Mathematicians prove perfectly fair elections are impossible

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.

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.