The Graders' Divide — a harsh 0-2 camp meets a gentle 3-5 camp¶
▶ Live on BetterVoting: vote · results ↗ (election 4jmgrd · test BV2234) — 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 Bruno rather than STAR's Clara, but this is an artifact of score→rank conversion, not a robust method difference: 9 of 31 ballots have tied non-zero scores, so their ranks are set by an arbitrary candidate-priority order. Ranked Robin still elects Clara, 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 | Clara |
| RCV-IRV | Bruno |
| Ranked Robin (RCV-RR) | Clara |
| Approval | Abby |
| Range / Score | Bruno |
| Condorcet | none (cycle) |
Flags: 9 tied-score ballot(s); RR conversion-sensitive (weak=Clara, strict=Bruno)
Source election: 06_Other/ballot_style_lab/cases/01_c3_b31_graders-divide.yaml · STAR tabulated mirror: 01_c3_b31_graders-divide_tabulated.txt
3 candidates, 31 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Abby | Bruno | Clara |
|---|---|---|---|
| 8 | 3 | 5 | 4 |
| 12 | 2 | 0 | 1 |
| 5 | 3 | 5 | 5 |
| 3 | 3 | 5 | 3 |
| 2 | 2 | 0 | 0 |
| 1 | 2 | 0 | 2 |
STAR result (official)¶
Scoring round (sum of scores): Bruno 80, Clara 80, Abby 78
Finalists (top two): Bruno and Clara
Automatic runoff: Bruno 11 vs Clara 13 (7 equal/no-preference)
STAR winner: Clara
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Bruno | * Clara |
-----------------------------------------------
* Bruno > | --- |11 - 7 - 13 |
* Clara > | 13 - 7 - 11 | --- |
[Divergence from STAR]
STAR = Clara
Choose-One (Plurality) = Bruno (differs from STAR)
RCV-IRV = Bruno (differs from STAR)
Approval = Abby (differs from STAR)
Note: 9 of 31 ballots (29%) 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 31 ballots.
Count × Abby,Bruno,Clara
12 × 2, 0, 1
8 × 3, 5, 4
5 × 3, 5, 5
3 × 3, 5, 3
2 × 2, 0, 0
1 × 2, 0, 2
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Abby 0 0 16 15 0 0 | 78 2.5
Bruno 16 0 0 0 0 15 | 80 2.6
Clara 5 8 3 1 12 2 | 80 2.6
Scoring Round
The two highest-scoring candidates advance to the next round.
Bruno -- 80 -- First place
Clara -- 80 -- Second place
Abby -- 78
Bruno and Clara advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Clara -- 13 -- First place
Bruno -- 11
Equal Support -- 7
Clara wins.
Voters with a preference: 24 of 31 (7 Equal Support).
Clara 13 (54%) vs Bruno 11 (46%); majority = 13.
Winner — STAR Voting Method (single winner)
Clara
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 31 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: Abby, Bruno, Clara
8 × Bruno > Clara > Abby (3, 5, 4)
12 × Abby > Clara (2, 0, 1)
5 × Bruno > Clara > Abby (3, 5, 5)
3 × Bruno > Abby > Clara (3, 5, 3)
2 × Abby (2, 0, 0)
1 × Abby > Clara (2, 0, 2)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Bruno 16 Elected
Abby 15 Rejected
Clara 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Bruno
--- 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): Abby, Bruno, Clara
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 Bruno 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 31 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Abby, Bruno, Clara
8 × Bruno > Clara > Abby (3, 5, 4)
12 × Abby > Clara > Bruno (2, 0, 1)
5 × Bruno=Clara > Abby (3, 5, 5)
3 × Bruno > Abby=Clara (3, 5, 3)
2 × Abby > Bruno=Clara (2, 0, 0)
1 × Abby=Clara > Bruno (2, 0, 2)
Round-Robin — every pair, head-to-head (For – Against):
Bruno beats Abby 16 – 15
Abby beats Clara 14 – 13
Clara beats Bruno 13 – 11
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Abby | Bruno | Clara |
------------------------------------------------------
Abby > | --- |15 - 0 - 16 |14 - 4 - 13 |
Bruno > | 16 - 0 - 15 | --- |11 - 7 - 13 |
Clara > | 13 - 4 - 14 |13 - 7 - 11 | --- |
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 Clara 1–1–0 1 +1 Bruno
2 Abby 1–1–0 1 +0 Clara
3 Bruno 1–1–0 1 -1 Abby
Winner — Ranked Robin (RCV-RR): Clara
*** 3 candidates tie for the most wins (Abby, Bruno, Clara) — 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): Abby, Bruno, Clara
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 Clara 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