Studying malapportionment using α-divergence

This study shows the superiority of α-divergence over Samuels and Snyder's MAL index for 73 countries, using Samuels and Snyder's database. As α-divergence rests on a philosophical basis, that is, a microfoundation, we calculate the degree of malapportionment in terms of each philosophy of apportionment and/or presume the apportionment principles of countries. Furthermore, we decompose the malapportionment factors into the existence of special districts, apportionment to the states, and districting. Therefore, measuring the degree of malapportionment must be based not on distance, but on α-divergence.