Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters of a society belong to this set, their majority relation has no cycles. We observe that, without loss of generality, every such domain can be assumed to be closed in the sense that it...

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...

This is the second out of four papers on the 2025 German federal elections continuing our analysis of the 2009, 2013, 2017 and 2021 Bundestag elections. We estimate the policy representation ability of the 29 parties that participated in the 2025 elections and of the 2025 Bundestag. For this...

This is the third out four papers on the 2025 German Bundestag elections continuing our analysis of the 2009, 2013, 2017 and 2021 elections. In particular, this paper contributes to the discussion of the imperfection of the German 2023/24 Electoral reform in [Tangian 2025a]. We show that policy...

This is the last out of four papers on the 2025 German federal elections continuing our analysis of the 2009, 2013, 2017 and 2021 Bundestag elections. First, we apply the model from [Tangian 2022b] to construct the 2025 German political spectrum understood as a contiguous party ordering, i.e.,...

We study the aggregation of partial orders into a complete ordering, and prove both possibility and impossibility results in this context. First, we show that the standard independence of irrelevant alternatives condition is stronger here since even dictatorial aggregation rules may fail to...

We reappraise the Arrow problem by studying the aggregation of choice functions. We do so in the general framework of judgment aggregation, in which choice functions are naturally representable by specifying, for each menu A and each alternative x in A, whether x is choosable from A, or not. Our...

Currently, only China has a parliament larger than the German Bundestag, which continues to grow due to the increasing number of overhang mandates. In 2016, Norbert Lammert, then president of the Bundestag, proposed to restrict it to 630 members by allocating mandates according to quotas for...

This is the first out of four papers devoted to the 2021 German federal elections continuing our analysis of the 2009, 2013 and 2017 Bundestag elections by the methods of the mathematical theory of democracy. This one estimates the policy representation ability of the 39 parties that...

This is the second out of four papers devoted to the 2021 German federal elections continuing our analysis of the 2009, 2013 and 2017 Bundestag elections. This paper arranges the contesting parties into a 'spectrum' that reflects the spatial proximity of their policy profiles. The latter are...