Kempten Autumn Talks

Title of the lecture

“Apportionment methods and practices”


Prof. Dr. László Á. Kóczy

Budapest University of Technology and Economics

Budapest, Hungary

Time of the lecture

December 07, 2020, 11:45 o’clock ETC


90 minutes (inclusive discussion)


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.

While virtually every Western-type democracy adopted the principle laid down in the US Constitution, their approaches differ on how they deal with the arising paradoxes and anomalies. The European Commission for Democracy through Law, better known as the Venice Commission published a comprehensive guidebook on good electoral laws in 2002. The Code of Good Practice in Electoral Matters contains original recommendations for a good practice of apportionment.

In this presentation we survey the apportionment methods and the impact of the policy recommendation by the Venice Commission. First we explain the problem of apportionment and related issues in designing voting systems. Then we give an overview on the apportionment methods and discuss their properties. Then we illustrate the usage of the Leximin Method, motivated by the recommendations of the Venice Commission, compared to the solutions by the current legislations.