Dynamic Models of Segregation

Thomas Schelling, 1971, Journal of Mathematical Sociology

US neighborhoods, schools and clubs tend to be “U-shaped”: nearly all one group or the other, with few stable mixes in between.
How much segregation can come from individuals’ own choices about who lives around them?

Even with only a mild preference for neighbors that are like them, the whole town ends up divided.

There is no simple correspondence of individual incentive to emergent collective results.

Let's explore Schelling's model

ncase.me/polygons · 2014 · public domain

This is a story of how harmless choices can make a harmful world.

These little cuties are 50% Triangles, 50% Squares, and 100% slightly shapist. But only slightly! In fact, every polygon prefers being in a diverse crowd:

You can only move them if they're unhappy with their immediate neighborhood. Once they're OK where they are, you can't move them until they're unhappy with their neighbors again. They've got one, simple rule:

“I wanna move if less than 1/3 of my neighbors are like me.”

Harmless, right? Every polygon would be happy with a mixed neighborhood. Surely their small bias can't affect the larger shape society that much? Well...

drag & drop unhappy polygons until nobody is unhappy:

(just move them to random empty spots. don't think too much about it.)

And... our shape society becomes super segregated. Daaaaang.

Sometimes a neighborhood just becomes square, and it's not their fault if no triangles wanna stick around. And a triangular neighborhood would welcome a square, but they can't help it if squares ain't interested.

In this next bit, unhappy shapes automatically move to random empty spots. There's also a graph that tracks how much segregation there is over time.

run this simulation a few times. what happens?

What's up with that?

These are good shapes, nice shapes. And yet, though every individual only has a slight bias, the entire shape society cracks and splits.

Small individual bias can lead to large collective bias.

Equality is an unstable equilibrium. The smallest of bias can push a whole society past the tipping point. Well, what if we taught these shapes to have zero bias? (Or if you're feeling particularly nasty today, more bias?)

use the slider to adjust the shapes' individual bias:

Notice how much more segregated things become, when you increase the bias beyond 33%.

What if the threshold was at 50%?

Seems reasonable for a shape to prefer not being in the minority...

So yeah, just turn everyone's bias down to zero, right? Haha, NOPE. The real world doesn't start anew with a random shuffling of citizens every day. Everyday, you're not shuffling.

world starts segregated. what happens when you lower the bias?

See what doesn't happen?

No change. No mixing back together. In a world where bias ever existed, being unbiased isn't enough! We're gonna need active measures. What if shapes wanted to seek out just a lil' more variety?

Woah. Even though each polygon would be okay with having up to 90% of their neighbors that are like them, they all mix together! Let's see this play out on a larger scale, when we change the amount of bias and anti-bias for all shapes.