The Apportionment Problem – How to
Distribute Parliamentary Seats among
Counties or States


In a representative democracy, citizens exert their influence via elected representatives. Representation will be fair if the citizens have more or less the same (indirect) influence, that is, if each representative stands for the same number of citizens. Establishing electoral districts with equal numbers of voters becomes nontrivial, when they must fit into the existing administrative structure of a country. For instance, the distribution of three seats between two equally populated regions will necessarily lead to inequalities. This example may seem artificial, but under more realistic circumstances with many regions and a high number of seats to be allocated the problem remains hard. The general problem of allocating seats between regions in a fair way is known as the apportionment problem.

Short description

A team of five students implemented various apportionment methods in the R programming language under the joint supervision of László Á. Kóczy and Balázs Sziklai, two renowned experts on apportionment methods from Budapest, and Jochen Staudacher who has expertise in establishing R packages, i.e. official extensions of the R programming environment on CRAN, the Comprehensive R Archive Network.

In addition to clearly structured routines for apportionment methods, the student team also provided a population distribution generator that can be used to run simulations.

We are hoping to establish the R package “Apportionment” on CRAN by early January 2020. The software will be distributed under general public licence, GPL-3.

Due to the Covid 19 pandemic the student team had to collaborate virtually. Weekly meetings via ZOOM worked stably throughout the semester and the student team enjoyed the Hungarian-German cooperation very much despite the difficult circumstances in spring 2020.

Outlook: Relation to another international project

The project’s content is strongly related to a second international student project on weighted voting systems at Kempten University in summer 2020. The latter project was (and still is) a Polish-Hungarian-German collaboration. Six Kempten students were jointly supervised by Izabella Stach from AGH University of Science and Technology in Kraków, László Á. Kóczy from Budapest University of Technology and Economics and Jochen Staudacher from Kempten. We shall report on the scientific content of this project in due course and we strive to make software publicly available, too. One of the six participants started writing his B.Sc. thesis under the joint supervision of Izabella Stach and Jochen Staudacher in October 2020 underlining a thriving scientific cooperation with colleagues from both AGH Kraków and various institutions in Budapest.


Students taking part in the project: Georg Lang (Game Engineering), Philipp Maruhn (Game Engineering), Alexander Rosenbohm (Business Information Systems), Dominik Schröder (Business Information Systems), Johannes Thoma (Business Information Systems).

Supervising professors: Prof. Dr. László Á. Kóczy (Budapest University of Technology and Economics), Prof. Dr. Balázs Sziklai (Corvinus University of Budapest) and Prof. Dr. Jochen Staudacher (HS Kempten)

Faculty: Faculty of Informatics

Project in cooperation with Budapest University of Technology and Economics and Corvinus University Budapest.

date of realization: Summer semester 2020