Apportionment “Population paradox” and the Paradox of population influence

Abstract

A new approach is grounded with respect to the population paradox (PPr). Further on, the paradox of population influence (PPi) is proposed. It is proven that Hamilton method is immune to the PPi, and that d’Hondt, Sainte-Lagu¨e, Huntington-Hill and Adapted Sainte-Lagu¨e methods – are not. By computer simulation, the percentage of non-immunity of Hamilton method to PPr, and the one of d’Hondt, Sainte-Lagu¨e, Huntington-Hill and Adapted Sainte-Lagu¨e divisor methods to PPi, is estimated. For a large range of initial data, this percentage, in the case of the four investigated divisor methods, does not exceed, on average, 0.6-0.8%, that is one case per a total of 120-170 cases.