Small Biases Can Lead to Segregation

Source: Wired,  Dec 2014
Original: http://ncase.me/polygons/

Parable of the Polygons, and was built by Vi Hart and Nicky Case. It’s what that they call a playable blog post, part story and part game, set in an imaginary world of squares and triangles. While it might at first seem like an odd mathematical game, it delivers a lucid and very relevant lesson on real-world segregation.

The goal of the game is to move the squares and triangles around until they’re all happy. These shapes like living in a diverse world inhabited by squares and triangles alike – in fact they prefer diversity. But there’s a small problem. Each shape is slightly ‘shapist’. Here’s how Hart and Case put it,

“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 of society that much? Well…”

By playing around with these squares and triangles, you’ll discover how even slight biases towards similarly shaped neighbors can lead to total segregation. It’s a tour of the counter-intuitive math of segregation, first spelt out by the Nobel Prize winning game theorist Thomas Schelling.

But it isn’t all gloom, for the post also teaches us that if all shapes demand even the smallest bit of diversity in their neighborhoods (a slight anti-bias, if you will), then segregation plummets. The lesson here is that small individual preferences can create a large societal effect. It’s up to us to determine which direction we want that effect to go – towards a diverse world or a completely segregated one.

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