Game of Votes

The Voting Game is a simple model of political process. The game board consists of a grid of squares, each representing a voter of one of two (or several in extended versions of the game) political options (see Fig. 1). The grid is finite, but boundless: it is a surface of a torus. That is to say that the top and bottom edges (as well as left and right) are actually connected.

Fig. 1. The Voting Game simulator.

Each turn, one of the voters is picked at random. The selected voter is influenced in his/hers opinions by the neighbours, and so picks up the colors of one of them chosen at random. Thus, the voter living in a politically uniform area is highly likely to vote the same as his peers. In this mathematical world you can follow a reason in people's opinions, however opportunistic it might be.

The evolution of this system is quite interesting to watch. It seems that once one of the parties develops a numerical advantage large enough, the collapse of the democracy is imminent. It is in fact unavoidable. It might take a surprisingly long time though.

Here you can check the interactive simulator of the Voting Game.
You can generate random distributions of voters in whatever proportion you fancy. You can watch the politics evolve and imagine the governments rise and fall. You can influence voters at a click of the mouse. Live out your political fantasies.

The code is available here.

Fig. 2a. Initial uniform distribution.

Fig. 2b. The distribution after some time.

Mathematical models, regardless how basic, are often very useful and enlightening tools. They let you experience the process as it plays out, and realize that very often the simple rules do not yield simple conclusions. Many people choose to see the world simply laid out; yet the complexity always finds a way to break out.

Please check Vi Harts's wonderful Parable of Polygons if you haven't seen it yet (see Fig. 2). It is a mathematical model in similar vein that illustrates the importance of personal bias in the shaping of the broader societies.

Fig. 3. Vi Hart's Parable of Polygons (from: http://ncase.me/polygons/).