Equal ranks — a bare majority puts Amira top, and Basil still wins¶
Bucket — IRV_DIFFERS_ARTIFACT: RCV-IRV differs — tie-break artifact
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
On these ballots RCV-IRV reports Amira rather than STAR's Basil, but this is an artifact of score→rank conversion, not a robust method difference: 94 of 200 ballots have tied non-zero scores, so their ranks are set by an arbitrary candidate-priority order; the RCV-IRV winner flips when that priority order is reversed. Ranked Robin and the Condorcet (pairwise) winner both agree with STAR (Basil). Do not use this case to criticize RCV-IRV — the disagreement is a coin-flip created by equal scores and would vanish under a different (equally arbitrary) tie-break.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Basil |
| RCV-IRV | Amira |
| Ranked Robin (RCV-RR) | Basil |
| Approval | Basil |
| Range / Score | Basil |
| Condorcet | Basil |
Flags: 94 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie); RR conversion-sensitive (weak=Basil, strict=Amira)
Source election: method_comparisons/equal_rank_irv/cases/equal_rank_majority_alternative.yaml · STAR tabulated mirror: equal_rank_majority_alternative_tabulated.txt
4 candidates, 200 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Amira | Basil | Cora | Dmitri |
|---|---|---|---|---|
| 94 | 5 | 5 | 2 | 0 |
| 8 | 5 | 4 | 2 | 0 |
| 50 | 0 | 4 | 5 | 2 |
| 48 | 0 | 4 | 2 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Basil 894, Cora 550, Amira 510, Dmitri 340
Finalists (top two): Basil and Cora
Automatic runoff: Basil 150 vs Cora 50
STAR winner: Basil
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Basil | * Cora |
--------------------------------------------------------
* Basil > | --- |150 - 0 - 50 |
* Cora > | 50 - 0 - 150 | --- |
[Divergence from STAR]
STAR = Basil
Choose-One (Plurality) = Amira (differs from STAR)
RCV-IRV = Amira (differs from STAR)
Note: 94 of 200 ballots (47%) had equal non-zero scores, so their ranks
were decided by candidate priority order. The RCV-IRV result may be
an artifact of score-to-rank tie-breaking rather than a deep
difference.
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 200 ballots.
Count × Amira,Basil,Cora,Dmitri
94 × 5, 5, 2, 0
50 × 0, 4, 5, 2
48 × 0, 4, 2, 5
8 × 5, 4, 2, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Amira 102 0 0 0 0 98 | 510 2.6
Basil 94 106 0 0 0 0 | 894 4.5
Cora 50 0 0 150 0 0 | 550 2.8
Dmitri 48 0 0 50 0 102 | 340 1.7
Scoring Round
The two highest-scoring candidates advance to the next round.
Basil -- 894 -- First place
Cora -- 550 -- Second place
Amira -- 510
Dmitri -- 340
Basil and Cora advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Basil -- 150 -- First place
Cora -- 50
Equal Support -- 0
Basil wins.
Voters with a preference: 200 of 200 (no Equal Support).
Basil 150 (75%) vs Cora 50 (25%); majority = 101.
Winner — STAR Voting Method (single winner)
Basil
RCV-IRV — round by round¶
⚠️ This election has a fragile IRV tie (equal scores force an arbitrary tie-break). The round table below is only one realization; a different tie-break can change the winner. See the flag above.
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 200 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: Amira, Basil, Cora, Dmitri
94 × Amira > Basil > Cora (5, 5, 2, 0)
8 × Amira > Basil > Cora (5, 4, 2, 0)
50 × Cora > Basil > Dmitri (0, 4, 5, 2)
48 × Dmitri > Basil > Cora (0, 4, 2, 5)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Amira 102 Elected
Cora 50 Rejected
Dmitri 48 Rejected
Basil 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Amira
--- 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 4): Basil
Outside (3): Amira, Cora, Dmitri
One member ⇒ Basil is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Amira is OUTSIDE the Smith set. ✗
Every member of the set (Basil) beats Amira head-to-head, yet
RCV-IRV elected Amira anyway. RCV-IRV is not Smith-efficient (nor
Condorcet-efficient) — this is the shape a center squeeze leaves behind.
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 200 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Amira, Basil, Cora, Dmitri
94 × Amira=Basil > Cora > Dmitri (5, 5, 2, 0)
8 × Amira > Basil > Cora > Dmitri (5, 4, 2, 0)
50 × Cora > Basil > Dmitri > Amira (0, 4, 5, 2)
48 × Dmitri > Basil > Cora > Amira (0, 4, 2, 5)
Round-Robin — every pair, head-to-head (For – Against):
Basil beats Amira 98 – 8
Amira beats Cora 102 – 98
Amira beats Dmitri 102 – 98
Basil beats Cora 150 – 50
Basil beats Dmitri 152 – 48
Cora beats Dmitri 152 – 48
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Amira | Basil | Cora | Dmitri |
---------------------------------------------------------------------------------
Amira > | --- | 8 - 94 - 98 |102 - 0 - 98 |102 - 0 - 98 |
Basil > | 98 - 94 - 8 | --- |150 - 0 - 50 |152 - 0 - 48 |
Cora > | 98 - 0 - 102 | 50 - 0 - 150 | --- |152 - 0 - 48 |
Dmitri > | 98 - 0 - 102 | 48 - 0 - 152 | 48 - 0 - 152 | --- |
Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by the Ranked Robin degrees, then lot order):
# Candidate W–L–T Copeland Margin Beats
1 Basil 3–0–0 3 +294 Amira, Cora, Dmitri
2 Amira 2–1–0 2 -82 Cora, Dmitri
3 Cora 1–2–0 1 +0 Dmitri
4 Dmitri 0–3–0 0 -212 —
Winner — Ranked Robin (RCV-RR): Basil
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 4): Basil
Outside (3): Amira, Cora, Dmitri
One member ⇒ Basil is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Basil 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