Pineapple progression (3/3) — 11% wins Choose-One, but Cheese is the real choice¶
▶ Live on BetterVoting: vote · results ↗ (election h34pp9 · test BV2218) — an independent tabulator to check the winners below against.
Bucket — IRV_OUTLIER_RR_WITH_STAR: RCV-IRV is the outlier (center squeeze)
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 elects Cheese — and so do Ranked Robin and Condorcet, because Cheese is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Pineapple: Cheese collects fewer top (first-choice) votes, so IRV eliminates Cheese early, and those ballots transfer to Pineapple. This is the classic center squeeze — the broadly acceptable candidate is knocked out by round-by-round elimination even though a majority prefers them in a direct matchup. Two methods (STAR + RR) against one (RCV-IRV): IRV is the outlier.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Cheese |
| RCV-IRV | Pineapple |
| Ranked Robin (RCV-RR) | Cheese |
| Approval | Cheese |
| Range / Score | Cheese |
| Condorcet | Cheese |
Flags: none
Source election: method_comparisons/minority_winner_progression/cases/pineapple_11pct.yaml · STAR tabulated mirror: pineapple_11pct_tabulated.txt
11 candidates, 100 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Pineapple | Anchovy | Mushroom | Olive | Sausage | Spinach | Jalapeno | Onion | Pepper | Basil | Cheese |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 11 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 10 | 0 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 10 | 0 | 0 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 10 | 0 | 0 | 0 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 10 | 0 | 0 | 0 | 0 | 5 | 0 | 0 | 0 | 0 | 0 | 4 |
| 10 | 0 | 0 | 0 | 0 | 0 | 5 | 0 | 0 | 0 | 0 | 4 |
| 10 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 0 | 0 | 0 | 4 |
| 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 0 | 0 | 4 |
| 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 0 | 4 |
| 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 4 |
STAR result (official)¶
Scoring round (sum of scores): Cheese 400, Pineapple 55, Anchovy 50, Mushroom 50, Olive 50, Sausage 50, Spinach 50, Jalapeno 50, Onion 50, Pepper 50, Basil 45
Finalists (top two): Cheese and Pineapple
Automatic runoff: Cheese 89 vs Pineapple 11
STAR winner: Cheese
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Pineapple | * Cheese |
--------------------------------------------------
* Pineapple > | --- |11 - 0 - 89 |
* Cheese > | 89 - 0 - 11 | --- |
[Divergence from STAR]
STAR = Cheese
Choose-One (Plurality) = Pineapple (differs from STAR)
RCV-IRV = Pineapple (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 100 ballots.
Count × Pineapple,Anchovy,Mushroom,Olive,Sausage,Spinach,Jalapeno,Onion,Pepper,Basil,Cheese
11 × 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4
10 × 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 4
10 × 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 4
10 × 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4
10 × 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 4
10 × 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 4
10 × 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4
10 × 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 4
10 × 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4
9 × 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Pineapple 11 0 0 0 0 89 | 55 0.6
Anchovy 10 0 0 0 0 90 | 50 0.5
Mushroom 10 0 0 0 0 90 | 50 0.5
Olive 10 0 0 0 0 90 | 50 0.5
Sausage 10 0 0 0 0 90 | 50 0.5
Spinach 10 0 0 0 0 90 | 50 0.5
Jalapeno 10 0 0 0 0 90 | 50 0.5
Onion 10 0 0 0 0 90 | 50 0.5
Pepper 10 0 0 0 0 90 | 50 0.5
Basil 9 0 0 0 0 91 | 45 0.5
Cheese 0 100 0 0 0 0 | 400 4.0
Scoring Round
The two highest-scoring candidates advance to the next round.
Cheese -- 400 -- First place
Pineapple -- 55 -- Second place
Anchovy -- 50
Jalapeno -- 50
Mushroom -- 50
Olive -- 50
Onion -- 50
Pepper -- 50
Sausage -- 50
Spinach -- 50
Basil -- 45
Cheese and Pineapple advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Cheese -- 89 -- First place
Pineapple -- 11
Equal Support -- 0
Cheese wins.
Voters with a preference: 100 of 100 (no Equal Support).
