27 January 2013
Let's look beyond the confines of one country. By trial and error, most countries have ended up with first house sizes that correspond to the cube root of their populations. For a US population of 315 million, this would mean 680 seats in the House. The US followed the cube root pattern up to the early 1900s, when the House size was frozen at 435. Yet the population kept growing. In contrast, most countries change the size of their houses when the population changes. The cube root of the population rule has been known for more than 30 years. (See, most recently, Rein Taagepera, Predicting Party Sizes, Oxford University Press, 2007).
Why does cube root work for most countries? Apply the engineering notion of minimizing major cost. Consider the communication load on a single representative. With too few representatives, each has too many constituents. With too many representatives, their communication load inside the assembly shoots up. Cube root of population turns out to be optimal. The US House needs to be bigger than the current one, but much smaller than in Johnson’s proposal.