Apportionment methods – mathematical and statistical issues of proportional representation systems

We study apportionment methods that are used for the allocation of parliamentary seats to parties or regional units based on the principles of proportional representation. Based on quantitative mathematical methods, the aim of the project is to explore to what extent the various apportionment methods are consistent with the political framework and constitutional requirements. This question arises in systems where the parliamentary seats are allocated proportionally to the vote shares of the parties. Another area of application are apportionment problems, e.g. for the European Parliament, where the seats are assigned degressively proportional to the Member States. We develop mathematical models and formulas and review the conclusions on basis of empirical data.