Cheese 89 (89%) vs Pineapple 11 (11%); majority = 51.
Winner — STAR Voting Method (single winner)
Cheese
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 100 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: Pineapple, Anchovy, Mushroom, Olive, Sausage, Spinach, Jalapeno, Onion, Pepper, Basil, Cheese
11 × Pineapple > Cheese (5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4)
10 × Anchovy > Cheese (0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 4)
10 × Mushroom > Cheese (0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 4)
10 × Olive > Cheese (0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4)
10 × Sausage > Cheese (0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 4)
10 × Spinach > Cheese (0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 4)
10 × Jalapeno > Cheese (0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4)
10 × Onion > Cheese (0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 4)
10 × Pepper > Cheese (0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4)
9 × Basil > Cheese (0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4)
ROUND 1
Candidate Votes Status
----------- ------- --------
Pineapple 11 Hopeful
Onion 10 Hopeful
Anchovy 10 Hopeful
Mushroom 10 Hopeful
Olive 10 Hopeful
Pepper 10 Hopeful
Sausage 10 Hopeful
Spinach 10 Hopeful
Jalapeno 10 Hopeful
Basil 9 Rejected
Cheese 0 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Pineapple 11 Hopeful
Onion 10 Hopeful
Olive 10 Hopeful
Spinach 10 Hopeful
Mushroom 10 Hopeful
Jalapeno 10 Hopeful
Pepper 10 Hopeful
Anchovy 10 Hopeful
Sausage 10 Rejected
Basil 0 Rejected
Cheese 0 Rejected
Blank Votes 9 Rejected
ROUND 3
Candidate Votes Status
----------- ------- --------
Pineapple 11 Hopeful
Anchovy 10 Hopeful
Pepper 10 Hopeful
Spinach 10 Hopeful
Jalapeno 10 Hopeful
Onion 10 Hopeful
Olive 10 Hopeful
Mushroom 10 Rejected
Sausage 0 Rejected
Basil 0 Rejected
Cheese 0 Rejected
Blank Votes 19 Rejected
ROUND 4
Candidate Votes Status
----------- ------- --------
Pineapple 11 Hopeful
Spinach 10 Hopeful
Jalapeno 10 Hopeful
Anchovy 10 Hopeful
Onion 10 Hopeful
Olive 10 Hopeful
Pepper 10 Rejected
Mushroom 0 Rejected
Sausage 0 Rejected
Basil 0 Rejected
Cheese 0 Rejected
Blank Votes 29 Rejected
ROUND 5
Candidate Votes Status
----------- ------- --------
Pineapple 11 Hopeful
Spinach 10 Hopeful
Olive 10 Hopeful
Anchovy 10 Hopeful
Jalapeno 10 Hopeful
Onion 10 Rejected
Pepper 0 Rejected
Mushroom 0 Rejected
Sausage 0 Rejected
Basil 0 Rejected
Cheese 0 Rejected
Blank Votes 39 Rejected
ROUND 6
Candidate Votes Status
----------- ------- --------
Pineapple 11 Hopeful
Anchovy 10 Hopeful
Jalapeno 10 Hopeful
Olive 10 Hopeful
Spinach 10 Rejected
Onion 0 Rejected
Pepper 0 Rejected
Mushroom 0 Rejected
Sausage 0 Rejected
Basil 0 Rejected
Cheese 0 Rejected
Blank Votes 49 Rejected
ROUND 7
Candidate Votes Status
----------- ------- --------
Pineapple 11 Hopeful
Olive 10 Hopeful
Anchovy 10 Hopeful
Jalapeno 10 Rejected
Spinach 0 Rejected
Onion 0 Rejected
Pepper 0 Rejected
Mushroom 0 Rejected
Sausage 0 Rejected
Basil 0 Rejected
Cheese 0 Rejected
Blank Votes 59 Rejected
ROUND 8
Candidate Votes Status
----------- ------- --------
Pineapple 11 Hopeful
Anchovy 10 Hopeful
Olive 10 Rejected
Jalapeno 0 Rejected
Spinach 0 Rejected
Onion 0 Rejected
Pepper 0 Rejected
Mushroom 0 Rejected
Sausage 0 Rejected
Basil 0 Rejected
