Crowded field, rung 7 — 7 candidates, 65 voters, counted by STAR¶
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 Felix rather than STAR's Clara, but this is an artifact of score→rank conversion, not a robust method difference: 65 of 65 ballots have tied non-zero scores, so their ranks are set by an arbitrary candidate-priority order. Ranked Robin and the Condorcet (pairwise) winner both agree with STAR (Clara). 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 | Felix |
| Ranked Robin (RCV-RR) | Clara |
| Approval | Diego |
| Range / Score | Clara |
| Condorcet | Clara |
Flags: 65 tied-score ballot(s)
Source election: method_comparisons/crowded_field/cases/crowded_field_c7_star.yaml · STAR tabulated mirror: crowded_field_c7_star_tabulated.txt
7 candidates, 65 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Ana | Bruno | Clara | Diego | Elsa | Felix | Greta |
|---|---|---|---|---|---|---|---|
| 6 | 5 | 4 | 3 | 3 | 2 | 1 | 0 |
| 10 | 5 | 5 | 4 | 3 | 2 | 2 | 0 |
| 13 | 3 | 5 | 5 | 4 | 3 | 2 | 0 |
| 9 | 0 | 2 | 4 | 5 | 4 | 4 | 0 |
| 12 | 0 | 2 | 3 | 3 | 4 | 5 | 3 |
| 8 | 0 | 1 | 2 | 3 | 4 | 4 | 5 |
| 7 | 0 | 1 | 2 | 2 | 3 | 4 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Clara 225, Diego 219, Elsa 208, Felix 208, Bruno 196, Ana 119, Greta 111
Finalists (top two): Clara and Diego
Automatic runoff: Clara 23 vs Diego 17 (25 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
| * Clara | * Diego |
-----------------------------------------------
* Clara > | --- |23 - 25 - 17 |
* Diego > | 17 - 25 - 23 | --- |
[Divergence from STAR]
STAR = Clara
Choose-One (Plurality) = Ana (differs from STAR)
RCV-IRV = Felix (differs from STAR)
Approval = Diego (differs from STAR)
Note: 65 of 65 ballots (100%) 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 65 ballots.
Count × Ana,Bruno,Clara,Diego,Elsa,Felix,Greta
13 × 3, 5, 5, 4, 3, 2, 0
12 × 0, 2, 3, 3, 4, 5, 3
10 × 5, 5, 4, 3, 2, 2, 0
9 × 0, 2, 4, 5, 4, 4, 0
8 × 0, 1, 2, 3, 4, 4, 5
7 × 0, 1, 2, 2, 3, 4, 5
6 × 5, 4, 3, 3, 2, 1, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Ana 16 0 13 0 0 36 | 119 1.8
Bruno 23 6 0 21 15 0 | 196 3.0
Clara 13 19 18 15 0 0 | 225 3.5
Diego 9 13 36 7 0 0 | 219 3.4
Elsa 0 29 20 16 0 0 | 208 3.2
Felix 12 24 0 23 6 0 | 208 3.2
Greta 15 0 12 0 0 38 | 111 1.7
Scoring Round
The two highest-scoring candidates advance to the next round.
Clara -- 225 -- First place
Diego -- 219 -- Second place
Elsa -- 208
Felix -- 208
Bruno -- 196
Ana -- 119
Greta -- 111
Clara and Diego advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Clara -- 23 -- First place
Diego -- 17
Equal Support -- 25
Clara wins.
Voters with a preference: 40 of 65 (25 Equal Support).
Clara 23 (57%) vs Diego 17 (42%); majority = 21.
Winner — STAR Voting Method (single winner)
Clara
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 65 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: Ana, Bruno, Clara, Diego, Elsa, Felix, Greta
6 × Ana > Bruno > Clara > Diego > Elsa > Felix (5, 4, 3, 3, 2, 1, 0)
10 × Ana > Bruno > Clara > Diego > Elsa > Felix (5, 5, 4, 3, 2, 2, 0)
13 × Bruno > Clara > Diego > Ana > Elsa > Felix (3, 5, 5, 4, 3, 2, 0)
9 × Diego > Clara > Elsa > Felix > Bruno (0, 2, 4, 5, 4, 4, 0)
12 × Felix > Elsa > Clara > Diego > Greta > Bruno (0, 2, 3, 3, 4, 5, 3)
8 × Greta > Elsa > Felix > Diego > Clara > Bruno (0, 1, 2, 3, 4, 4, 5)
7 × Greta > Felix > Elsa > Clara > Diego > Bruno (0, 1, 2, 2, 3, 4, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Ana 16 Hopeful
Greta 15 Hopeful
Bruno 13 Hopeful
Felix 12 Hopeful
Diego 9 Rejected
Clara 0 Rejected
Elsa 0 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Felix 21 Hopeful
Ana 16 Hopeful
Greta 15 Hopeful
Bruno 13 Rejected
Diego 0 Rejected
Clara 0 Rejected
Elsa 0 Rejected
ROUND 3
Candidate Votes Status
----------- ------- --------
Ana 29 Hopeful
Felix 21 Hopeful
Greta 15 Rejected
Bruno 0 Rejected
Diego 0 Rejected
Clara 0 Rejected
Elsa 0 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Felix 36 Elected
Ana 29 Rejected
Greta 0 Rejected
Bruno 0 Rejected
Diego 0 Rejected
Clara 0 Rejected
Elsa 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Felix
--- 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 7): Clara
Outside (6): Ana, Bruno, Diego, Elsa, Felix, Greta
One member ⇒ Clara is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Felix is OUTSIDE the Smith set. ✗
Every member of the set (Clara) beats Felix head-to-head, yet
RCV-IRV elected Felix anyway. RCV-IRV is not Smith-efficient (nor
Condorcet-efficient) — this is the shape a center squeeze leaves behind.
