All options demo¶
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 Strawberry. Only Approval differs, electing Vanilla: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Vanilla's breadth of acceptability over Strawberry's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Strawberry |
| RCV-IRV | Strawberry |
| Ranked Robin (RCV-RR) | Strawberry |
| Approval | Vanilla |
| Range / Score | Strawberry |
| Condorcet | Strawberry |
Flags: none
Source election: 01_STAR/02_Examples/cases/04b_c4_b3_display-options-all.yaml · STAR tabulated mirror: 04b_c4_b3_display-options-all_tabulated.txt
4 candidates, 3 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Choco | Almond | Vanilla | Strawberry |
|---|---|---|---|---|
| 2 | 0 | 2 | 3 | 5 |
| 1 | 0 | 2 | 5 | 3 |
STAR result (official)¶
Scoring round (sum of scores): Strawberry 13, Vanilla 11, Almond 6, Choco 0
Finalists (top two): Strawberry and Vanilla
Automatic runoff: Strawberry 2 vs Vanilla 1
STAR winner: Strawberry
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Vanilla | * Strawberry |
-----------------------------------------------------
* Vanilla > | --- | 1 - 0 - 2 |
* Strawberry > | 2 - 0 - 1 | --- |
[Divergence from STAR]
STAR = Strawberry
Approval = Vanilla (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 3 ballots.
Count × Choco,Almond,Vanilla,Strawberry
2 × 0, 2, 3, 5
1 × 0, 2, 5, 3
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Choco 0 0 0 0 0 3 | 0 0.0
Almond 0 0 0 3 0 0 | 6 2.0
Vanilla 1 0 2 0 0 0 | 11 3.7
Strawberry 2 0 1 0 0 0 | 13 4.3
Scoring Round
The two highest-scoring candidates advance to the next round.
Strawberry -- 13 -- First place
Vanilla -- 11 -- Second place
Almond -- 6
Choco -- 0
Strawberry and Vanilla advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Strawberry -- 2 -- First place
Vanilla -- 1
Equal Support -- 0
Strawberry wins.
Voters with a preference: 3 of 3 (no Equal Support).
Strawberry 2 (67%) vs Vanilla 1 (33%); majority = 2.
Winner — STAR Voting Method (single winner)
Strawberry
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 3 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: Choco, Almond, Vanilla, Strawberry
2 × Strawberry > Vanilla > Almond (0, 2, 3, 5)
1 × Vanilla > Strawberry > Almond (0, 2, 5, 3)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Strawberry 2 Elected
Vanilla 1 Rejected
Almond 0 Rejected
Choco 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Strawberry
--- 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): Strawberry
Outside (3): Choco, Almond, Vanilla
One member ⇒ Strawberry is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Strawberry 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 3 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Choco, Almond, Vanilla, Strawberry
2 × Strawberry > Vanilla > Almond > Choco (0, 2, 3, 5)
1 × Vanilla > Strawberry > Almond > Choco (0, 2, 5, 3)
Round-Robin — every pair, head-to-head (For – Against):
Almond beats Choco 3 – 0
Vanilla beats Choco 3 – 0
Strawberry beats Choco 3 – 0
Vanilla beats Almond 3 – 0
Strawberry beats Almond 3 – 0
Strawberry beats Vanilla 2 – 1
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Choco | Almond | Vanilla | Strawberry |
-------------------------------------------------------------------------
Choco > | --- | 0 - 0 - 3 | 0 - 0 - 3 | 0 - 0 - 3 |
Almond > | 3 - 0 - 0 | --- | 0 - 0 - 3 | 0 - 0 - 3 |
Vanilla > | 3 - 0 - 0 | 3 - 0 - 0 | --- | 1 - 0 - 2 |
Strawberry > | 3 - 0 - 0 | 3 - 0 - 0 | 2 - 0 - 1 | --- |
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 Strawberry 3–0–0 3 +7 Vanilla, Almond, Choco
2 Vanilla 2–1–0 2 +5 Almond, Choco
3 Almond 1–2–0 1 -3 Choco
4 Choco 0–3–0 0 -9 —
Winner — Ranked Robin (RCV-RR): Strawberry
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): Strawberry
Outside (3): Choco, Almond, Vanilla
One member ⇒ Strawberry is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Strawberry 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