Plurality
Park
Only first choices count. This is simple, but it can ignore second-choice support.
Park26
Sports Hall26
Library24
Game theory and decisions
Voting systems reveal that fairness is mathematical, not automatic.
This prototype explores a deceptively simple question: if the same people vote under different rules, do we always get the same winner?
Use it as a neutral mathematical lab for plurality, ranked choices, runoff voting, Borda scores and head-to-head fairness checks. The aim is not to tell students what to think politically, but to show that rules shape outcomes.
Voter profile
Change the electorate, then predict who wins.
Each row is a group of voters with the same ranked preferences. The candidates are deliberately neutral: imagine a school is choosing which shared space to improve.
Total voters: 76
Before looking at the result cards, choose a rule and predict whether it rewards first choices, broad support or majority support.
Library
24 first-choice votes, 32%
Park
26 first-choice votes, 34%
Sports Hall
26 first-choice votes, 34%
Borda count
Library
Rankings earn points: 2 for first, 1 for second, 0 for third. This often rewards compromise candidates.
Library96
Park68
Sports Hall64
Instant runoff
Park
The lowest first-choice candidate is eliminated, then those ballots transfer to their next active choice.
Park42
Sports Hall34
Library0
Pairwise fairness check
Does anyone beat every other candidate head-to-head?
Condorcet winner: Library
Library vs Park
50 prefer Library; 26 prefer Park.
Head-to-head winner: Library
Library vs Sports Hall
46 prefer Library; 30 prefer Sports Hall.
Head-to-head winner: Library
Park vs Sports Hall
42 prefer Park; 34 prefer Sports Hall.
Head-to-head winner: Park
Majority
No candidate has more than half of first choices, so the idea of a fair winner is less obvious.
Rule sensitivity
Different voting rules currently choose different winners. That is the mathematical discomfort worth discussing.
Runoff story
Round 1: Library is eliminated. Round 2: Park wins.
Joy in the process
The point is not just to finish. It is to notice, test and return.
These tools are invitations to explore. A good mistake, a surprising pattern or a question you cannot yet answer is part of the work, not a failure of it.
The challenge is deliberate: the site should support thinking, not remove the need for it.
Before changing a setting, pause and predict what you think will happen.
Change one thing at a time. What stayed the same, and what changed?
Try to create a surprising case, a broken case, or a beautiful pattern.
Ask what this connects to outside the page: maps, movement, nature, systems or decisions.
Reset, then try again with a new question in mind.
Guided exploration
Use the prototype to create predictions, not just observations.
Before changing the sliders, predict which voting rule will choose each winner.
Find a voter profile where plurality and instant runoff choose different winners.
Try to make the Condorcet winner lose under plurality. What feels unfair about that?
Look for a compromise candidate: not the most first choices, but rarely ranked last.
Future extensions
This can become a wider social choice and fairness strand.
Add approval voting and score voting for comparison.
Add a spoiler-candidate mode where a new similar option enters the election.
Add Arrow's impossibility theorem as a guided, visual discussion.
Add classroom election templates for anonymous preference collection.