QLunch: Frederik Ravn Klausen

Speaker: Frederik Ravn Klausen from QMATH

Title: Christmas special: Two-tier electoral systems, the Danish election in 2022, unclarities and impossibility results. 

Abstract: Election systems struggle with the trade-off between geographical and proportional representation. Two-tier electoral systems with multi-member constituencies (da:storkredse) is the gold standard for obtaining both. 

We introduce the Danish electoral system for parliament elections (da:folketingsvalg) and the distribution of the direct mandates (da:kredsmandater)  and leveling seats (da: tillægsmandater). 

Describe how the system in 2022 for the first time did not meet a certain criteria for proportional representation and how it led to errors in the media's reporting of the results on the election night. 

Then we show examples of distribution of votes in multi-member constituencies, where the algorithm for the distribution of levelling seats in the Danish Election Law does not describe how to distribute the mandates. 

We describe how the Swedish, Norwegian/Bosnia-Hercegovinian, Icelandic and German two-tier systems all have different ways to circumvent the problem and formalize this into an impossibility Theorem. The Theorem shows how you can't simultaneously have a certain sense of proportional representation, geographical representation and fixed parliament size.