Equal ranks — the same 74 voters use the whole scale, and Delia wins¶
▶ Live on BetterVoting: vote · results ↗ (election j9wvv4 · test BV2297) — an independent tabulator to check the winners below against.
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 Alice rather than STAR's Delia, but this is an artifact of score→rank conversion, not a robust method difference: 54 of 74 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 still elects Delia, and there is no Condorcet winner — the pairwise results cycle, so no ranked method has a clean anchor. 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 | Delia |
| RCV-IRV | Alice |
| Ranked Robin (RCV-RR) | Delia |
| Approval | Delia |
| Range / Score | Delia |
| Condorcet | none (cycle) |
Flags: 54 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_wide_gaps.yaml · STAR tabulated mirror: equal_rank_cohesive_wide_gaps_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 | 0 |
| 10 | 5 | 5 | 0 | 3 |
| 10 | 5 | 0 | 5 | 3 |
| 16 | 0 | 5 | 5 | 5 |
| 20 | 0 | 0 | 0 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Delia 240, Bilal 220, Cato 220, Alice 190
Finalists (top two): Delia and Bilal
Automatic runoff: Delia 30 vs Bilal 28 (16 equal/no-preference)
STAR winner: Delia
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
Note: Bilal and Cato tied at 220 in the Scoring Round, and the lot
rung (the ballots could not separate them) advanced Bilal. The *
marks who advanced, not who scored highest. Cato is filtered out
of this grid — see the Scoring Round for how the tie was
settled.
| * Bilal | * Delia |
-----------------------------------------------
* Bilal > | --- |28 - 16 - 30 |
* Delia > | 30 - 16 - 28 | --- |
[Divergence from STAR]
STAR = Delia
Choose-One (Plurality) = Alice (differs from STAR)
RCV-IRV = Alice (differs from STAR)
Note: 54 of 74 ballots (73%) 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 74 ballots.
Count × Alice,Bilal,Cato,Delia
20 × 0, 0, 0, 5
18 × 5, 5, 5, 0
16 × 0, 5, 5, 5
10 × 5, 5, 0, 3
10 × 5, 0, 5, 3
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Alice 38 0 0 0 0 36 | 190 2.6
Bilal 44 0 0 0 0 30 | 220 3.0
Cato 44 0 0 0 0 30 | 220 3.0
Delia 36 0 20 0 0 18 | 240 3.2
Scoring Round
The two highest-scoring candidates advance to the next round.
Delia -- 240 -- First place
Bilal -- 220 -- Tied for second place
Cato -- 220 -- Tied for second place
Alice -- 190
Delia advances, but there's a two-way tie for second.
Scoring Round: First tiebreaker
The candidate preferred in the most head-to-head matchups advances.
Bilal -- 10 -- Tied for second place
Cato -- 10 -- Tied for second place
Equal Support -- 54
There's still a two-way tie for second.
Scoring Round: Second tiebreaker
The candidate with the most votes of score 5 advances.
Bilal -- 44 -- Tied for second place
Cato -- 44 -- Tied for second place
There's still a two-way tie for second.
*(Ties are resolved by choosing the tied candidate with the highest-priority official lot number.)*
Lot-number priority order: ['Alice', 'Bilal', 'Cato', 'Delia']
[Tiebreaker: Lot Number Priority]
Tie among: ['Bilal', 'Cato']
Resolved: ['Bilal'] (selected by lot-number priority).
[Lot-decided tie — rare]
⚠ The ballots did not break this tie: the deterministic rungs
(pairwise / score, then five-star) all came back equal, so the
pre-published LOT order chose among the tied candidates — the
result here was set by lot, not by the votes. Usually the
"dead rung": no tied candidate held a score-5 vote (five-star
counts fives, not fours). Verify the tied candidates' 5-counts.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Delia -- 30 -- First place
Bilal -- 28
Equal Support -- 16
Delia wins.
Voters with a preference: 58 of 74 (16 Equal Support).
Delia 30 (52%) vs Bilal 28 (48%); majority = 30.
Winner — STAR Voting Method (single winner)
Delia
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 (5, 5, 5, 0)
10 × Alice > Bilal > Delia (5, 5, 0, 3)
10 × Alice > Cato > Delia (5, 0, 5, 3)
16 × Bilal > Cato > Delia (0, 5, 5, 5)
20 × Delia (0, 0, 0, 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, 0)
10 × Alice=Bilal > Delia > Cato (5, 5, 0, 3)
10 × Alice=Cato > Delia > Bilal (5, 0, 5, 3)
16 × Bilal=Cato=Delia > Alice (0, 5, 5, 5)
20 × Delia > Alice=Bilal=Cato (0, 0, 0, 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