STINKING HIPPIES ARE AN EMERGENT EQUILIBRIUM.

Saturday's Power Line "Week in Pictures" included among the amusing headlines, "Mathematics explains why non-conformists always end up looking alike."  Look, you can do sensitivity analysis with evolutionary game theory, but logic and proportion feed your head, even if you've had some kind of mushroom.

While anti-conformists may, at first, succeed in devising their own personal brand of sartorial rebelliousness, it’s followed by an inevitable, if unintentional, synchronization around a single appearance. [Brandeis mathematician Jonathan] Touboul’s study looks at how such people seem to inevitably become synchronized. He suspects that a major influence on the way it happens may be the speed of propagation of styles through a culture.

Not everyone learns about or adopts new styles in the same way. Some follow fashion closely, some go by word of mouth, and some emulate the appearance of well-known individuals they admire. In the latter case, the tipping-point may occur after a mutually-revered celebrity adopts a new fashion.

The modelling is simple enough (two types of individuals, different speeds of propagation of a fashion choice, or a perception that stocks are trading at unsustainably high or unsustainably low price) and yet the outcomes are deterministic chaos.

In Touboul’s simple model, one is either a member of the mainstream or a hipster (no snarky connotation intended), and he explores different hipster-to-mainstream ratios. He also factors in different amounts of time it might take a hipster to detect a new style and respond to it.

Simple as his model is, Touboul has found that experimenting with those two factors produces a surprisingly complex set of behaviors, though synchronization always occurs. Even when he revises his model to allow for more than two types of people, synchronization still occurs.

Often, of course, roles may swap when there are so many hipsters that they become the mainstream. “For example,” says Touboul, “if a majority of individuals shave their beard, then most hipsters will want to grow a beard, and if this trend propagates to a majority of the population, it will lead to new, synchronized, switch to shaving.” An odd sudden swap occurs when the number of mainstreamers and hipsters is roughly equal — everybody winds up switching together between different trends.

The work appears to be in the simulation stage, calibration of the dynamics to such phenomena as long hair or tattoos or skirt lengths, let alone testable implications that might be susceptible to statistical analysis are for future research.

It's likely asking too much at this stage of modelling to capture whether mutations in style or behavior confer evolutionary advantage on adopters of them.