Economix: Expand the US House

It is good to see the undersized nature of the US House of Representatives get attention in the New York Times‘s Economix blog. The author is Bruce Bartlett, who “held senior policy roles in the Reagan and George H.W. Bush administrations and served on the staffs of Representatives Jack Kemp and Ron Paul”.

Bartlett notes that,

according to the Inter-Parliamentary Union, the House of Representatives is on the very high side of population per representative at 729,000. The population per member in the lower house of other major countries is considerably smaller: Britain and Italy, 97,000; Canada and France, 114,000; Germany, 135,000; Australia, 147,000; and Japan, 265,000.

The strongest empirical relationship of which I am aware between population size and assembly size is the cube root law. Backed by a theoretical model, it was originally proposed by Rein Taagepera in the 1970s. A nation’s assembly tends to be about the cube root of its population, as shown in this graph.*

Fig 7.1

Note the flat line for the USA, indicating lack of increase in House size, since the population was less than a third what it is today. This recent static period is in contrast to earlier times, depicted by the zig-zag black line, in which the USA regularly adjusted House size, keeping it reasonably close to the cube-root expectation.

At only about two thirds of the cube-root value of the population (as of 2010 census), the current US House is indeed one of the world’s most undersized. However, there are some even more deviant cases. Taking actual size over expected size (from cube root) , the USA has the seventh most undersized first or sole chamber among thirty-one democracies in my comparison set. The seven are:

    .466 Colombia
    .469 Chile
    .518 India
    .538 Australia
    .590 Netherlands
    .614 Israel
    .659 USA

As expected, the mean ratio for the thirty-one countries is very close to one (0.992, with a standard deviation of .37). The five most oversized, all greater than 1.4, are France, Germany, UK (at 1.67), Sweden, and Hungary. (The latter was at a whopping 1.80, but has since sharply reduced its assembly size.) Spain, Denmark, Switzerland, Portugal, and Mexico all get the cube root prize for having assembly sizes from .975 to 1.03 of the expectation.

One thing I did not know is that an amendment to the original US constitution was proposed by Madison. According to Bartlett, it read:

After the first enumeration required by the first article of the Constitution, there shall be one representative for every 30,000, until the number shall amount to 100, after which the proportion shall be so regulated by Congress, that there shall be not less than 100 representatives, nor less than one representative for every 40,000 persons, until the number of representatives shall amount to 200; after which the proportion shall be so regulated by Congress, that there shall not be less than 200 representatives, nor more than one representative for every 50,000 persons.

Obviously, Madison’s formula would have run into some excessive size issues over time. And Bartlett does not suggest how much the House should be increased, only noting that its ratio of one Representative for very 729,000 people is excessive. On the other hand, Madison’s ratio of one per 50,000 would produce an absurdly large House! It is just the need to balance the citizen-representative ratio with the need for representatives to be able to communicate effectively with one another that Taagepera devised the model of the cube root, which as we have seen, fits actual legislatures very well.

The cube root rule says the USA “should have” a House of around 660 members today, which would remain a workable size. (If the USA and UK swapped houses, each would be at just about the “right” size!) Even an increase to just 530 would put it within about 80% of the cube root.

As Bartlett notes, at some point the US House will be in violation of the principle of one person, one vote (due to the mandatory representative for each state, no matter how small). However, a case filed in 2009 went nowhere.



* Each country is plotted according to its population, P (in millions), and the size, S, of its assembly. In addition, the size of the US House is plotted against US population at each decennial census from 1830 to 2010.
The solid diagonal line corresponds to the “cube root rule”: S=P^(1/3).
The dashed lines correspond to the cube root of twice or half the actual population, i.e. S=(2P)^(1/3) and S=(.5P)^(1/3).

A variant of the graph will be included in Steven L. Taylor, Matthew S. Shugart, Arend Lijphart, and Bernard Grofman, A Different Democracy (Yale University Press).

An even earlier version of the graph was posted here at F&V in 2005.