Cube Root of U.N. Member Populations
Exploring the appropriate size of Congress
In part 3 of my six-part series scrutinizing representation in the United States, I explored different methods by which we could be more optimally apportioning seats in our House of Representatives. In the end, I concluded that taking the cube root of each state’s population to determine the number of seats each state gets in the House leads to the most practical and fair solution. I intend to further explore the implications of applying the cube root to apportionment in the United States over the coming days, but today let’s first look at how other countries fair by the cube root rule.
Based on the 2017 estimated populations and seat counts tabulated here, the chart below illustrates the 86 U.N. member nations with populations exceeding 10 million people who have more or less seats than the cube root of their populations (sorted from most to least populous):
Against my expectations, the trend line shows that as populations decrease in size countries trend towards underrepresentation below the cube root. Across all 192 U.N. member nations with lower or unicameral houses, countries are an average 54% underrepresented by the cube root rule.
As such, it will be more difficult to defend the cube root rule as the method for U.S. House apportionment with the argument that it will be mathematically comparable to other countries when 82% of other United Nations member countries are underrepresented by this rule.
Still, we need more representation in the United States. When dividing population by number of seats to get a representation ratio, the cube root of our population would only bump up the United States from 2nd worst represented to 4th worst represented (at that point only besting India, Pakistan, and Nigeria). Long way to go.