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 65 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Ana, Bruno, Clara, Diego, Elsa, Felix, Greta
6 × Ana > Bruno > Clara=Diego > Elsa > Felix > Greta (5, 4, 3, 3, 2, 1, 0)
10 × Ana=Bruno > Clara > Diego > Elsa=Felix > Greta (5, 5, 4, 3, 2, 2, 0)
13 × Bruno=Clara > Diego > Ana=Elsa > Felix > Greta (3, 5, 5, 4, 3, 2, 0)
9 × Diego > Clara=Elsa=Felix > Bruno > Ana=Greta (0, 2, 4, 5, 4, 4, 0)
12 × Felix > Elsa > Clara=Diego=Greta > Bruno > Ana (0, 2, 3, 3, 4, 5, 3)
8 × Greta > Elsa=Felix > Diego > Clara > Bruno > Ana (0, 1, 2, 3, 4, 4, 5)
7 × Greta > Felix > Elsa > Clara=Diego > Bruno > Ana (0, 1, 2, 2, 3, 4, 5)
Round-Robin — every pair, head-to-head (For – Against):
Bruno beats Ana 49 – 6
Clara beats Ana 49 – 16
Diego beats Ana 49 – 16
Elsa beats Ana 36 – 16
Felix beats Ana 36 – 29
Ana beats Greta 29 – 27
Clara beats Bruno 36 – 16
Diego beats Bruno 36 – 29
Elsa beats Bruno 36 – 29
Felix beats Bruno 36 – 29
Bruno beats Greta 38 – 27
Clara beats Diego 23 – 17
Clara beats Elsa 29 – 27
Clara beats Felix 29 – 27
Clara beats Greta 38 – 15
Diego beats Elsa 38 – 27
Diego beats Felix 38 – 27
Diego beats Greta 38 – 15
Elsa ties Felix 19 – 19
Elsa beats Greta 50 – 15
Felix beats Greta 50 – 15
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Ana | Bruno | Clara | Diego | Elsa | Felix | Greta |
--------------------------------------------------------------------------------------------------------------
Ana > | --- | 6 - 10 - 49 |16 - 0 - 49 |16 - 0 - 49 |16 - 13 - 36 |29 - 0 - 36 |29 - 9 - 27 |
Bruno > | 49 - 10 - 6 | --- |16 - 13 - 36 |29 - 0 - 36 |29 - 0 - 36 |29 - 0 - 36 |38 - 0 - 27 |
Clara > | 49 - 0 - 16 |36 - 13 - 16 | --- |23 - 25 - 17 |29 - 9 - 27 |29 - 9 - 27 |38 - 12 - 15 |
Diego > | 49 - 0 - 16 |36 - 0 - 29 |17 - 25 - 23 | --- |38 - 0 - 27 |38 - 0 - 27 |38 - 12 - 15 |
Elsa > | 36 - 13 - 16 |36 - 0 - 29 |27 - 9 - 29 |27 - 0 - 38 | --- |19 - 27 - 19 |50 - 0 - 15 |
Felix > | 36 - 0 - 29 |36 - 0 - 29 |27 - 9 - 29 |27 - 0 - 38 |19 - 27 - 19 | --- |50 - 0 - 15 |
Greta > | 27 - 9 - 29 |27 - 0 - 38 |15 - 12 - 38 |15 - 12 - 38 |15 - 0 - 50 |15 - 0 - 50 | --- |
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 6–0–0 6 +86 Diego, Elsa, Felix, Bruno, Ana, Greta
2 Diego 5–1–0 5 +79 Elsa, Felix, Bruno, Ana, Greta
3 Elsa 3–2–1 3.5 +49 Bruno, Ana, Greta
4 Felix 3–2–1 3.5 +36 Bruno, Ana, Greta
5 Bruno 2–4–0 2 +13 Ana, Greta
6 Ana 1–5–0 1 -134 Greta
7 Greta 0–6–0 0 -129 —
Winner — Ranked Robin (RCV-RR): Clara
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 7): Clara
Outside (6): Ana, Bruno, Diego, Elsa, Felix, Greta
One member ⇒ Clara is the Condorcet winner, beating every rival head-to-head.
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