Behind the Cube Rule: Implications of,and Evidence against a Fractal Electoral Geography

In 1909 Parker Smith showed that the ratio of seats won by the two major parties in Britain was close to the cube of the ratio of their votes. Taagepera and Shugart argue, wrongly, that a fractal electoral map implies this. In fact, their premises imply that the seats' ratio will be the votes' ratio to the power of √3, not 3. However, in the six countries we examine, the figure is between 2 and 3. This implies that the electoral map is nonfractal, political allegiances becoming less ‘clustered’ as you move from a macro to a micro scale. Taking the United Kingdom, we ask if this is a result of the geographical pattern of income distribution, and find that this is even further away from fractality than is voting. This fits the well-known ‘neighbourhood effect’ whereby poor (rich) people in rich (poor) constituencies vote as if richer (poorer) than they really are.