Mathematical research identifies limits in electoral systems

Researchers Sebastian Tim Holdum from the University of Copenhagen and Frederik Ravn Klausen from the University of Cambridge have identified a mathematical impossibility in electoral systems. Their research demonstrates that no electoral system with a fixed-size parliament can simultaneously satisfy three key conditions: proportionality, regional representation, and a fixed number of parliamentary seats.

According to the researchers, as the number of political parties increases, one of these three components must inevitably be sacrificed. The study clarifies that this issue is not the result of corruption or fraud, but rather a mathematical constraint that occurs when converting vote counts into a limited number of parliamentary mandates.

To maintain proportionality (where a party's seats match its percentage of votes) and regional representation (ensuring local winners retain their seats), the total number of parliamentarians would likely have to increase. Conversely, maintaining a fixed number of seats or regional representation will eventually compromise the mathematical proportionality of the results.