Crowded field, rung 5 — 5 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 Elsa rather than STAR's Diego, but this is an artifact of score→rank conversion, not a robust method difference: 23 of 65 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 and the Condorcet (pairwise) winner both agree with STAR (Diego). 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 | Diego |
| RCV-IRV | Elsa |
| Ranked Robin (RCV-RR) | Diego |
| Approval | Diego |
| Range / Score | Diego |
| Condorcet | Diego |
Flags: 23 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie)
Source election: method_comparisons/crowded_field/cases/crowded_field_c5_star.yaml · STAR tabulated mirror: crowded_field_c5_star_tabulated.txt
5 candidates, 65 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Ana | Bruno | Diego | Elsa | Greta |
|---|---|---|---|---|---|
| 6 | 5 | 4 | 3 | 2 | 0 |
| 10 | 5 | 5 | 3 | 2 | 0 |
| 13 | 3 | 5 | 5 | 3 | 0 |
| 9 | 0 | 2 | 5 | 4 | 0 |
| 12 | 0 | 2 | 4 | 5 | 3 |
| 8 | 0 | 1 | 3 | 4 | 5 |
| 7 | 0 | 1 | 2 | 3 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Diego 244, Elsa 220, Bruno 196, Ana 119, Greta 111
Finalists (top two): Diego and Elsa
Automatic runoff: Diego 38 vs Elsa 27
STAR winner: Diego
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Diego | * Elsa |
-----------------------------------------------
* Diego > | --- |38 - 0 - 27 |
* Elsa > | 27 - 0 - 38 | --- |
[Divergence from STAR]
STAR = Diego
Choose-One (Plurality) = Ana (differs from STAR)
RCV-IRV = Elsa (differs from STAR)
Note: 23 of 65 ballots (35%) 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,Diego,Elsa,Greta
13 × 3, 5, 5, 3, 0
12 × 0, 2, 4, 5, 3
10 × 5, 5, 3, 2, 0
9 × 0, 2, 5, 4, 0
8 × 0, 1, 3, 4, 5
7 × 0, 1, 2, 3, 5
6 × 5, 4, 3, 2, 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
Diego 22 12 24 7 0 0 | 244 3.8
Elsa 12 17 20 16 0 0 | 220 3.4
Greta 15 0 12 0 0 38 | 111 1.7
Scoring Round
The two highest-scoring candidates advance to the next round.
Diego -- 244 -- First place
Elsa -- 220 -- Second place
Bruno -- 196
Ana -- 119
Greta -- 111
Diego and Elsa advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Diego -- 38 -- First place
Elsa -- 27
Equal Support -- 0
Diego wins.
Voters with a preference: 65 of 65 (no Equal Support).
Diego 38 (58%) vs Elsa 27 (42%); majority = 33.
Winner — STAR Voting Method (single winner)
Diego
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 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, Diego, Elsa, Greta
6 × Ana > Bruno > Diego > Elsa (5, 4, 3, 2, 0)
10 × Ana > Bruno > Diego > Elsa (5, 5, 3, 2, 0)
13 × Bruno > Diego > Ana > Elsa (3, 5, 5, 3, 0)
9 × Diego > Elsa > Bruno (0, 2, 5, 4, 0)
12 × Elsa > Diego > Greta > Bruno (0, 2, 4, 5, 3)
8 × Greta > Elsa > Diego > Bruno (0, 1, 3, 4, 5)
7 × Greta > Elsa > Diego > Bruno (0, 1, 2, 3, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Ana 16 Hopeful
Greta 15 Hopeful
Bruno 13 Hopeful
Elsa 12 Hopeful
Diego 9 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Elsa 21 Hopeful
Ana 16 Hopeful
Greta 15 Hopeful
Bruno 13 Rejected
Diego 0 Rejected
ROUND 3
Candidate Votes Status
----------- ------- --------
Ana 29 Hopeful
Elsa 21 Hopeful
Greta 15 Rejected
Bruno 0 Rejected
Diego 0 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Elsa 36 Elected
Ana 29 Rejected
Greta 0 Rejected
Bruno 0 Rejected
Diego 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Elsa
--- 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 5): Diego
Outside (4): Ana, Bruno, Elsa, Greta
One member ⇒ Diego is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Elsa is OUTSIDE the Smith set. ