How Votes Become Seats, and Why It Matters
Democracy is not just about voting—it’s about counting. The same million ballots can produce wildly different parliaments depending on the method used to convert votes into seats. D’Hondt favors large parties. Sainte-Laguë is more proportional. First-past-the-post can give a majority to a party with a minority of votes. Gerrymanders pack and crack voters into districts drawn for political advantage. Explore 10 interactive simulations that reveal the mathematics, trade-offs, and paradoxes lurking inside every electoral system.
The algorithms that turn raw vote counts into legislative seats. Each method makes different trade-offs between proportionality and governability.
The most widely used highest-averages method. Divide votes by 1, 2, 3... and award seats to the highest quotients. Adjust party sliders and watch the hemicycle parliament fill seat by seat.
Side-by-side comparison of two rival methods. Sainte-Laguë divides by 1, 3, 5... instead of 1, 2, 3..., giving small parties a fairer shake. Same votes, different parliaments.
Compare Hare and Droop quotas. Each party gets floor(votes/quota) seats, then remainders decide the rest. Watch exact quotients, remainders, and final allocations side by side.
From ranked-choice ballots to winner-take-all districts, these demos show how different voting rules shape democratic outcomes.
Rank candidates by preference, then watch the STV algorithm work: calculate the Droop quota, elect winners, transfer surplus votes, eliminate losers, repeat until all seats are filled.
Run the same election under first-past-the-post and proportional representation. See district maps, wasted votes, and the Gallagher disproportionality index reveal the gap between votes and seats.
Paint district boundaries on a grid of red and blue voters. Pack, crack, and gerrymander to your heart’s content. The efficiency gap updates in real time to measure your handiwork.
The mathematics that reveal hidden power structures, measure fairness, and expose the impossible paradoxes lurking in every apportionment scheme.
The least-squares disproportionality index, computed live across four allocation methods. Grouped bar charts show vote share vs seat share, with deviation lines and color-coded gauges.
Weight does not equal power. Set voter weights and a quota, then see every winning coalition and who is critical in each. Presets include the UN Security Council and corporate boards.
Explore three famous paradoxes of Hamilton’s method: Alabama (more seats, fewer for you), Population (grow faster, lose a seat), and New State (adding a state shuffles everyone else).
Race six allocation methods head-to-head on the same random election. Six hemicycle parliaments appear simultaneously, ranked by their Gallagher disproportionality score. Auto-animate for endless comparisons.