How the Voting Rule Changes the Outcome

Introduces a concrete scenario: 100 voters rank three candidates (A, B, C) in order of preference, and announces that four common voting rules will be applied to the same ballots.

• Three candidates, 100 voters, ranked ballots
• Four rules will be applied to identical ballots
• Question: does the rule actually change who wins?

Learners distribute 100 voters across ranked-ballot types and watch the running totals update before any rule is applied.

• Drag voters into A>B>C, B>A>C, B>C>A, or C>B>A groups
• Watch the bar chart of preferences update live
• Notice which candidate leads in raw first-choice votes

Before the four rules are run, learners commit to which candidate will win under each rule, locking in their hypothesis.

• One question, four predictions
• Tests intuition about what each rule rewards

Applies plurality, runoff, Borda count, and Condorcet to the same ballots in sequence, with each panel highlighting its winner in a shared results grid.

• Plurality: most first-choice votes
• Runoff: top two advance, second round decides
• Borda: points by rank position
• Condorcet: beats every rival head-to-head

Explains that each rule encodes a different definition of 'most preferred' — most first choices, broadest acceptability, strongest head-to-head record — and these criteria diverge when there are three or more candidates.

• Plurality rewards peak first-choice support
• Borda rewards consistent high ranking across voters
• Runoff and Condorcet reward head-to-head strength
• With three candidates, these definitions need not agree

Learners shift voters between ranking groups and observe which winners change under which rules, building intuition for how sensitive each rule is to the preference profile.

• Move 10 voters from one group to another
• Watch each rule's winner update independently
• Notice rules that flip easily vs rules that resist change

Shows that with only two candidates every standard rule yields the same winner, framing the divergence as a feature of multi-candidate elections rather than a flaw of any single rule.

• Two-candidate elections: every rule agrees
• Three or more candidates: definitions of 'most preferred' can split
• The disagreement is structural, not procedural error

Resolves the driving question directly: the voting rule changes the outcome because each rule operationalizes a different definition of victory, and with three or more candidates these definitions can pick different winners from the same ballots.

• Direct answer to the driving question
• Same ballots, different rules, different winners
• Choosing a rule is choosing a definition of 'most preferred'