Keep the ballots.
Every ranking stays fixed.
Follow the same preferences through different rules.
CONCEPTS / VALUE & POWER
Voting rules
A set of preferences needs a way to become a collective choice.
Follow the idea.
A concept, in three framesChange the rule.
Each procedure recognizes different preferences.
Compare the outcomes.
A winner depends on the counting rule.
A voting rule turns preferences into a collective outcome.
Complete rankings alone do not specify the procedure. In this study, the same three proposals and ranked ballots enter each rule.
Three ways to count
Plurality uses first choices. Instant runoff follows the next available choice after eliminating the unique lowest total, stopping when a proposal has a strict majority. Borda adds points for every position: 2, 1 and 0.
Keep units and ties explicit
Borda points are scores, not voters. Our runoff stops at tied-lowest elimination and reports the unresolved choice; it does not name those candidates as winners. A final equal split remains a tie.
Same people, different outcomes
Our 25 constructed ballots give A 11 first choices, B 13 final runoff votes and C 29 Borda points. Other profiles may agree across all three rules. Rankings do not express intensity, and no result here proves a uniquely fair rule.
Primary source and teaching convention
Boehmer, N., Bredereck, R., & Peters, D. (2022). Rank aggregation using scoring rules. arXiv. Sections 2–3 define scoring rules and repeated elimination. This study uses the equivalent shifted three-candidate Borda weights 2/1/0. Its stop-on-elimination-tie policy is a disclosed local convention.
The ballots are an original constructed fixture, not research data from the paper.