Cheese 0 Rejected
Blank Votes 69 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Pineapple 11 Elected
Anchovy 10 Rejected
Olive 0 Rejected
Jalapeno 0 Rejected
Spinach 0 Rejected
Onion 0 Rejected
Pepper 0 Rejected
Mushroom 0 Rejected
Sausage 0 Rejected
Basil 0 Rejected
Cheese 0 Rejected
Blank Votes 79 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Pineapple
--- 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 11): Cheese
Outside (10): Pineapple, Anchovy, Mushroom, Olive, Sausage, Spinach, Jalapeno, Onion, Pepper, Basil
One member ⇒ Cheese is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Pineapple is OUTSIDE the Smith set. ✗
Every member of the set (Cheese) beats Pineapple head-to-head, yet
RCV-IRV elected Pineapple 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 100 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Pineapple, Anchovy, Mushroom, Olive, Sausage, Spinach, Jalapeno, Onion, Pepper, Basil, Cheese
11 × Pineapple > Cheese > Anchovy=Mushroom=Olive=Sausage=Spinach=Jalapeno=Onion=Pepper=Basil (5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4)
10 × Anchovy > Cheese > Pineapple=Mushroom=Olive=Sausage=Spinach=Jalapeno=Onion=Pepper=Basil (0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 4)
10 × Mushroom > Cheese > Pineapple=Anchovy=Olive=Sausage=Spinach=Jalapeno=Onion=Pepper=Basil (0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 4)
10 × Olive > Cheese > Pineapple=Anchovy=Mushroom=Sausage=Spinach=Jalapeno=Onion=Pepper=Basil (0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 4)
10 × Sausage > Cheese > Pineapple=Anchovy=Mushroom=Olive=Spinach=Jalapeno=Onion=Pepper=Basil (0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 4)
10 × Spinach > Cheese > Pineapple=Anchovy=Mushroom=Olive=Sausage=Jalapeno=Onion=Pepper=Basil (0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 4)
10 × Jalapeno > Cheese > Pineapple=Anchovy=Mushroom=Olive=Sausage=Spinach=Onion=Pepper=Basil (0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4)
10 × Onion > Cheese > Pineapple=Anchovy=Mushroom=Olive=Sausage=Spinach=Jalapeno=Pepper=Basil (0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 4)
10 × Pepper > Cheese > Pineapple=Anchovy=Mushroom=Olive=Sausage=Spinach=Jalapeno=Onion=Basil (0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4)
9 × Basil > Cheese > Pineapple=Anchovy=Mushroom=Olive=Sausage=Spinach=Jalapeno=Onion=Pepper (0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4)
Round-Robin — every pair, head-to-head (For – Against):
Pineapple beats Anchovy 11 – 10
Pineapple beats Mushroom 11 – 10
Pineapple beats Olive 11 – 10
Pineapple beats Sausage 11 – 10
Pineapple beats Spinach 11 – 10
Pineapple beats Jalapeno 11 – 10
Pineapple beats Onion 11 – 10
Pineapple beats Pepper 11 – 10
Pineapple beats Basil 11 – 9
Cheese beats Pineapple 89 – 11
Anchovy ties Mushroom 10 – 10
Anchovy ties Olive 10 – 10
Anchovy ties Sausage 10 – 10
Anchovy ties Spinach 10 – 10
Anchovy ties Jalapeno 10 – 10
Anchovy ties Onion 10 – 10
Anchovy ties Pepper 10 – 10
Anchovy beats Basil 10 – 9
Cheese beats Anchovy 90 – 10
Mushroom ties Olive 10 – 10
Mushroom ties Sausage 10 – 10
Mushroom ties Spinach 10 – 10
Mushroom ties Jalapeno 10 – 10
Mushroom ties Onion 10 – 10
Mushroom ties Pepper 10 – 10
Mushroom beats Basil 10 – 9
Cheese beats Mushroom 90 – 10
Olive ties Sausage 10 – 10
