How Voting Systems Work
Brazil is holding a presidential runoff because no one won more than half the valid votes in the first round. Why do some countries vote twice, some rank candidates, and some hand out seats in proportion to votes? This film explains the main families of electoral systems, the spoiler effect, why plurality voting tends to produce two big parties, and two famous results from mathematics: Condorcet's paradox and Arrow's impossibility theorem. Count the same nine ballots under three rules yourself, and see why every system is a trade-off. The film takes no side on any election or party.
Same votes, different winners
How the rules of counting shape who wins.
A machine for turning votes into power
Every election runs on a rule.
First past the post
The simplest rule of all.
The spoiler effect
Similar candidates can split their side’s vote.
Duverger’s law
Why plurality tends to leave two big parties.
More than half
Brazil’s rule: if no one has a majority, vote again.
One ballot, many rounds
Ranked or preferential voting runs the runoff on paper.
The candidate every rule missed
A wins every one-on-one contest, and still loses.
Rock, paper, scissors
Sometimes there is no Condorcet winner at all.
Arrow’s theorem
A proof that no ranking rule is perfect.
Thirty percent, thirty percent
Proportional representation matches seats to votes.
A mixed system
Some seats by district, some by party list.
Same votes, different winners
Every system is a choice about what matters most.
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