Reversal symmetry — STAR, original: B (STAR does not winner=loser here)¶
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=B, RCV-IRV=A, Ranked Robin=B (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 | B |
| RCV-IRV | A |
| Ranked Robin (RCV-RR) | B |
| Approval | B |
| Range / Score | B |
| Condorcet | none (cycle) |
Flags: none
Source election: method_comparisons/reversal_symmetry/cases/reversal_star_original.yaml · STAR tabulated mirror: reversal_star_original_tabulated.txt
3 candidates, 24 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | A | B | C |
|---|---|---|---|
| 9 | 0 | 5 | 3 |
| 8 | 5 | 3 | 0 |
| 7 | 3 | 0 | 5 |
STAR result (official)¶
Scoring round (sum of scores): B 69, C 62, A 61
Finalists (top two): B and C
Automatic runoff: B 17 vs C 7
STAR winner: B
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * B | * C |
-----------------------------------------------
* B > | --- |17 - 0 - 7 |
* C > | 7 - 0 - 17 | --- |
[Divergence from STAR]
STAR = B
RCV-IRV = A (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 24 ballots.
Count × A,B,C
9 × 0,5,3
8 × 5,3,0
7 × 3,0,5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
A 8 0 7 0 0 9 | 61 2.5
B 9 0 8 0 0 7 | 69 2.9
C 7 0 9 0 0 8 | 62 2.6
Scoring Round
The two highest-scoring candidates advance to the next round.
B -- 69 -- First place
C -- 62 -- Second place
A -- 61
B and C advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
B -- 17 -- First place
C -- 7
Equal Support -- 0
B wins.
Voters with a preference: 24 of 24 (no Equal Support).
B 17 (71%) vs C 7 (29%); majority = 13.
Winner — STAR Voting Method (single winner)
B
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 24 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: A, B, C
9 × B > C (0, 5, 3)
8 × A > B (5, 3, 0)
7 × C > A (3, 0, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
B 9 Hopeful
A 8 Hopeful
C 7 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
A 15 Elected
B 9 Rejected
C 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
A
--- 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): A, B, C
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 A 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 24 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: A, B, C
9 × B > C > A (0, 5, 3)
8 × A > B > C (5, 3, 0)
7 × C > A > B (3, 0, 5)
Round-Robin — every pair, head-to-head (For – Against):
A beats B 15 – 9
C beats A 16 – 8
B beats C 17 – 7
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| A | B | C |
--------------------------------------------------
A > | --- |15 - 0 - 9 | 8 - 0 - 16 |
B > | 9 - 0 - 15 | --- |17 - 0 - 7 |
C > | 16 - 0 - 8 | 7 - 0 - 17 | --- |
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 B 1–1–0 1 +4 C
2 A 1–1–0 1 -2 B
3 C 1–1–0 1 -2 A
Winner — Ranked Robin (RCV-RR): B
*** 3 candidates tie for the most wins (A, B, C) — 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): A, B, C
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 B 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