STAR's runoff is spoiler-sensitive under a Condorcet cycle — a losing candidate (Ben) flips Alice vs Carla (BV2212, g3f7r2)¶
▶ Live on BetterVoting: vote · results ↗ (election g3f7r2 · test BV2212) — an independent tabulator to check the winners below against.
Bucket — CYCLE_OR_THREE_WAY: Cycle / three-way split
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
There is no Condorcet winner — the head-to-head results form a cycle (X beats Y beats Z beats X). With no pairwise anchor the methods split: STAR=Alice, RCV-IRV=Carla, Ranked Robin=Alice (RR breaks the cycle by total margin). No rule is clearly 'right'; a genuinely hard election, not an indictment of any one method.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Alice |
| RCV-IRV | Carla |
| Ranked Robin (RCV-RR) | Alice |
| Approval | Alice |
| Range / Score | Alice |
| Condorcet | none (cycle) |
Flags: none
Source election: 01_STAR/03_Criteria/iia_cycle_spoiler/cases/bv2212_g3f7r2_cycle_spoiler.yaml · STAR tabulated mirror: bv2212_g3f7r2_cycle_spoiler_tabulated.txt
3 candidates, 23 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Alice | Ben | Carla |
|---|---|---|---|
| 7 | 3 | 0 | 5 |
| 10 | 5 | 3 | 0 |
| 6 | 0 | 5 | 3 |
STAR result (official)¶
Scoring round (sum of scores): Alice 71, Ben 60, Carla 53
Finalists (top two): Alice and Ben
Automatic runoff: Alice 17 vs Ben 6
STAR winner: Alice
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Alice | * Ben |
-----------------------------------------------
* Alice > | --- |17 - 0 - 6 |
* Ben > | 6 - 0 - 17 | --- |
[Divergence from STAR]
STAR = Alice
RCV-IRV = Carla (differs from STAR)
Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
method difference, not a tie-breaking artifact.
Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
outlier — the classic center-squeeze signature.
--- STAR Voting Method (single winner) ---
Tabulating 23 ballots.
Count × Alice,Ben,Carla
10 × 5, 3, 0
7 × 3, 0, 5
6 × 0, 5, 3
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Alice 10 0 7 0 0 6 | 71 3.1
Ben 6 0 10 0 0 7 | 60 2.6
Carla 7 0 6 0 0 10 | 53 2.3
Scoring Round
The two highest-scoring candidates advance to the next round.
Alice -- 71 -- First place
Ben -- 60 -- Second place
Carla -- 53
Alice and Ben advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Alice -- 17 -- First place
Ben -- 6
Equal Support -- 0
Alice wins.
Voters with a preference: 23 of 23 (no Equal Support).
Alice 17 (74%) vs Ben 6 (26%); majority = 12.
Winner — STAR Voting Method (single winner)
Alice
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 23 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: Alice, Ben, Carla
7 × Carla > Alice (3, 0, 5)
10 × Alice > Ben (5, 3, 0)
6 × Ben > Carla (0, 5, 3)
ROUND 1
Candidate Votes Status
----------- ------- --------
Alice 10 Hopeful
Carla 7 Hopeful
Ben 6 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Carla 13 Elected
Alice 10 Rejected
Ben 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Carla
--- 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 (3 of 3): Alice, Ben, Carla
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
cycle, so the strongest "candidate" is a set, not a person. Which member of
the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
RCV-IRV winner Carla 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 23 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Alice, Ben, Carla
7 × Carla > Alice > Ben (3, 0, 5)
10 × Alice > Ben > Carla (5, 3, 0)
6 × Ben > Carla > Alice (0, 5, 3)
Round-Robin — every pair, head-to-head (For – Against):
Alice beats Ben 17 – 6
Carla beats Alice 13 – 10
Ben beats Carla 16 – 7
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Alice | Ben | Carla |
------------------------------------------------------
Alice > | --- |17 - 0 - 6 |10 - 0 - 13 |
Ben > | 6 - 0 - 17 | --- |16 - 0 - 7 |
Carla > | 13 - 0 - 10 | 7 - 0 - 16 | --- |
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 Alice 1–1–0 1 +8 Ben
2 Ben 1–1–0 1 -2 Carla
3 Carla 1–1–0 1 -6 Alice
Winner — Ranked Robin (RCV-RR): Alice
*** 3 candidates tie for the most wins (Alice, Ben, Carla) — a Condorcet cycle (no candidate beats all others). Resolved by total margin, then lot order. (This is where Minimax / Ranked Pairs / Schulze differ — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.)
--- 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 (3 of 3): Alice, Ben, Carla
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
cycle, so the strongest "candidate" is a set, not a person. Which member of
the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
Ranked Robin (RCV-RR) winner Alice 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