Favorite betrayal in STAR (2 of 2) — nine voters demote their favorite and it pays¶
▶ Live on BetterVoting: vote · results ↗ (election b6xrdr · test BV2207) — an independent tabulator to check the winners below against.
Bucket — APPROVAL_OR_MINOR: Only Approval differs
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
STAR, RCV-IRV and Ranked Robin all agree on Bluebell. Only Approval differs, electing Clover: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Clover's breadth of acceptability over Bluebell's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Bluebell |
| RCV-IRV | Bluebell |
| Ranked Robin (RCV-RR) | Bluebell |
| Approval | Clover |
| Range / Score | Clover |
| Condorcet | Bluebell |
Flags: none
Source election: 01_STAR/03_Criteria/favorite_betrayal/cases/bv2207_b6xrdr_fbc_betrayal_pays.yaml · STAR tabulated mirror: bv2207_b6xrdr_fbc_betrayal_pays_tabulated.txt
3 candidates, 57 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Aster | Bluebell | Clover |
|---|---|---|---|
| 9 | 4 | 5 | 0 |
| 6 | 5 | 0 | 0 |
| 24 | 0 | 1 | 0 |
| 18 | 0 | 0 | 4 |
STAR result (official)¶
Scoring round (sum of scores): Clover 72, Bluebell 69, Aster 66
Finalists (top two): Clover and Bluebell
Automatic runoff: Clover 18 vs Bluebell 33 (6 equal/no-preference)
STAR winner: Bluebell
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Bluebell | * Clover |
-----------------------------------------------
* Bluebell > | --- |33 - 6 - 18 |
* Clover > | 18 - 6 - 33 | --- |
[Divergence from STAR]
STAR = Bluebell
Approval = Clover (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Clover)
- Runoff Round Winner = (Bluebell)
Candidate Clover earned the highest total score, but
Candidate Bluebell won the automatic runoff — not a malfunction,
STAR working as designed: the runoff elects the finalist preferred
by the majority (of voters with a preference).
--- STAR Voting Method (single winner) ---
Tabulating 57 ballots.
Count × Aster,Bluebell,Clover
24 × 0, 1, 0
18 × 0, 0, 4
9 × 4, 5, 0
6 × 5, 0, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Aster 6 9 0 0 0 42 | 66 1.2
Bluebell 9 0 0 0 24 24 | 69 1.2
Clover 0 18 0 0 0 39 | 72 1.3
Scoring Round
The two highest-scoring candidates advance to the next round.
Clover -- 72 -- First place
Bluebell -- 69 -- Second place
Aster -- 66
Clover and Bluebell advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Bluebell -- 33 -- First place
Clover -- 18
Equal Support -- 6
Bluebell wins.
Voters with a preference: 51 of 57 (6 Equal Support).
Bluebell 33 (65%) vs Clover 18 (35%); majority = 26.
Winner — STAR Voting Method (single winner)
Bluebell
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 57 ballots (converted from score ballots; 0 = unranked, equal scores broken by candidate priority).
Ballots:
the ranking RCV-IRV reads (0 = unranked, equal scores broken by priority);
the source score ballot follows in () per column: Aster, Bluebell, Clover
9 × Bluebell > Aster (4, 5, 0)
6 × Aster (5, 0, 0)
24 × Bluebell (0, 1, 0)
18 × Clover (0, 0, 4)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Bluebell 33 Elected
Clover 18 Rejected
Aster 6 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Bluebell
--- 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): Bluebell
Outside (2): Aster, Clover
One member ⇒ Bluebell is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Bluebell is INSIDE the Smith set. ✓
Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
More: 07_Concepts/topics/smith_set.md
NOTE: a generated cross-method view of the STAR ballots, for comparison only — not the official STAR result.
Ranked Robin (RCV-RR) — every pair, head-to-head¶
--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
Tabulating 57 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Aster, Bluebell, Clover
9 × Bluebell > Aster > Clover (4, 5, 0)
6 × Aster > Bluebell=Clover (5, 0, 0)
24 × Bluebell > Aster=Clover (0, 1, 0)
18 × Clover > Aster=Bluebell (0, 0, 4)
Round-Robin — every pair, head-to-head (For – Against):
Bluebell beats Aster 33 – 6
Clover beats Aster 18 – 15
Bluebell beats Clover 33 – 18
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Aster | Bluebell | Clover |
---------------------------------------------------------
Aster > | --- | 6 - 18 - 33 |15 - 24 - 18 |
Bluebell > | 33 - 18 - 6 | --- |33 - 6 - 18 |
Clover > | 18 - 24 - 15 |18 - 6 - 33 | --- |
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 Bluebell 2–0–0 2 +42 Clover, Aster
2 Clover 1–1–0 1 -12 Aster
3 Aster 0–2–0 0 -30 —
Winner — Ranked Robin (RCV-RR): Bluebell
beats every opponent head-to-head — the Condorcet winner.
--- 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): Bluebell
Outside (2): Aster, Clover
One member ⇒ Bluebell is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Bluebell 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