The Parable of the Polygons: How Individual Decisions Create Large Collective Impacts

No, Lake Michigan Has Not Been Invaded by Little Shapes With Faces…

This blog and firm are based on the premise that a group of people making seemingly independent, individual decisions can have colossally large collective impacts to wreck or save the world; our decisions are often more important than we realize. Today I have a perfect illustration of how this can work. It has to do with the age-old question of what happens when you combine game theory, sociological theories of segregation, visualization, and little shapes with faces on them.

…You weren’t asking that? Well, I’m going to tell you anyway. The answer is “The Parable of the Polygons,” and it is nothing short of brilliant.  

It starts with a very basic premise: We’ve got triangles and squares, and they really benefit from living together in diversity. However…


This doesn’t seem unreasonable, right? No one wants to be the only person like themselves in their neighborhood (yes, I know that race should not be our only determinant for whether we are like our neighbors, but let me stop you there: we don’t live in a post-racial society, and, like it or not, this is how most people at least subconsciously think about these things). The problem is that, since we don’t just live in a checkerboard, such a simple request, when scaled up to the level of society as a whole, has drastic impacts. When everyone who is unhappy moves to a different location, we reach this equilibrium:

No one is unhappy, but I'm seeing a whole lot of "meh" as well...

No one is unhappy, but I’m seeing a whole lot of “meh” as well…

The problem in loose economic terms is that while the utility gained from living in a place of diversity is higher than the utility gained from living in conformity, the cost of moving is high enough that only those who are truly in minority have enough incentive to move to a new place. As everyone else accepts the status quo, the equilibrium is a state in which all individuals have huddled together with like-minded others, only experiencing diversity at the margins of their neighborhoods.  In the real world, it could sometimes be said that there is no such diversity at the margins, as roads or other formal structures create social or physical barriers that we seldom have a necessity to cross (the old “other side of the tracks” adage is a good example).  This is how we end up with the racial map of Chicago at the top of this post where few neighborhoods exhibit any kind of diversity.

Fortunately, the people at Parable of the Polygons have a solution.  If people’s priorities change incrementally, just to the point that each individual desires to have one neighbor who is not like them, segregation decreases drastically:

As Vi Hart and Nicky Case, the creators of “The Parable of the Polygons” conclude, “All it takes is a change in the perception of what an acceptable environment looks like. So, fellow shapes, remember it’s not about triangles vs squares, it’s about deciding what we want the world to look like, and settling for no less.”

So please, try it out for yourself! You can see the original post here, or you can check out a modified version here, which adds in pentagons and gives you some extra information in the graphs as well (here’s a quick key to their graphs: red=segregation %, blue = % unhappy, yellow = % meh). It’s definitely worth a look. Plus, both include a “sandbox” at the bottom which allows you to set your own parameters and play around.

What are your thoughts? Let me know in the comment section below!

I want to personally thank Vi Hart and Nicky Case for coming up with such a beautiful visualization, and for putting it in the public domain as well. If you are interested in further reading on this topic, check out Thomas Schelling’s original 1971 paper which theorized this model for segregation, and W.A.V. Clark’s 1991 paper which tested out the model.  Schelling’s original is chock full of interesting insights like this:

Small minorities cluster together even more strongly than those that are more evenly distributed

“With extreme color ratios, like five to one or more… the proportion of initially satisfied individuals is so small that nearly everybody in the minority moves.  Everybody, furthermore, moves toward whatever cluster of like-colored individuals he can find; and the number of such clusters declines disproportionately as the minority becomes smaller.  The result is that the minority forms larger clusters, large enough to cause even a tolerant majority to become locally dissatisfied.” -Thomas Schelling




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