Reversal symmetry — STAR, reversed: A (differs from original B — no winner=loser)¶
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 A. Only Approval differs, electing C: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding C's breadth of acceptability over A's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | A |
| RCV-IRV | A |
| Ranked Robin (RCV-RR) | A |
| Approval | C |
| Range / Score | C |
| Condorcet | none (cycle) |
Flags: none
Source election: method_comparisons/reversal_symmetry/cases/reversal_star_reversed.yaml · STAR tabulated mirror: reversal_star_reversed_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 | 5 | 0 | 3 |
| 8 | 0 | 3 | 5 |
| 7 | 3 | 5 | 0 |
STAR result (official)¶
Scoring round (sum of scores): C 67, A 66, B 59
Finalists (top two): C and A
Automatic runoff: C 8 vs A 16
STAR winner: A
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * A | * C |
-----------------------------------------------
* A > | --- |16 - 0 - 8 |
* C > | 8 - 0 - 16 | --- |
[Divergence from STAR]
STAR = A
Approval = C (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (C)
- Runoff Round Winner = (A)
Candidate C earned the highest total score, but
Candidate A 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 24 ballots.
Count × A,B,C
9 × 5,0,3
8 × 0,3,5
7 × 3,5,0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
A 9 0 7 0 0 8 | 66 2.8
B 7 0 8 0 0 9 | 59 2.5
C 8 0 9 0 0 7 | 67 2.8
Scoring Round
The two highest-scoring candidates advance to the next round.
C -- 67 -- First place
A -- 66 -- Second place
B -- 59
C and A advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
A -- 16 -- First place
C -- 8
Equal Support -- 0
A wins.
Voters with a preference: 24 of 24 (no Equal Support).
A 16 (67%) vs C 8 (33%); majority = 13.
Winner — STAR Voting Method (single winner)
A
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 × A > C (5, 0, 3)
8 × C > B (0, 3, 5)
7 × B > A (3, 5, 0)
ROUND 1
Candidate Votes Status
----------- ------- --------
A 9 Hopeful
C 8 Hopeful
B 7 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
A 16 Elected
C 8 Rejected
B 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 × A > C > B (5, 0, 3)
8 × C > B > A (0, 3, 5)
7 × B > A > C (3, 5, 0)
Round-Robin — every pair, head-to-head (For – Against):
B beats A 15 – 9
A beats C 16 – 8
C beats B 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 > | --- | 9 - 0 - 15 |16 - 0 - 8 |
B > | 15 - 0 - 9 | --- | 7 - 0 - 17 |
C > | 8 - 0 - 16 |17 - 0 - 7 | --- |
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 A 1–1–0 1 +2 C
2 C 1–1–0 1 +2 B
3 B 1–1–0 1 -4 A
Winner — Ranked Robin (RCV-RR): A
*** 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 A 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