Mathematical aspects of degressive proportionality

Utilitarianism, Degressive Proportionality and the Constitution of a Federal Assembly

On Bounds for Allocation of Seats in the European Parliament

Rules i.–iii. are clear and do not require any comments, but rule iv. may raise some doubts. Although the very notion of degressive proportionality can, in principle, be defined in a mathematically rigorous way, one may construct several different methods of distribution of the seats in the Parliament consistent with this rule. Roughly speaking, degressive proportionality means a conjunction of...

Welfare, Voting and the Constitution of a Federal Assembly

Equal and proportional representation are two poles of a continuum of models of representation for the assembly of a federation of states. The choice of a model has repercussions on the welfare distribution in the federation. We determine, first by means of Monte Carlo simulations, what welfare distributions result after assemblies that were constituted on the basis of different models of repre...

An Improvement in Larsa and Its Implementation on Allocation of Seats to Categories in an Organization

In this paper, we propose modifications to LaRSA a fast exact algorithm for the allocation of seat for the EU Parliament. This improvement shall reduce its run time by a considerable amount. Further, we apply this modified version of LaRSA which uses the concept of degressive proportionality on the seat allocation system in Joint Entrance Examination(JEE), India. This modified algorithm takes a...

Affine Transformations, Polynomials, and Proportionality

In the articles [1] and [3], standard tools and techniques of calculus are used to establish a variety of proportionality results concerning areas defined by the lines tangent to a cubic curve, and by the lengths of certain arcs of a parabola, where the arcs themselves are determined by an area-proportionality criterion. We demonstrate here that these results can be viewed as consequences of so...