Olive ties Spinach 10 – 10
Olive ties Jalapeno 10 – 10
Olive ties Onion 10 – 10
Olive ties Pepper 10 – 10
Olive beats Basil 10 – 9
Cheese beats Olive 90 – 10
Sausage ties Spinach 10 – 10
Sausage ties Jalapeno 10 – 10
Sausage ties Onion 10 – 10
Sausage ties Pepper 10 – 10
Sausage beats Basil 10 – 9
Cheese beats Sausage 90 – 10
Spinach ties Jalapeno 10 – 10
Spinach ties Onion 10 – 10
Spinach ties Pepper 10 – 10
Spinach beats Basil 10 – 9
Cheese beats Spinach 90 – 10
Jalapeno ties Onion 10 – 10
Jalapeno ties Pepper 10 – 10
Jalapeno beats Basil 10 – 9
Cheese beats Jalapeno 90 – 10
Onion ties Pepper 10 – 10
Onion beats Basil 10 – 9
Cheese beats Onion 90 – 10
Pepper beats Basil 10 – 9
Cheese beats Pepper 90 – 10
Cheese beats Basil 91 – 9
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Pineapple | Anchovy | Mushroom | Olive | Sausage | Spinach | Jalapeno | Onion | Pepper | Basil | Cheese |
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Pineapple > | --- |11 - 79 - 10 |11 - 79 - 10 |11 - 79 - 10 |11 - 79 - 10 |11 - 79 - 10 |11 - 79 - 10 |11 - 79 - 10 |11 - 79 - 10 |11 - 80 - 9 |11 - 0 - 89 |
Anchovy > | 10 - 79 - 11 | --- |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 81 - 9 |10 - 0 - 90 |
Mushroom > | 10 - 79 - 11 |10 - 80 - 10 | --- |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 81 - 9 |10 - 0 - 90 |
Olive > | 10 - 79 - 11 |10 - 80 - 10 |10 - 80 - 10 | --- |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 81 - 9 |10 - 0 - 90 |
Sausage > | 10 - 79 - 11 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 | --- |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 81 - 9 |10 - 0 - 90 |
Spinach > | 10 - 79 - 11 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 | --- |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 81 - 9 |10 - 0 - 90 |
Jalapeno > | 10 - 79 - 11 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 | --- |10 - 80 - 10 |10 - 80 - 10 |10 - 81 - 9 |10 - 0 - 90 |
Onion > | 10 - 79 - 11 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 | --- |10 - 80 - 10 |10 - 81 - 9 |10 - 0 - 90 |
Pepper > | 10 - 79 - 11 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 |10 - 80 - 10 | --- |10 - 81 - 9 |10 - 0 - 90 |
Basil > | 9 - 80 - 11 | 9 - 81 - 10 | 9 - 81 - 10 | 9 - 81 - 10 | 9 - 81 - 10 | 9 - 81 - 10 | 9 - 81 - 10 | 9 - 81 - 10 | 9 - 81 - 10 | --- | 9 - 0 - 91 |
Cheese > | 89 - 0 - 11 |90 - 0 - 10 |90 - 0 - 10 |90 - 0 - 10 |90 - 0 - 10 |90 - 0 - 10 |90 - 0 - 10 |90 - 0 - 10 |90 - 0 - 10 |91 - 0 - 9 | --- |
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 Cheese 10–0–0 10 +800 Pineapple, Anchovy, Mushroom, Olive, Sausage, Spinach, Jalapeno, Onion, Pepper, Basil
2 Pineapple 9–1–0 9 -68 Anchovy, Mushroom, Olive, Sausage, Spinach, Jalapeno, Onion, Pepper, Basil
3 Anchovy 1–2–7 4.5 -80 Basil
4 Mushroom 1–2–7 4.5 -80 Basil
5 Olive 1–2–7 4.5 -80 Basil
6 Sausage 1–2–7 4.5 -80 Basil
7 Spinach 1–2–7 4.5 -80 Basil
8 Jalapeno 1–2–7 4.5 -80 Basil
9 Onion 1–2–7 4.5 -80 Basil
10 Pepper 1–2–7 4.5 -80 Basil
11 Basil 0–10–0 0 -92 —
Winner — Ranked Robin (RCV-RR): Cheese
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 11): Cheese
Outside (10): Pineapple, Anchovy, Mushroom, Olive, Sausage, Spinach, Jalapeno, Onion, Pepper, Basil
One member ⇒ Cheese is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Cheese 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