Follow the same preferences through different rules.

INSTRUMENTS / VOTING EXPLORER

Constructed example

Keep the ballots. Change the rule.

Compare first choices, transfers and ranking points with every ballot accounted for.

Change the rule. Keep the ballots fixed.

01 / THE PREFERENCES

Set the ballots.

Everyone ranks the same choices. These preferences stay fixed as you change the rule.

Six complete rankings · total at most 200 voters. Applied total: 25.

All ballots applied.

02 / THE COUNTING RULE

Start with first choices.

Plurality · count in votes

BALLOT GROUPSFIRST CHOICES11 · A › C › B10 · B › C › A1 · C › A › B3 · C › B › AA11B10C4
One thin strand per ballot; follow a ranking using the control below.

Count first choices. The proposal with the most first-choice votes leads.

PluralityAProposal A selected
Instant runoffBProposal B selected
Borda pointsCProposal C selected

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.

Read the investigation →
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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.

  1. PreferenceWhat is ranked?
  2. RuleWhat counts?
  3. OutcomeWho is chosen?
Inspect the complete counts and workings
25 complete ballots · constructed example · voting-v1
RankingVotersA pointsB pointsC points
A → B → C00 × 2 = 00 × 1 = 00 × 0 = 0
A → C → B1111 × 2 = 2211 × 0 = 011 × 1 = 11
B → A → C00 × 1 = 00 × 2 = 00 × 0 = 0
B → C → A1010 × 0 = 010 × 2 = 2010 × 1 = 10
C → A → B11 × 1 = 11 × 0 = 01 × 2 = 2
C → B → A33 × 0 = 03 × 1 = 33 × 2 = 6
Total25232329
Runoff rounds · strict majority is more than 12.5 votes
RoundA votesB votesC votesNext step
111104Eliminate C
21213EliminatedProposal B selected
All outcomes from the same profile
RuleOutcomeUnits
PluralityProposal A selectedVotes
Instant runoffProposal B selectedVotes
Borda pointsProposal C selectedPoints

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.

Rule definitions, sources and limits →