Mathematicians have concluded that a perfectly fair election system is impossible in a specific mathematical sense. No voting method can always ensure that local victories produce local seats, national seat totals accurately reflect overall vote shares, and the size of parliament remains fixed.
Researchers from the University of Cambridge and the University of Copenhagen examined proportional representation and first-past-the-post systems. Their analysis found that every method for electing a national legislature involves compromises, usually among local representation, national proportionality, and the total number of parliamentary seats.
Election Systems Under Growing Pressure
Several northern European elections over the past decade have demonstrated these tensions. The problem has become more visible as voters increasingly divide their support among a larger number of political parties.
In Denmark, the left bloc won the 2022 election despite receiving fewer votes than the right bloc, even though the country uses proportional representation. In Germany, efforts to preserve both local representation and proportionality caused the Bundestag to expand sharply before reforms were introduced in 2023. In the UK, the 2024 general election produced the country's least proportional result on record, with Labour securing 63% of the seats after receiving 33.7% of the vote.
