In a Proportional Representation (PR) electoral system it is assumed that seats are apportioned to the different electoral districts/states according to the corresponding voters’ distribution. In a previous paper we proposed a MILP (Mixed Integer Linear Programming) model to apportion the seats in the European Parliament (EP). Since the exact solution to the problem is not computationally effic...

Extensions of the Castigliano theorems are developed in the context of modeling the behavior of both discrete coupled linear systems and various coupled beams. It is shown that the minimization of the displacement of a parallel system determined from Castigliano’s second theorem can be used to formally define the apportionment of loads among the system elements, while the minimization of the lo...

Radiocarbon enables a distinction between contemporary and fossil carbon, which can be used for the apportionment of biogenic and anthropogenic sources in environmental studies. In order to apply this approach to carbonaceous atmospheric aerosols, it is necessary to adapt pretreatment procedures to the requirements of 14C measurements. In this work, we followed an approach in which total carbon...

This study models and empirically tests the impact on local employment from switching to a single sales factor (SSF) formula for state corporate income tax purposes. The study first models the optimal location choice decisions of a firm in response to differential state income apportionment rules while controlling for different tax structures. The model is then tested in five states which recen...

In the classic apportionment problem, goal is to decide how many seats of a parliament should be allocated each party as result an election. The divisor methods solve this problem by defining notion proportionality guided some rounding rule. Motivated recent challenges in context electoral apportionment, we consider question allocate under parity constraints between candidate types (e.g., equal...