Three brothers, one fruit — Ranked Robin confirms the majoritarian winner¶
Generated from bv2279_qywq7d_ranked_robin.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.
Method: Ranked Robin (RCV-RR / Copeland) · 1 seat · Expected winner: Banana
▶ Live on BetterVoting: vote · results ↗ (election qywq7d · test BV2279).
Scenario¶
Race 2 of 3 in the three-brothers election (BV2279, bvid qywq7d; BV-confirmed). The setup, the source and the x5/11 rescale are documented in the STAR race, bv2279_qywq7d_star.yaml.
The same three opinions written as ranks. Boys 1 and 2 rank Banana first; boy 3 ranks Banana LAST, behind a fruit he scored a 2.
Ranked Robin elects Banana on 2 pairwise wins — Banana beats Orange 2-1 and Apple 2-1, Orange beats Apple 3-0. Banana is the Condorcet winner, Apple the Condorcet loser.
This race exists to show that the majoritarian answer is not an artifact of STAR's runoff. A method that reads only the order, and reads all of it, lands on Banana too — because the majoritarian ideal is exactly what pairwise counting measures.
And it shows what the ranks cost. Written this way, boy 3's ballot says "Orange, then Apple, then Banana" — the same sentence he would write if Banana were merely his least favorite rather than worth nothing at all. The 0 that makes Orange the utilitarian winner is not in this file. Compare the Approval race (bv2279_qywq7d_approval.yaml), which keeps enough of the level to elect Orange.
Ballots¶
Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).
Banana>Orange>Apple # Boy 1
Banana>Orange>Apple # Boy 2
Orange>Apple>Banana # Boy 3
What the engine says¶
The count, step by step — the rounds and how the winner is reached:
--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
Tabulating 3 ballots (ranked ballots).
Ballots:
2 × Banana > Orange > Apple
1 × Orange > Apple > Banana
Round-Robin — every pair, head-to-head (For – Against):
Banana beats Orange 2 – 1
Banana beats Apple 2 – 1
Orange beats Apple 3 – 0
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Banana | Orange | Apple |
----------------------------------------------
Banana > | --- |2 - 0 - 1 |2 - 0 - 1 |
Orange > | 1 - 0 - 2 | --- |3 - 0 - 0 |
Apple > | 1 - 0 - 2 |0 - 0 - 3 | --- |
Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by total margin, then lot order):
# Candidate W–L–T Copeland Margin Beats
1 Banana 2–0–0 2 +2 Orange, Apple
2 Orange 1–1–0 1 +2 Apple
3 Apple 0–2–0 0 -4 —
Winner — Ranked Robin (RCV-RR): Banana
beats every opponent head-to-head — the Condorcet winner.
Full audit — preference matrix, Condorcet, and score distribution¶
--- Smith Set (the generalized Condorcet winner) ---
The smallest group whose every member beats every candidate outside it —
the honest answer to "who is even in contention?".
Smith set (1 of 3): Banana
Outside (2): Orange, Apple
One member ⇒ Banana is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Banana is INSIDE the Smith set. ✓
Guaranteed: Ranked Robin (Copeland) is Smith-efficient — every member of
the set outscores every outsider, so the top of the win–loss table is
always inside the set, however the tie among them is then broken.
More: 07_Concepts/topics/smith_set.md
Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).
Run it yourself:
python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/majoritarian_vs_utilitarian/cases/bv2279_qywq7d_ranked_robin.yaml
See also¶
More cases in this set: bv2279_qywq7d_approval · bv2279_qywq7d_star