Pineapple progression (2/3) — 25% wins Choose-One, but Cheese is the real choice¶
▶ Live on BetterVoting: vote · results ↗ (election mvxbxr · test BV2217) — 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_25pct.yaml · STAR tabulated mirror: pineapple_25pct_tabulated.txt
5 candidates, 100 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Pineapple | Anchovy | Mushroom | Olive | Cheese |
|---|---|---|---|---|---|
| 25 | 5 | 0 | 0 | 0 | 4 |
| 23 | 0 | 5 | 0 | 0 | 4 |
| 23 | 0 | 0 | 5 | 0 | 4 |
| 23 | 0 | 0 | 0 | 5 | 4 |
| 6 | 0 | 0 | 0 | 0 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Cheese 406, Pineapple 125, Anchovy 115, Mushroom 115, Olive 115
Finalists (top two): Cheese and Pineapple
Automatic runoff: Cheese 75 vs Pineapple 25
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 > | --- |25 - 0 - 75 |
* Cheese > | 75 - 0 - 25 | --- |
[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,Cheese
25 × 5, 0, 0, 0, 4
23 × 0, 5, 0, 0, 4
23 × 0, 0, 5, 0, 4
23 × 0, 0, 0, 5, 4
6 × 0, 0, 0, 0, 5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Pineapple 25 0 0 0 0 75 | 125 1.3
Anchovy 23 0 0 0 0 77 | 115 1.2
Mushroom 23 0 0 0 0 77 | 115 1.2
Olive 23 0 0 0 0 77 | 115 1.2
Cheese 6 94 0 0 0 0 | 406 4.1
Scoring Round
The two highest-scoring candidates advance to the next round.
Cheese -- 406 -- First place
Pineapple -- 125 -- Second place
Anchovy -- 115
Mushroom -- 115
Olive -- 115
Cheese and Pineapple advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Cheese -- 75 -- First place
Pineapple -- 25
Equal Support -- 0
Cheese wins.
Voters with a preference: 100 of 100 (no Equal Support).
Cheese 75 (75%) vs Pineapple 25 (25%); 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, Cheese
25 × Pineapple > Cheese (5, 0, 0, 0, 4)
23 × Anchovy > Cheese (0, 5, 0, 0, 4)
23 × Mushroom > Cheese (0, 0, 5, 0, 4)
23 × Olive > Cheese (0, 0, 0, 5, 4)
6 × Cheese (0, 0, 0, 0, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Pineapple 25 Hopeful
Anchovy 23 Hopeful
Mushroom 23 Hopeful
Olive 23 Hopeful
Cheese 6 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Pineapple 25 Hopeful
Anchovy 23 Hopeful
Mushroom 23 Hopeful
Olive 23 Rejected
Cheese 0 Rejected
Blank Votes 6 Rejected
ROUND 3
Candidate Votes Status
----------- ------- --------
Pineapple 25 Hopeful
Anchovy 23 Hopeful
Mushroom 23 Rejected
Olive 0 Rejected
Cheese 0 Rejected
Blank Votes 29 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Pineapple 25 Elected
Anchovy 23 Rejected
Mushroom 0 Rejected
Olive 0 Rejected
Cheese 0 Rejected
Blank Votes 52 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 5): Cheese
Outside (4): Pineapple, Anchovy, Mushroom, Olive
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, Cheese
25 × Pineapple > Cheese > Anchovy=Mushroom=Olive (5, 0, 0, 0, 4)
23 × Anchovy > Cheese > Pineapple=Mushroom=Olive (0, 5, 0, 0, 4)
23 × Mushroom > Cheese > Pineapple=Anchovy=Olive (0, 0, 5, 0, 4)
23 × Olive > Cheese > Pineapple=Anchovy=Mushroom (0, 0, 0, 5, 4)
6 × Cheese > Pineapple=Anchovy=Mushroom=Olive (0, 0, 0, 0, 5)
Round-Robin — every pair, head-to-head (For – Against):
Pineapple beats Anchovy 25 – 23
Pineapple beats Mushroom 25 – 23
Pineapple beats Olive 25 – 23
Cheese beats Pineapple 75 – 25
Anchovy ties Mushroom 23 – 23
Anchovy ties Olive 23 – 23
Cheese beats Anchovy 77 – 23
Mushroom ties Olive 23 – 23
Cheese beats Mushroom 77 – 23
Cheese beats Olive 77 – 23
--- 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 | Cheese |
--------------------------------------------------------------------------------------
Pineapple > | --- |25 - 52 - 23 |25 - 52 - 23 |25 - 52 - 23 |25 - 0 - 75 |
Anchovy > | 23 - 52 - 25 | --- |23 - 54 - 23 |23 - 54 - 23 |23 - 0 - 77 |
Mushroom > | 23 - 52 - 25 |23 - 54 - 23 | --- |23 - 54 - 23 |23 - 0 - 77 |
Olive > | 23 - 52 - 25 |23 - 54 - 23 |23 - 54 - 23 | --- |23 - 0 - 77 |
Cheese > | 75 - 0 - 25 |77 - 0 - 23 |77 - 0 - 23 |77 - 0 - 23 | --- |
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 4–0–0 4 +212 Pineapple, Anchovy, Mushroom, Olive
2 Pineapple 3–1–0 3 -44 Anchovy, Mushroom, Olive
3 Anchovy 0–2–2 1 -56 —
4 Mushroom 0–2–2 1 -56 —
5 Olive 0–2–2 1 -56 —
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 5): Cheese
Outside (4): Pineapple, Anchovy, Mushroom, Olive
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