Beware Simple Models

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

Thus begins a rather interesting and fun post by Vi Hart and Nicky Case on “The Parable of the Polygons,” which explores a simple model for the segregation of neighborhoods.  It’s got some cool interactive parts of the page, and I encourage you to read it.  But the short version is that they explore this model:

  1. There’s a population of two types of entities, squares and triangles, in a grid.
  2. The “happiness” of an entity is based on how many of its eight neighbors are like or unlike it.
  3. Unhappy entities move to a random free square in the grid.
  4. With these rules, even a fairly small bias towards wanting to have some neighbors of like shape (eg, if you’re a triangle, wanting at least three of your eight neighbors to also be triangles) lead to fairly highly segregated total populations.
  5. But also, if you become unhappy if all of your eight neighbors are of like shapes, the overall population desegregates.

And this is all interesting, and very well-illustrated on the page.  The interactive elements are neat.


The article is pretty strongly trying to tell you that this model explains some profound truths about why American society remains in some areas pretty strongly de facto segregated.  And they extrapolate to the model to tell you how you can contribute to desegregating American society.

And those lessons are wrong.

So here’s the deal:  this model is based on the work Thomas Schelling, who is a Nobel-prize winning economist, and he did some work that basically they turned into the above model, in the late 1960’s and early 1970’s.  As you might imagine for work that won the Nobel prize, Schelling’s work has been fairly well-examined, and it’s certainly not without merit.  But I imagine that Schelling would not draw the straightforward and personal conclusions that Hart and Case do.  The problems with drawing the conclusions they do from the model are several:

One thing that the model predicts is that segregation, once it happens, does not reverse itself naturally unless individuals actively move out of segregated neighborhoods because they are segregated.  That is, it’s not enough to simply not seek out segregated neighborhoods, you must actively look for diverse ones.  But that is because the model assumes that there is no reason anyone will ever move unless the “kind” of neighbors they have falls outside their preferences.  In the real world, people move for a variety of exogenous reasons — if you simply said that every model has a 2% chance to move on any given “turn,” you would find that the persistence of segregation no longer holds — that is, the state of the population would reflect current preferences and recent past, not long-past.

Clearly, in the real world, segregation has persisted.  That’s because the real world is not this model.

And more so: models can have predictive power while not actually accurately representing the thought processes of any individual.  That is, you shouldn’t draw an individual lesson, as Hart and Case do, from a model even if the model does a good job to predicting the world.

In this case, particularly, in the modern world, it is clear that a substantial amount of segregation has an economic component.  That is, if you say, “Why doesn’t white person A move into black neighborhood B,” then a good percentage of the time, the answer is, “Well, white person A thinks that that neighborhood has insufficiently nice houses, an overly high crime rate, and bad schools.”  In other words, basically white person A is richer than neighborhood B.  We know that being white is correlated with wealth, and being black is correlated with being poor, so certainly some part of segregation is explained by this.

For the sake of argument, imagine that white person A genuinely has no problem with black people who are sufficiently wealthy, and genuinely would have no problem moving into black neighborhood C, which is wealthy.  In that case, it does no good to tell that white person to seek out slightly racially diverse neighborhoods.  They’re happy to do that, but that causes them to only move to already-integrated neighborhoods, and does not increase the diversity of the overall population at all.

Then take it one step further.  Imagine that white person A tends to imagine that black neighborhoods they see are poorer, higher crime, and have less good schools than is the reality.  So white person A is indeed part of the force of segregation — but this is so without white person A having any animus towards any particular black person.  If you tell white person A to seek out diversity per se, they are again happy to do so, but they’ll tend to seek out neighborhoods at the high end of their acceptable price range (because they will tend to imagine that those neighborhoods are slightly less good than the actually are).  This pulls whites in the middle income towards upper-income areas, and leaves poorer areas more segregated than they otherwise would be.

Of course Hart and Case understand that their little squares-and-triangles model does not capture the full complexity of the world.  They say as much.  But they still want you to draw lessons from it, and those lessons — even if they are in and of themselves correct (I think they’re virtuous things to believe, though I also don’t think that even if they’re adopted by everyone will they cause much change in the world) — aren’t based on truths about the real world.

Simple models can be really powerful ways to understand parts of complex things.  But simple models are also the way that people develop dogmatic, black-and-white views of the world, and end up pursuing agendas that are actually harmful to their intended goals.  Imagining that the world is simpler than it is is a pervasive intellectual error.  Neat interactive elements to a page should not distract us from that.  Nobody builds web-pages that show squares and triangles and then say, “Squares don’t live next to triangles due to complex self-reinforcing systems that are the results of fifty different semi-dependent factors, and nobody knows how to change this.”  But that’s the truth, and it serves nobody to pretend that segregation is simpler than it is.


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