How the Voting Rule Changes the Outcome
Voting outcomes depend on the counting rule, not just on what voters want — a fact demonstrated by running identical ballots through plurality, Borda count, and instant-runoff voting.
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Start when you are ready to enter this Stage's 7 scenes and explore, respond, and learn as you go.
Can changing only the voting rule change who wins an election, even when every voter's preference stays the same?
The same five voters, the same five ranked ballots — yet three different voting rules elect three different winners.
Most people assume elections have one 'correct' winner. Plurality feels fair, but what if a different rule would overturn that result?
Side-by-side ballots fed into three voting systems (plurality, Borda, instant-runoff) showing how each tally leads to a different winner.
The outcome of an election is not a property of the voters alone — it is a property of the rule that counts them.
If voters know what they want, the winner is fixed; the voting rule just records it.
- Strategic voting behavior
- Real-world election reform policy debates
- Condorcet's method and pairwise comparison math beyond a brief mention
- 01One Ballot, Three Winners?slideQuestion
Present a concrete scenario: five candidates, five voters, each ranking the candidates. The question is posed: who wins under three different rules?
- Five voters rank five candidates on identical ballots
- Three voting rules will be applied to the same ballots
- The driving question: must all three rules agree on a winner?
- 02Predict the Plurality WinnerinteractivePrediction
A simulation where learners tally first-place votes by hand before the rule reveals it. They commit to a prediction.
- Count only first-place marks
- Candidate with most top votes wins
- Predict who wins before the tally is shown
- 03Run Three Rules on the Same BallotsinteractiveEvidence
A diagram widget showing the identical ballots fed through plurality, Borda count, and instant-runoff voting side by side, revealing three different winners.
- Same five ballots enter each panel
- Plurality: top votes only
- Borda: points by rank position
- Instant-runoff: eliminate last, redistribute
- Three rules, three different winners
- 04Why the Rules DisagreeslideExplanation
Explain that each rule operationalizes 'most preferred' differently: plurality privileges top-rank intensity, Borda weights all ranks, instant-runoff mimics a series of head-to-head runoffs.
- Plurality ignores everything below first place
- Borda assigns decreasing points down the ballot
- Instant-runoff transfers lower-rank support after eliminations
- The winner is a function of the rule, not just the voters
- 05Design Your Own ElectioninteractiveTransfer
Learners drag ballot preferences onto a set of voters and watch how changing one ballot reshuffles the winner under each rule.
- Edit one voter's ranking
- See updated winner under each rule
- Notice how sensitive each rule is to small ballot changes
- 06When Rules Agree and When They Don'tslideBoundary
Show the boundary: when preferences are 'single-peaked' or one candidate dominates, rules often agree. Under more complex preference profiles, they diverge.
- Strong Condorcet winners tend to win under many rules
- Divergence emerges with cyclical or split preferences
- No rule is universally 'fairest'
- 07Answering the Driving QuestionslideResolution
Restate the question and resolve it: yes, the voting rule alone can change the winner, because the rule defines what 'winning' means.
- Driving question directly answered: yes
- Outcome = preferences + counting rule
- Choosing a voting rule is a substantive choice, not a neutral one
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