Voting styles — low-score ballots¶
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 Choco: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Choco'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 | Choco |
| Range / Score | Almond |
| Condorcet | Almond |
Flags: none
Source election: 01_STAR/02_Examples/cases/03b_c3_b3_1_style-protest-vote.yaml · STAR tabulated mirror: 03b_c3_b3_1_style-protest-vote_tabulated.txt
3 candidates, 3 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Choco | Almond | Vanilla |
|---|---|---|---|
| 2 | 0 | 1 | 0 |
| 1 | 0 | 0 | 1 |
STAR result (official)¶
Scoring round (sum of scores): Almond 2, Vanilla 1, Choco 0
Finalists (top two): Almond and Vanilla
Automatic runoff: Almond 2 vs Vanilla 1
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 | * Vanilla |
--------------------------------------------
* Almond > | --- | 2 - 0 - 1 |
* Vanilla > | 1 - 0 - 2 | --- |
[Divergence from STAR]
STAR = Almond
Approval = Choco (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 3 ballots.
Count × Choco,Almond,Vanilla
2 × 0, 1, 0
1 × 0, 0, 1
[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 0 2 1 | 2 0.7
Vanilla 0 0 0 0 1 2 | 1 0.3
Scoring Round
The two highest-scoring candidates advance to the next round.
Almond -- 2 -- First place
Vanilla -- 1 -- Second place
Choco -- 0
Almond and Vanilla advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Almond -- 2 -- First place
Vanilla -- 1
Equal Support -- 0
Almond wins.
Voters with a preference: 3 of 3 (no Equal Support).
Almond 2 (67%) vs Vanilla 1 (33%); majority = 2.
Winner — STAR Voting Method (single winner)
Almond
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
2 × Almond (0, 1, 0)
1 × Vanilla (0, 0, 1)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Almond 2 Elected
Vanilla 1 Rejected
Choco 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): Choco, Vanilla
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 3 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Choco, Almond, Vanilla
2 × Almond > Choco=Vanilla (0, 1, 0)
1 × Vanilla > Choco=Almond (0, 0, 1)
Round-Robin — every pair, head-to-head (For – Against):
Almond beats Choco 2 – 0
Vanilla beats Choco 1 – 0
Almond 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 |
-----------------------------------------------
Choco > | --- |0 - 1 - 2 |0 - 2 - 1 |
Almond > | 2 - 1 - 0 | --- |2 - 0 - 1 |
Vanilla > | 1 - 2 - 0 |1 - 0 - 2 | --- |
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 +3 Vanilla, Choco
2 Vanilla 1–1–0 1 +0 Choco
3 Choco 0–2–0 0 -3 —
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): Choco, Vanilla
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