BV2182 — why the automatic runoff (and Equal Support)¶
▶ Live on BetterVoting: vote · results ↗ (election tg4779 · test BV2182) — 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 Berry: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Berry'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 | Berry |
| Range / Score | Berry |
| Condorcet | Almond |
Flags: 1 tied-score ballot(s)
Source election: 01_STAR/02_Examples/cases/bv2182_tg4779_faq_runoff_reversal.yaml · STAR tabulated mirror: bv2182_tg4779_faq_runoff_reversal_tabulated.txt
3 candidates, 10 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Almond | Berry | Cocoa |
|---|---|---|---|
| 4 | 5 | 4 | 1 |
| 2 | 5 | 4 | 0 |
| 3 | 0 | 5 | 2 |
| 1 | 5 | 5 | 0 |
STAR result (official)¶
Scoring round (sum of scores): Berry 44, Almond 35, Cocoa 10
Finalists (top two): Berry and Almond
Automatic runoff: Berry 3 vs Almond 6 (1 equal/no-preference)
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 > | --- |6 - 1 - 3 |
* Berry > | 3 - 1 - 6 | --- |
[Divergence from STAR]
STAR = Almond
Approval = Berry (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Berry)
- Runoff Round Winner = (Almond)
Candidate Berry earned the highest total score, but
Candidate Almond 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 10 ballots.
Count × Almond,Berry,Cocoa
4 × 5, 4, 1
3 × 0, 5, 2
2 × 5, 4, 0
1 × 5, 5, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Almond 7 0 0 0 0 3 | 35 3.5
Berry 4 6 0 0 0 0 | 44 4.4
Cocoa 0 0 0 3 4 3 | 10 1.0
Scoring Round
The two highest-scoring candidates advance to the next round.
Berry -- 44 -- First place
Almond -- 35 -- Second place
Cocoa -- 10
Berry and Almond advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Almond -- 6 -- First place
Berry -- 3
Equal Support -- 1
Almond wins.
Voters with a preference: 9 of 10 (1 Equal Support).
Almond 6 (67%) vs Berry 3 (33%); majority = 5.
Winner — STAR Voting Method (single winner)
Almond
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 10 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
4 × Almond > Berry > Cocoa (5, 4, 1)
2 × Almond > Berry (5, 4, 0)
3 × Berry > Cocoa (0, 5, 2)
1 × Almond > Berry (5, 5, 0)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Almond 7 Elected
Berry 3 Rejected
Cocoa 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 10 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Almond, Berry, Cocoa
4 × Almond > Berry > Cocoa (5, 4, 1)
2 × Almond > Berry > Cocoa (5, 4, 0)
3 × Berry > Cocoa > Almond (0, 5, 2)
1 × Almond=Berry > Cocoa (5, 5, 0)
Round-Robin — every pair, head-to-head (For – Against):
Almond beats Berry 6 – 3
Almond beats Cocoa 7 – 3
Berry beats Cocoa 10 – 0
--- 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 > | --- | 6 - 1 - 3 | 7 - 0 - 3 |
Berry > | 3 - 1 - 6 | --- |10 - 0 - 0 |
Cocoa > | 3 - 0 - 7 | 0 - 0 - 10 | --- |
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 +7 Berry, Cocoa
2 Berry 1–1–0 1 +7 Cocoa
3 Cocoa 0–2–0 0 -14 —
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