INVESTIGATIONS / VALUE & POWER
Constructed exampleWho wins when we change the rules?
The same people. The same preferences. A different way to decide.
YOUR TASK / CONSTRUCTED EXAMPLE
Decide what a voting rule should recognize
You’re helping a fictional group choose among three proposals. Name a criterion, inspect the complete ballots and compare how different rules turn the same preferences into an outcome.
An evidence trail.
Your decision.
Begin with a provisional judgment
Loading the supplied example…
Keep a private first thought (optional)
Private writing stays out of links and default downloads. A reopened link does not restore it.
This records a provisional judgment and the starting configuration. It does not change a mathematical setting or save automatically.
01 / THE PREFERENCES
25 people.
Three proposals.
Everyone ranks the same choices. These preferences stay fixed as you change the rule.
Left to right: first → second → third
Before you compare
Optional, private and ungraded.
02 / THE COUNTING RULE
Start with first choices.
Plurality · count in votes
Count first choices. The proposal with the most first-choice votes leads.
Plurality: Proposal A selected. 25 ballots.
Follow one ballot group
The complete profile stays fixed. Selecting a group highlights its source and transfer paths.
A choice of rule is a choice about what counts.
Inspect the preferences. Then inspect the procedure.
Save this experiment
MODEL & LIMITS
What a counting rule cannot settle
Rankings tell us an order, not how strongly people feel. These rules calculate outcomes from complete preferences; they do not establish a uniquely fair choice.
- PreferenceWhat is ranked?
- RuleWhat counts?
- OutcomeWho is chosen?
Inspect the complete counts and workings
| Ranking | Voters | A points | B points | C points |
|---|---|---|---|---|
| A → B → C | 0 | 0 × 2 = 0 | 0 × 1 = 0 | 0 × 0 = 0 |
| A → C → B | 11 | 11 × 2 = 22 | 11 × 0 = 0 | 11 × 1 = 11 |
| B → A → C | 0 | 0 × 1 = 0 | 0 × 2 = 0 | 0 × 0 = 0 |
| B → C → A | 10 | 10 × 0 = 0 | 10 × 2 = 20 | 10 × 1 = 10 |
| C → A → B | 1 | 1 × 1 = 1 | 1 × 0 = 0 | 1 × 2 = 2 |
| C → B → A | 3 | 3 × 0 = 0 | 3 × 1 = 3 | 3 × 2 = 6 |
| Total | 25 | 23 | 23 | 29 |
| Round | A votes | B votes | C votes | Next step |
|---|---|---|---|---|
| 1 | 11 | 10 | 4 | Eliminate C |
| 2 | 12 | 13 | Eliminated | Proposal B selected |
| Rule | Outcome | Units |
|---|---|---|
| Plurality | Proposal A selected | Votes |
| Instant runoff | Proposal B selected | Votes |
| Borda points | Proposal C selected | Points |
Borda awards 75 points in total. Every runoff round retains 25 ballots. Tied-lowest elimination stops this teaching procedure; tied final leaders remain tied.
Assumptions, sources and evidence status
Original fixture constructed-ranked-ballots-v1. Three proposals, sincere complete strict rankings and at most 200 voters. No partial rankings, exhausted ballots, preference intensity or strategic behavior. The example does not describe an election jurisdiction.