Kim (A,B)-scoring, A=1 — the middle choice is worth everything (Negative voting)¶
▶ Live on BetterVoting: vote · results ↗ (election 6mcgkq · test BV2275) — an independent tabulator to check the winners below against.
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 Almond rather than STAR's Berry, but this is an artifact of score→rank conversion, not a robust method difference: 36 of 36 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 (Berry). 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 | Berry |
| RCV-IRV | Almond |
| Ranked Robin (RCV-RR) | Berry |
| Approval | Berry |
| Range / Score | Berry |
| Condorcet | Berry |
Flags: 36 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie); RR conversion-sensitive (weak=Berry, strict=Almond)
Source election: method_comparisons/kim_ordinal_vs_cardinal/cases/bv2275_6mcgkq_a1_negative.yaml · STAR tabulated mirror: bv2275_6mcgkq_a1_negative_tabulated.txt
3 candidates, 36 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Almond | Berry | Cocoa |
|---|---|---|---|
| 20 | 4 | 4 | 0 |
| 7 | 4 | 0 | 4 |
| 9 | 0 | 4 | 4 |
STAR result (official)¶
Scoring round (sum of scores): Berry 116, Almond 108, Cocoa 64
Finalists (top two): Berry and Almond
Automatic runoff: Berry 9 vs Almond 7 (20 equal/no-preference)
STAR winner: Berry
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Almond | * Berry |
-----------------------------------------------
* Almond > | --- | 7 - 20 - 9 |
* Berry > | 9 - 20 - 7 | --- |
[Divergence from STAR]
STAR = Berry
Choose-One (Plurality) = Almond (differs from STAR)
RCV-IRV = Almond (differs from STAR)
Note: 36 of 36 ballots (100%) 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 36 ballots.
Count × Almond,Berry,Cocoa
20 × 4, 4, 0
9 × 0, 4, 4
7 × 4, 0, 4
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Almond 0 27 0 0 0 9 | 108 3.0
Berry 0 29 0 0 0 7 | 116 3.2
Cocoa 0 16 0 0 0 20 | 64 1.8
Scoring Round
The two highest-scoring candidates advance to the next round.
Berry -- 116 -- First place
Almond -- 108 -- Second place
Cocoa -- 64
Berry and Almond advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Berry -- 9 -- First place
Almond -- 7
Equal Support -- 20
Berry wins.
Voters with a preference: 16 of 36 (20 Equal Support).
Berry 9 (56%) vs Almond 7 (44%); majority = 9.
Winner — STAR Voting Method (single winner)
Berry
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 36 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: Almond, Berry, Cocoa
20 × Almond > Berry (4, 4, 0)
7 × Almond > Cocoa (4, 0, 4)
9 × Berry > Cocoa (0, 4, 4)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Almond 27 Elected
Berry 9 Rejected
Cocoa 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Almond
--- 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 3): Berry
Outside (2): Almond, Cocoa
One member ⇒ Berry is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Almond is OUTSIDE the Smith set. ✗
Every member of the set (Berry) beats Almond head-to-head, yet
RCV-IRV elected Almond 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 36 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Almond, Berry, Cocoa
20 × Almond=Berry > Cocoa (4, 4, 0)
7 × Almond=Cocoa > Berry (4, 0, 4)
9 × Berry=Cocoa > Almond (0, 4, 4)
Round-Robin — every pair, head-to-head (For – Against):
Berry beats Almond 9 – 7
Almond beats Cocoa 20 – 9
Berry beats Cocoa 20 – 7
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Almond | Berry | Cocoa |
-------------------------------------------------------
Almond > | --- | 7 - 20 - 9 |20 - 7 - 9 |
Berry > | 9 - 20 - 7 | --- |20 - 9 - 7 |
Cocoa > | 9 - 7 - 20 | 7 - 9 - 20 | --- |
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 Berry 2–0–0 2 +15 Almond, Cocoa
2 Almond 1–1–0 1 +9 Cocoa
3 Cocoa 0–2–0 0 -24 —
Winner — Ranked Robin (RCV-RR): Berry
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 3): Berry
Outside (2): Almond, Cocoa
One member ⇒ Berry is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Berry 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