Degree of favoring in apportionments

Abstract

To quantitatively estimate the degree of favoring the beneficiaries in proportional apportionments of entities of the same kind (seats, PCs, etc.), five quantitative criteria were defined. By computer simulation, the degree of favoring the large or small beneficiaries by 6 apportionment methods is identified. Thus, favoring large beneficiaries by the d’Hondt method can overpass 10.7-12.1 entities (entities in excess) and that of small beneficiaries by the Huntington-Hill method -- 2.7-11.0 entities, and by the Adapted Sainte-Lagu\"{e} method -- 1.7-9.7 entities. The Huntington-Hill method favors small beneficiaries up to 5.70 times stronger than the Adapted Sainte-Laguë one does. Also, the d’Hondt method favors beneficiaries (the large ones) much stronger than the Adapted Sainte-Laguë one does (the small ones) -- for very many cases the respective ratio exceeds 10 times.