Kim (A,B)-scoring, A=1/2 — the middle choice is worth half (Borda)¶
▶ Live on BetterVoting: vote · results ↗ (election 6mcgkq · test BV2275) — an independent tabulator to check the winners below against.
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 Almond. Only Approval differs, electing Cocoa: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Cocoa's breadth of acceptability over Almond's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Almond |
| RCV-IRV | Almond |
| Ranked Robin (RCV-RR) | Almond |
| Approval | Cocoa |
| Range / Score | Almond |
| Condorcet | Almond |
Flags: none
Source election: method_comparisons/kim_ordinal_vs_cardinal/cases/bv2275_6mcgkq_ahalf_borda.yaml · STAR tabulated mirror: bv2275_6mcgkq_ahalf_borda_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 |
|---|---|---|---|
| 12 | 4 | 2 | 0 |
| 8 | 2 | 4 | 0 |
| 7 | 2 | 0 | 4 |
| 9 | 0 | 2 | 4 |
STAR result (official)¶
Scoring round (sum of scores): Almond 78, Berry 74, Cocoa 64
Finalists (top two): Almond and Berry
Automatic runoff: Almond 19 vs Berry 17
STAR winner: Almond
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 > | --- |19 - 0 - 17 |
* Berry > | 17 - 0 - 19 | --- |
[Divergence from STAR]
STAR = Almond
Choose-One (Plurality) = Cocoa (differs from STAR)
Approval = Cocoa (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 36 ballots.
Count × Almond,Berry,Cocoa
12 × 4, 2, 0
9 × 0, 2, 4
8 × 2, 4, 0
7 × 2, 0, 4
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Almond 0 12 0 15 0 9 | 78 2.2
Berry 0 8 0 21 0 7 | 74 2.1
Cocoa 0 16 0 0 0 20 | 64 1.8
Scoring Round
The two highest-scoring candidates advance to the next round.
Almond -- 78 -- First place
Berry -- 74 -- Second place
Cocoa -- 64
Almond and Berry advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Almond -- 19 -- First place
Berry -- 17
Equal Support -- 0
Almond wins.
Voters with a preference: 36 of 36 (no Equal Support).
Almond 19 (53%) vs Berry 17 (47%); majority = 19.
Winner — STAR Voting Method (single winner)
Almond
RCV-IRV — round by round¶
--- 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
12 × Almond > Berry (4, 2, 0)
8 × Berry > Almond (2, 4, 0)
7 × Cocoa > Almond (2, 0, 4)
9 × Cocoa > Berry (0, 2, 4)
ROUND 1
Candidate Votes Status
----------- ------- --------
Cocoa 16 Hopeful
Almond 12 Hopeful
Berry 8 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Almond 20 Elected
Cocoa 16 Rejected
Berry 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): Almond
Outside (2): Berry, Cocoa
One member ⇒ Almond is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Almond 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 36 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Almond, Berry, Cocoa
12 × Almond > Berry > Cocoa (4, 2, 0)
8 × Berry > Almond > Cocoa (2, 4, 0)
7 × Cocoa > Almond > Berry (2, 0, 4)
9 × Cocoa > Berry > Almond (0, 2, 4)
Round-Robin — every pair, head-to-head (For – Against):
Almond beats Berry 19 – 17
Almond beats Cocoa 20 – 16
Berry beats Cocoa 20 – 16
--- 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 > | --- |19 - 0 - 17 |20 - 0 - 16 |
Berry > | 17 - 0 - 19 | --- |20 - 0 - 16 |
Cocoa > | 16 - 0 - 20 |16 - 0 - 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 Almond 2–0–0 2 +6 Berry, Cocoa
2 Berry 1–1–0 1 +2 Cocoa
3 Cocoa 0–2–0 0 -8 —
Winner — Ranked Robin (RCV-RR): Almond
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): Almond
Outside (2): Berry, Cocoa
One member ⇒ Almond is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Almond 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