Violence decline is just a scaling effect

AAAS Science mag reports:

Are people in big, modern societies more or less violent than our forebears? The answer is neither, according to a controversial new study: People who lived in small bands in the past had no more proclivity toward violence than we do today. The finding—based on estimates of war casualties throughout history—undercuts the popular argument that humans have become a more peaceful species over time, thanks to advances in technology and governance. ...

But a team led by anthropologist Rahul Oka at the University of Notre Dame in Indiana wondered whether there was a mathematical explanation for why fewer people proportionally are lost to violence nowadays. They reasoned that as populations get bigger, their armies don’t necessarily grow at the same rate. In a small group of 100 adults, for example, it would be perfectly reasonable to have 25 warriors, says anthropologist and study co-author Mark Golitko, also at Notre Dame. But in a population of 100 million, supporting and coordinating an army of 25 million soldiers is logistically impossible, to say nothing of such an army’s effectiveness. Researchers call that incongruity a scaling effect.

I made a similar point on this blog in a 2011 post:

Steven Pinker's The Better Angels of Our Nature is one of the better-selling science-related books of the year. As noted below, it claims that violence has declined over history in spite of Christianity.

Pinker's quantitative analysis seems to based on the assumption that violence should be expected to scale linearly with population size. So he compares the Mongol invasion to recent wars by counting deaths, as a proportion of the population at the time. His trick has the effect of making the Mongol invasion seem much more deadly than it was.

This assumption seems dubious. If we have a population of N people, and we assume that each pair of people has a 1% chance of being enemies, then we expect about 0.01N² pairs of enemies. If violence occurs between enemies, then we might expect violence to grow quadratically in N.

However civilization would be impossible if violence grew that rapidly. Maybe it makes more sense to assume that potential friendships grow quadratically in N. Then maybe societies can use those friendships to self-organize into peaceful communities, and violence would grow sublinearly in N. Maybe violence only grows like the square root of N, or even the logarithm of N.

I posted some additional criticisms of Pinker's book in 2012.

Pinker's book got a lot of praise, and this scaling problem seemed obvious to me. Was I really the only person to notice this problem in 6 years? Hard to believe.