Tactical maximization in STAR (1 of 2) — honest ballots: the hedgers' preference decides the runoff¶
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 Alma. Only Approval differs, electing Bruno: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Bruno's breadth of acceptability over Alma's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Alma |
| RCV-IRV | Alma |
| Ranked Robin (RCV-RR) | Alma |
| Approval | Bruno |
| Range / Score | Bruno |
| Condorcet | Alma |
Flags: none
Source election: 01_STAR/03_Criteria/tactical_maximization/cases/tactical_max_c3_b9_honest.yaml · STAR tabulated mirror: tactical_max_c3_b9_honest_tabulated.txt
3 candidates, 9 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Alma | Bruno | Celia |
|---|---|---|---|
| 4 | 5 | 3 | 0 |
| 1 | 4 | 2 | 1 |
| 3 | 1 | 5 | 3 |
| 1 | 0 | 2 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Bruno 31, Alma 27, Celia 15
Finalists (top two): Bruno and Alma
Automatic runoff: Bruno 4 vs Alma 5
STAR winner: Alma
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Alma | * Bruno |
-----------------------------------------
* Alma > | --- |5 - 0 - 4 |
* Bruno > | 4 - 0 - 5 | --- |
[Divergence from STAR]
STAR = Alma
Approval = Bruno (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Bruno)
- Runoff Round Winner = (Alma)
Candidate Bruno earned the highest total score, but
Candidate Alma won the automatic runoff — not a malfunction,
STAR working as designed: the runoff elects the finalist preferred
by the majority (of voters with a preference).
--- STAR Voting Method (single winner) ---
Tabulating 9 ballots.
Count × Alma,Bruno,Celia
4 × 5, 3, 0
3 × 1, 5, 3
1 × 4, 2, 1
1 × 0, 2, 5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Alma 4 1 0 0 3 1 | 27 3.0
Bruno 3 0 4 2 0 0 | 31 3.4
Celia 1 0 3 0 1 4 | 15 1.7
Scoring Round
The two highest-scoring candidates advance to the next round.
Bruno -- 31 -- First place
Alma -- 27 -- Second place
Celia -- 15
Bruno and Alma advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Alma -- 5 -- First place
Bruno -- 4
Equal Support -- 0
Alma wins.
Voters with a preference: 9 of 9 (no Equal Support).
Alma 5 (56%) vs Bruno 4 (44%); majority = 5.
Winner — STAR Voting Method (single winner)
Alma
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 9 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: Alma, Bruno, Celia
4 × Alma > Bruno (5, 3, 0)
1 × Alma > Bruno > Celia (4, 2, 1)
3 × Bruno > Celia > Alma (1, 5, 3)
1 × Celia > Bruno (0, 2, 5)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Alma 5 Elected
Bruno 3 Rejected
Celia 1 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Alma
--- 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): Alma
Outside (2): Bruno, Celia
One member ⇒ Alma is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Alma 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 9 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Alma, Bruno, Celia
4 × Alma > Bruno > Celia (5, 3, 0)
1 × Alma > Bruno > Celia (4, 2, 1)
3 × Bruno > Celia > Alma (1, 5, 3)
1 × Celia > Bruno > Alma (0, 2, 5)
Round-Robin — every pair, head-to-head (For – Against):
Alma beats Bruno 5 – 4
Alma beats Celia 5 – 4
Bruno beats Celia 8 – 1
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Alma | Bruno | Celia |
---------------------------------------------
Alma > | --- |5 - 0 - 4 |5 - 0 - 4 |
Bruno > | 4 - 0 - 5 | --- |8 - 0 - 1 |
Celia > | 4 - 0 - 5 |1 - 0 - 8 | --- |
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 Alma 2–0–0 2 +2 Bruno, Celia
2 Bruno 1–1–0 1 +6 Celia
3 Celia 0–2–0 0 -8 —
Winner — Ranked Robin (RCV-RR): Alma
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): Alma
Outside (2): Bruno, Celia
One member ⇒ Alma is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Alma 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