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.

Degree of favoring in apportionments

“…At the same time, as mentioned in [16], there are no known such methods that would be used in practice; one and the same APP method in some apportionments can favor, predominantly, large beneficiaries, and in other apportionments, predominantly, small beneficiaries. This is why, as noted in [16], this approach can be used to identify the "total favoring" or "full favoring" of large or small beneficiaries in particular apportionments. It is easy to observe that "full favoring" are particular cases of "favoring" the beneficiaries -large (predominantly) or small (predominantly).…”