May 12, 2016
The Adams Method
Well, not the sixth president of the United States specifically, but the apportionment method he devised back in 1822. Ever wonder how congressional representatives get divvied up? Well, it's proportional to population, but the actual process can get complicated, a subject for lovers of word problems in algebra.
The Mathematical Association of American explains the different methods and provides the applicable equations.
The underlying math problem is that, using only whole numbers (the population of a state), the end product has to be a whole and fixed number (the total number of representatives). The wrong formula can result in an "apportionment paradox," that has a state gaining population but losing representatives.
The United States uses the Huntington-Hill Method. The Webster Method (named after Daniel) was adopted by the Congress in 1842, then replaced by the Hamilton Method (named after Alexander) in 1852. And again in 1901. And again in 1911. Finally, the current Huntington-Hill Method was adopted in 1941.
The Adams Method (アダムズ方式) was never adopted in the United States. But Japan seems to have taken a shine to it, perhaps because of its built-in bias toward small prefectures. The problem right now is that small prefectures are hugely--unconstitutionally, according to Japan's Supreme Court--overweighted.
As the population shifted to the cities, the hard-coded apportionments in the 1947 constitution drifted out of whack. Piecemeal fixes were made without repairing the underlying system. And then a string of elections, most recently the 2010 House of Councillors election, were ruled unconstitutional.
The elections themselves were not invalidated, as that would have caused chaos. Rather, the Supreme Court admonished the Diet to enact a permanent fix to adjust representational disparities between the smallest and largest prefectures to below 2:1.
Like the GOP, the Liberal Democratic Party (LDP) enjoys substantial support in rural districts and has been dragging its feet. In March, the LDP grudgingly approved the adoption of the Adams Method for distributing House of Representatives seats, with full implementation to come following the 2020 census.
Meanwhile, minority parties (which have the most to gain from increased urban representation) continue to campaign for earlier implementation using the 2010 census.
In the United States, population growth favors conservatives, Utah being a case in point. In 2000, Utah missed out on a 4th congressional district by the number of Mormon missionaries serving out of state. Utah would have benefited from the Adams Method then. By 2010, Utah got its 4th district with room to spare.