Analysis of the 2021 Bundestag elections. 3/4. Tackling the Bundestag growth

This is the third of four papers devoted to the 2021 German federal elections continuing our analysis of the 2009, 2013 and 2017 Bundestag elections. Currently, only China has a parliament larger than the German Bundestag, which still grows due to the increasing number of overhang mandates. The unfettered growth of the Bundestag - caused by allotting too many direct mandates to parties that received too few second votes - can be prevented by relaxing the principle of 'one man-one vote' and introducing adjustable vote weights of Bundestag members. Such a practice could make numerous adjustment (leveling) seats unnecessary and the basic 598 Bundestag seats sufficient under most circumstances. For this purpose, the members of the overrepresented parties (because they receive too many direct mandates) should have vote power = 1 and the members of other parties should have adjustment vote weights > 1. We explain the adjustment vote weights using the example of the 2021 Bundestag. The second point discussed is the incomplete compliance of the Sainte-Lague/Schepers method, which dates back to 1832 and is used to apportion the Bundestag, with the mathematical standards of the 21st century. This method results in apportionments that are often not the best ones found by discrete optimization.