Equal ranks — 38 of 74 rally to Alice, and consecutive scores elect her¶
▶ Live on BetterVoting: vote · results ↗ (election j9wvv4 · test BV2297) — 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=Alice, RCV-IRV=Alice, Ranked Robin=Delia (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 | Alice |
| RCV-IRV | Alice |
| Ranked Robin (RCV-RR) | Delia |
| Approval | Alice |
| Range / Score | Alice |
| Condorcet | none (cycle) |
Flags: 74 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie); RR conversion-sensitive (weak=Delia, strict=Alice)
Source election: method_comparisons/equal_rank_irv/cases/equal_rank_cohesive_consecutive.yaml · STAR tabulated mirror: equal_rank_cohesive_consecutive_tabulated.txt
4 candidates, 74 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Alice | Bilal | Cato | Delia |
|---|---|---|---|---|
| 18 | 5 | 5 | 5 | 4 |
| 10 | 5 | 5 | 3 | 4 |
| 10 | 5 | 3 | 5 | 4 |
| 16 | 4 | 5 | 5 | 5 |
| 20 | 4 | 4 | 4 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Alice 334, Delia 332, Bilal 330, Cato 330
Finalists (top two): Alice and Delia
Automatic runoff: Alice 38 vs Delia 36
STAR winner: Alice
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Alice | * Delia |
-----------------------------------------------
* Alice > | --- |38 - 0 - 36 |
* Delia > | 36 - 0 - 38 | --- |
[Divergence from STAR]
STAR = Alice
RCV-RR = Delia (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 74 ballots.
Count × Alice,Bilal,Cato,Delia
20 × 4, 4, 4, 5
18 × 5, 5, 5, 4
16 × 4, 5, 5, 5
10 × 5, 5, 3, 4
10 × 5, 3, 5, 4
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Alice 38 36 0 0 0 0 | 334 4.5
Bilal 44 20 10 0 0 0 | 330 4.5
Cato 44 20 10 0 0 0 | 330 4.5
Delia 36 38 0 0 0 0 | 332 4.5
Scoring Round
The two highest-scoring candidates advance to the next round.
Alice -- 334 -- First place
Delia -- 332 -- Second place
Bilal -- 330
Cato -- 330
Alice and Delia advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Alice -- 38 -- First place
Delia -- 36
Equal Support -- 0
Alice wins.
Voters with a preference: 74 of 74 (no Equal Support).
Alice 38 (51%) vs Delia 36 (49%); majority = 38.
Winner — STAR Voting Method (single winner)
Alice
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 74 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: Alice, Bilal, Cato, Delia
18 × Alice > Bilal > Cato > Delia (5, 5, 5, 4)
10 × Alice > Bilal > Delia > Cato (5, 5, 3, 4)
10 × Alice > Cato > Delia > Bilal (5, 3, 5, 4)
16 × Bilal > Cato > Delia > Alice (4, 5, 5, 5)
20 × Delia > Alice > Bilal > Cato (4, 4, 4, 5)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Alice 38 Elected
Delia 20 Rejected
Bilal 16 Rejected
Cato 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Alice
--- 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 (4 of 4): Delia, Bilal, Cato, Alice
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.
Note: the Copeland leaders (Delia) are only part of the set — the
win–loss table's top block understates how wide the contention is.
RCV-IRV winner Alice is INSIDE the Smith set. ✓
Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
may be smaller 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 74 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Alice, Bilal, Cato, Delia
18 × Alice=Bilal=Cato > Delia (5, 5, 5, 4)
10 × Alice=Bilal > Delia > Cato (5, 5, 3, 4)
10 × Alice=Cato > Delia > Bilal (5, 3, 5, 4)
16 × Bilal=Cato=Delia > Alice (4, 5, 5, 5)
20 × Delia > Alice=Bilal=Cato (4, 4, 4, 5)
Round-Robin — every pair, head-to-head (For – Against):
Bilal beats Alice 16 – 10
Cato beats Alice 16 – 10
Alice beats Delia 38 – 36
Bilal ties Cato 10 – 10
Delia beats Bilal 30 – 28
Delia beats Cato 30 – 28
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Alice | Bilal | Cato | Delia |
--------------------------------------------------------------------
Alice > | --- |10 - 48 - 16 |10 - 48 - 16 |38 - 0 - 36 |
Bilal > | 16 - 48 - 10 | --- |10 - 54 - 10 |28 - 16 - 30 |
Cato > | 16 - 48 - 10 |10 - 54 - 10 | --- |28 - 16 - 30 |
Delia > | 36 - 0 - 38 |30 - 16 - 28 |30 - 16 - 28 | --- |
Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by the Ranked Robin degrees, then lot order):
# Candidate W–L–T Copeland Margin Beats
1 Delia 2–1–0 2 +2 Bilal, Cato
2 Bilal 1–1–1 1.5 +4 Alice
3 Cato 1–1–1 1.5 +4 Alice
4 Alice 1–2–0 1 -10 Delia
Winner — Ranked Robin (RCV-RR): Delia
the most head-to-head wins (2).
--- 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 (4 of 4): Delia, Bilal, Cato, Alice
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.
Note: the Copeland leaders (Delia) are only part of the set — the
win–loss table's top block understates how wide the contention is.
Ranked Robin (RCV-RR) winner Delia 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.
Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
may be smaller here.
More: 07_Concepts/topics/smith_set.md