Total favoring in proportional apportionments

Abstract

The notion of “total favoring” of large or of small beneficiaries in proportional apportionments of entities is defined as a particular case of favoring. It is proven that the number of known conditions of total favoring of beneficiaries in an apportionment (APP) can be considerably reduced. Thus, the volume of calculations to be performed for the respective computer simulation was reduced. In order to quantitatively estimate the total favoring of beneficiaries by APP methods, three indicators were used: the percentage of apportionments, in which large beneficiaries are totally favored; the percentage of apportionments, in which small beneficiaries are totally favored; the percentage of total favoring of large or of small beneficiaries, depending on the APP method applied. A total of five APP methods are being researched: Hamilton (Hare), Sainte-Laguë (Webster), d’Hondt (Jefferson), Huntington-Hill and Adapted Sainte-Laguë. Based on results of computer simulation, the total favoring of beneficiaries by these five APP methods was estimated, including comparatively. For example, it has been identified that the d’Hondt method does not always totally favors beneficiaries to a greater extent than the Huntington-Hill method. At the same time, the Adapted Sainte-Laguë method always totally favors small beneficiaries less compared to the Huntington-Hill method.