Analysis of the 2025 Bundestag elections. Part 1 of 4: Imperfection of the electoral reform

This is the first of four articles on the 2025 German federal elections, continuing our analysis of the 2009, 2013, 2017 and 2021 elections. We begin with the 2023/24 electoral reform, which aimed to curb the uncontrolled growth of the Bundestag caused by political developments not envisaged in the original election rules. The reform fixes the size of the Bundestag at 630 members and introduces limits to parties' mandates at the level of federal states (Länder). All this makes the proportional allocation of Bundestag seats to parties less accurate and skews the balance between the two concepts implemented in the German mixed-member proportional representation system - the descriptive one (parliament consists of local representatives in order to 'mirror' the society) and the agent one (parliament consists of credible political experts from political parties) - in favor of the agent concept at the expense of the descriptive one. We show that the accuracy of Bundestag seat allocation to parties can be improved by applying modern discrete optimization techniques instead of the currently used historical Sainte-Lague/Webster method. The balance between the two concepts of representation can be restored by replacing the official two-tier distribution of Bundestag seats between federal state party associations with that computed directly in one step. Finally, all apportionment problems can be completely solved by introducing adjustment vote weights. All these devices are illustrated using hypothetical redistributions of Bundestag seats.