Plurality
Only the candidate ranked first on each ballot receives one point. The candidate with the most first-place votes wins.
Observe: vote splitting, spoiler effects, and incentives to abandon a sincere favorite for a more viable candidate.
Voting Rules Lab
Choose your sincere ranking:
How this teaches game theory
Rule, Mode and Level Guide
Use this guide to understand what each setting changes, what to observe, and which game-theory idea the activity illustrates.
Voting rules
Borda count
In a three-candidate election, a first-place ranking gives 2 points, second place gives 1 point, and last place gives 0 points.
Observe: broad compromise candidates can defeat polarizing candidates, while changing lower rankings may alter the winner.
Approval voting
The first two candidates on every ballot are treated as approved and each receives one point. The last-ranked candidate receives no point.
Observe: the approval threshold matters. A voter may strategically approve a compromise or withhold approval from a close rival.
Modes
Human vs Computer voters
The computer generates all other voters and you submit the final ballot. This mode focuses on whether one strategic voter can influence an electorate created by the computer.
Best for: comparing a sincere ballot with a manipulated ballot.
Human-controlled electorate
You repeatedly choose rankings and can replace the latest ballot to explore how changes in the preference profile affect scores and the winner.
Best for: constructing examples, ties, close contests, and voting paradoxes.
Computer simulation
The initial electorate is generated automatically. Use New election repeatedly to compare many random preference profiles under the selected rule.
Best for: observing how often different rules produce decisive, close, or surprising outcomes.
Implementation note: all three modes currently use the same ballot controls. The mode selection describes the intended classroom role: individual strategic voter, manually explored electorate, or repeated computer-generated demonstration.
Levels
Level 1 — 5 voters
A small electorate makes every ballot easy to inspect. Four computer-generated ballots are created and your ballot completes the five-voter election.
Learning goal: calculate scores manually and understand the basic aggregation rule.
Level 2 — 9 voters
A larger electorate creates more varied preference profiles and reduces the visible impact of a single ballot in many elections.
Learning goal: compare robustness, close outcomes, and the effect of electorate size.
Level 3 — Strategic voter
The electorate still contains nine voters, but the Try strategic vote button tests alternative rankings for your final ballot. It searches for a report that elects a candidate ranked higher in your sincere preference order.
Learning goal: distinguish sincere voting from beneficial misreporting and study manipulability.
How the combinations behave
| Mode | Level 1 | Level 2 | Level 3 |
|---|---|---|---|
| Human vs Computer voters | Submit the decisive fifth ballot against four generated voters. | Submit one ballot against eight generated voters and compare your reduced influence. | Submit a sincere ballot, then test whether another ranking improves the elected result for you. |
| Human-controlled electorate | Build and inspect a compact five-voter profile. | Explore more complex nine-voter profiles and close score totals. | Construct a profile, identify a sincere ranking, and test a strategic deviation. |
| Computer simulation | Generate small elections whose scores are easy to verify. | Generate larger elections to compare outcome variation. | Generate strategic-voting cases and use the manipulation test on the final ballot. |
Suggested learning path
- Start with Plurality + Human vs Computer voters + Level 1 to learn score calculation.
- Keep the same electorate size and compare Borda count and Approval voting.
- Move to Level 2 to study how a single voter’s influence changes.
- Finish with Level 3, cast a sincere ballot, record the winner, and then run Try strategic vote.