Parable of the Polygons
Parable of the polygons, developed by Vi Hart and Nicky Case, is a game that is based on a well-known economist Thomas Schelling’s model of segregation. Schelling’s model shows how individual bias could lead to segregation, which is especially useful in studies of neighborhood segregation of ethnic groups.
In the Parable, neighborhoods are occupied by even number of cute triangles and squares that are slightly “shapist”, and players only need to follow one rule, “I wanna move if less than 1/3 of my neighbors are like me.” In other words, if a shape is surrounded by less than 33% of its own type, it will be unhappy and reallocate to a new location.
This game can be related to the structure of balanced networks. If a complete graph is balanced, then either all edges are positive or nodes can be divided into two groups so that there are positive edges within each group and negative edges between two groups. When a shape is happy or meh, we may assume that they form positive edges with each other. In this case, it is a balanced network with all positive edges. With bias, on the other hand, we may assume that when a shape is unhappy, it forms negative edges with differing shapes. The nodes (shapes) can then be divided into two groups (the graph below, for example): the square node as a single group and all the other triangles as the other group. Triangles form positive edges within the group, while the square forms negative edges with the triangles. It becomes a balanced graph with two divided groups.
However, as unhappy shapes quickly reallocate, the 33% of bias can also cause an initially randomly generated neighborhood to soon become drastically more divided. It seems that segregation is inevitable. But is it?
Although it might be impossible to eliminate bias, the game, Parable of the Polygons provides us with a rather optimistic ending, which diverges from Schelling’s model of segregation in that it shows that the effects of segregation can be reversed when enough people take measure. The shapes will reallocate if less than 10% and more than 80% of their neighbors are the same. When the mode of the game is set differently, the shapes’ world looks quite diverse.