Tactical maximization in STAR (2 of 2) — four voters hedge to a 5, and hand the seat to the hedge¶
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 Alma rather than STAR's Bruno, but this is an artifact of score→rank conversion, not a robust method difference: 4 of 9 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 (Bruno). 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 | Bruno |
| RCV-IRV | Alma |
| Ranked Robin (RCV-RR) | Bruno |
| Approval | Bruno |
| Range / Score | Bruno |
| Condorcet | Bruno |
Flags: 4 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie); RR conversion-sensitive (weak=Bruno, strict=Alma)
Source election: 01_STAR/03_Criteria/tactical_maximization/cases/tactical_max_c3_b9_hedged.yaml · STAR tabulated mirror: tactical_max_c3_b9_hedged_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 | 5 | 0 |
| 1 | 4 | 2 | 1 |
| 3 | 1 | 5 | 3 |
| 1 | 0 | 2 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Bruno 39, Alma 27, Celia 15
Finalists (top two): Bruno and Alma
Automatic runoff: Bruno 4 vs Alma 1 (4 equal/no-preference)
STAR winner: Bruno
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 > | --- |1 - 4 - 4 |
* Bruno > | 4 - 4 - 1 | --- |
[Divergence from STAR]
STAR = Bruno
Choose-One (Plurality) = Alma (differs from STAR)
RCV-IRV = Alma (differs from STAR)
Note: 4 of 9 ballots (44%) 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 9 ballots.
Count × Alma,Bruno,Celia
4 × 5, 5, 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 7 0 0 2 0 0 | 39 4.3
Celia 1 0 3 0 1 4 | 15 1.7
Scoring Round
The two highest-scoring candidates advance to the next round.
Bruno -- 39 -- 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.
Bruno -- 4 -- First place
Alma -- 1
Equal Support -- 4
Bruno wins.
Voters with a preference: 5 of 9 (4 Equal Support).
Bruno 4 (80%) vs Alma 1 (20%); majority = 3.
Winner — STAR Voting Method (single winner)
Bruno
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 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, 5, 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): Bruno
Outside (2): Alma, Celia
One member ⇒ Bruno is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Alma is OUTSIDE the Smith set. ✗
Every member of the set (Bruno) beats Alma head-to-head, yet
RCV-IRV elected Alma 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 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, 5, 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):
Bruno beats Alma 4 – 1
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 > | --- |1 - 4 - 4 |5 - 0 - 4 |
Bruno > | 4 - 4 - 1 | --- |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 Bruno 2–0–0 2 +10 Alma, Celia
2 Alma 1–1–0 1 -2 Celia
3 Celia 0–2–0 0 -8 —
Winner — Ranked Robin (RCV-RR): Bruno
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): Bruno
Outside (2): Alma, Celia
One member ⇒ Bruno is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Bruno 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