From Votes to Seats
The central challenge of representative democracy is converting millions of individual votes into a finite number of legislative seats. Proportional representation (PR) systems attempt to make seat shares match vote shares as closely as possible. But the mathematics of rounding discrete seats from continuous vote percentages creates unavoidable distortions — and different rounding methods create different kinds of bias.
Three Allocation Methods
This simulation implements three major PR allocation methods. D'Hondt (used in Spain, Belgium, Japan) divides votes by successive integers and awards seats to the highest quotients — it slightly favors larger parties. Sainte-Lague (used in Norway, Sweden, New Zealand) divides by odd numbers (1, 3, 5...) and is more favorable to smaller parties. Largest Remainder (used in Italy, Hong Kong) gives each party its integer quota of seats, then distributes remaining seats to parties with the largest fractional remainders.
The Threshold Effect
Electoral thresholds act as gatekeepers. A 5% threshold (common in Germany, Poland) means any party below 5% gets zero seats — their voters are effectively disenfranchised. Raise the threshold slider and watch small parties disappear from the legislature, their seats redistributed to larger parties. The 'wasted votes' metric shows how many citizens' preferences are excluded from representation entirely.
Measuring Fairness
The Gallagher disproportionality index quantifies how far the result deviates from perfect proportionality. The effective number of parties (Laakso-Taagepera) measures how many parties truly matter in the legislature. Compare these metrics across methods and threshold levels to understand the tradeoffs inherent in any electoral system design. No system is neutral — each embeds choices about fragmentation versus representation, stability versus diversity.