Same voters. Different winners.
The rules for counting votes can decide an election as much as the votes do. Drag the candidates and voter groups below and watch nine counting methods disagree about who won.
Each dot is a voter, colored by the candidate closest to them. Voters prefer nearer candidates. Drag a lettered circle to move a candidate, or a numbered ring to move a voter group.
Count real ranked ballots by hand
Pick a classic paradox, or build your own electorate from groups of ranked ballots. Change a group’s size or its ranking and every count updates.
Twelve ways to count a vote
Filed by what the ballot asks you to do: choose one, rank, or rate. The last group fills many seats at once so that parliaments mirror the vote. Tap a method to open it.
Which promises each method keeps
Mathematicians test single-winner methods against fairness criteria. No method passes them all; Arrow and Gibbard proved none can. Each method chooses which flaw to live with.
| Method | Elects the Condorcet winner when there is one | A first-choice majority always wins | More support never hurts (monotonic) | Ranking a backup can’t hurt your favorite | Similar candidates don’t split the vote | Ballot |
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Condorcet row assumes a modern Condorcet method such as Ranked Pairs or Schulze. Approval, score and majority judgment pass the split-vote test as long as voters grade each candidate on its own merits. Criteria definitions follow the standard social-choice literature.