Margins matter — STAR on the same twelve ballots (rank converted 5/3/0)¶
▶ Live on BetterVoting: vote · results ↗ (election kdjjkq · test BV2251) — an independent tabulator to check the winners below against.
Bucket — CYCLE_OR_THREE_WAY: Cycle / three-way split
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
There is no Condorcet winner — the head-to-head results form a cycle (X beats Y beats Z beats X). With no pairwise anchor the methods split: STAR=Almond, RCV-IRV=Cocoa, Ranked Robin=Berry (RR breaks the cycle by total margin). No rule is clearly 'right'; a genuinely hard election, not an indictment of any one method.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Almond |
| RCV-IRV | Cocoa |
| Ranked Robin (RCV-RR) | Berry |
| Approval | Berry |
| Range / Score | Berry |
| Condorcet | none (cycle) |
Flags: none
Source election: method_comparisons/copeland_vs_borda_margins/cases/margins_star.yaml · STAR tabulated mirror: margins_star_tabulated.txt
3 candidates, 12 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Almond | Berry | Cocoa |
|---|---|---|---|
| 5 | 5 | 3 | 0 |
| 3 | 0 | 5 | 3 |
| 2 | 3 | 0 | 5 |
| 2 | 0 | 3 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Berry 36, Almond 31, Cocoa 29
Finalists (top two): Berry and Almond
Automatic runoff: Berry 5 vs Almond 7
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 > | --- |7 - 0 - 5 |
* Berry > | 5 - 0 - 7 | --- |
[Divergence from STAR]
STAR = Almond
RCV-IRV = Cocoa (differs from STAR)
Approval = Berry (differs from STAR)
RCV-RR = Berry (differs from STAR)
Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
method difference, not a tie-breaking artifact.
[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 12 ballots.
Count × Almond,Berry,Cocoa
5 × 5, 3, 0
3 × 0, 5, 3
2 × 3, 0, 5
2 × 0, 3, 5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Almond 5 0 2 0 0 5 | 31 2.6
Berry 3 0 7 0 0 2 | 36 3.0
Cocoa 4 0 3 0 0 5 | 29 2.4
Scoring Round
The two highest-scoring candidates advance to the next round.
Berry -- 36 -- First place
Almond -- 31 -- Second place
Cocoa -- 29
Berry and Almond advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Almond -- 7 -- First place
Berry -- 5
Equal Support -- 0
Almond wins.
Voters with a preference: 12 of 12 (no Equal Support).
Almond 7 (58%) vs Berry 5 (42%); majority = 7.
Winner — STAR Voting Method (single winner)
Almond
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 12 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
5 × Almond > Berry (5, 3, 0)
3 × Berry > Cocoa (0, 5, 3)
2 × Cocoa > Almond (3, 0, 5)
2 × Cocoa > Berry (0, 3, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Almond 5 Hopeful
Cocoa 4 Hopeful
Berry 3 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Cocoa 7 Elected
Almond 5 Rejected
Berry 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Cocoa
--- 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 (3 of 3): Almond, Berry, Cocoa
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
cycle, so the strongest "candidate" is a set, not a person. Which member of
the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
RCV-IRV winner Cocoa 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 12 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Almond, Berry, Cocoa
5 × Almond > Berry > Cocoa (5, 3, 0)
3 × Berry > Cocoa > Almond (0, 5, 3)
2 × Cocoa > Almond > Berry (3, 0, 5)
2 × Cocoa > Berry > Almond (0, 3, 5)
Round-Robin — every pair, head-to-head (For – Against):
Almond beats Berry 7 – 5
Cocoa beats Almond 7 – 5
Berry beats Cocoa 8 – 4
--- 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 > | --- |7 - 0 - 5 |5 - 0 - 7 |
Berry > | 5 - 0 - 7 | --- |8 - 0 - 4 |
Cocoa > | 7 - 0 - 5 |4 - 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 Berry 1–1–0 1 +2 Cocoa
2 Almond 1–1–0 1 +0 Berry
3 Cocoa 1–1–0 1 -2 Almond
Winner — Ranked Robin (RCV-RR): Berry
*** 3 candidates tie for the most wins (Almond, Berry, Cocoa) — a Condorcet cycle (no candidate beats all others). Resolved by total margin, then lot order. (This is where Minimax / Ranked Pairs / Schulze differ — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.)
--- 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 (3 of 3): Almond, Berry, Cocoa
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
cycle, so the strongest "candidate" is a set, not a person. Which member of
the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
Ranked Robin (RCV-RR) winner Berry 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