Elections 2025: Mathematical revelations and new laws in view!

Elections 2025: Mathematical revelations and new laws in view!

On March 8, 2025, the traditional Rose Monday lecture took place at the University of Siegen, which this year shed light on the exciting and complex topic of the elections. In a humorous lecture, the geomathematician Prof. Dr. Volker Michel talked about how elections work and conveyed important mathematical basics that are essential for understanding electoral processes. The high level of participation in the lecture shows the great interest of citizens in the topic.

Prof. Michel discussed various electoral systems and their advantages and disadvantages, while also addressing the possibilities for manipulating electoral systems. A central element of his remarks was the importance of democracy and transparency in elections. In a relaxed manner, he asked questions about overhang and compensation mandates and discussed the results of the 2025 federal election as well as the calculation of the distribution of seats in the new political context.

New voting law and its effects

In June 2023, a new electoral law came into force, which fundamentally changed the framework conditions for the federal election. This law, in accordance with Federal Law Gazette 2023 I No. 147, preserves the basic character of proportional representation, but aims to reduce the size of the German Bundestag and make its size more predictable. In the future, the statutory size of the Bundestag will be set at 630 members, instead of the previous 598, which was actually 736 members after the 2021 election.

The number of constituencies remains at 299, and voters can still cast two votes. With the first vote they elect a candidate in their constituency, while with the second vote they support a party's state list. The proportional composition of the Bundestag is now based exclusively on the second votes, which means that overhang and compensatory mandates are no longer applicable.

The reform in detail

The procedure for calculating the distribution of seats was modified by an amendment to the Federal Election Act on June 8, 2023. From the 2025 federal election onwards, the seats must also be covered by second votes. A key point for the parties is the five percent threshold. This rule states that only parties that receive at least five percent of the second votes take part in the distribution of seats. On the other hand, the provisions on the basic mandate clause, which allowed parties with at least three direct mandates to win seats, were abolished.

On July 30, 2024, the Federal Constitutional Court ruled that the five percent threshold partially violated the Basic Law. However, until a new regulation is adopted, it will remain in force for the time being, although a modification states that parties with less than five percent will only be excluded if they receive the most first votes in fewer than three constituencies.

The upper distribution of seats is carried out in proportion to the second votes for the state lists of the parties, while the lower distribution distributes the determined seats among the state lists in the proportion of the second votes. Constituency candidates are ranked according to their first vote share, which is intended to ensure that mandates are awarded in the order of votes received.

These changes are part of a comprehensive reform that aims to make the Bundestag more efficient and democratic. Prof. Michel concluded his lecture by emphasizing that a deeper understanding of the material basis of elections is crucial for the active participation of citizens in democratic processes.

For further information on the changes in electoral law, please visit the website Federal Returning Officer as well as that Bundestag portal be consulted.