge variety of subject matter from comic book sales to species abundance in the Borneo rainforest. It is squarely aimed at  anyone interested in science, or business, or culture, or mathematics.

The same pattern exists in nature as well. It applies to the spread and lethality of viruses, cell metabolic rates, and much more.