Characterization of some apportionment methods

Abstract

In this work known main characteristics of 11 apportionment methods are systemized, including the Hondt, Hamilton, Sainte-Laguë and Huntington-Hill methods, and some new ones are determined by computer simulation. To such characteristics, refer the disproportionality of solutions and the percentage of Quota rule violation, of the Alabama, Population and New state paradoxes occur and of favoring of beneficiaries. For a large range of initial data, where determined the preferences order of the explored apportionment methods by each of these characteristics. No one of methods is preferable by all of the six characteristics-criteria. Of the immune to the three paradoxes, d’Hondt, Huntington-Hill, Sainte-Laguë and adapted Sainte-Laguë methods, by disproportionality of solutions the best is Sainte-Laguë method, followed by the adapted Sainte-Laguë, then by the Huntington-Hill and, finally, by the d’Hondt one. The same order for these four methods is by compliance with the Quota rule. The percentage of Sainte-Laguë method’s Quota rule violation is little influenced by the total number of seats value, but it strongly decreases (over 400 times) with the increase of the number of states – from approx. 0.045% for 4 states, up to 0.0001-0.0004% for 30 states. Based on multi-aspectual comparative analyses, it is shown that from explored methods there is reasonable to use, in specific areas, only three or four: the Hamilton, Sainte-Laguë and Adapted Sainte-Laguë methods and may be the Quota linear divisor one.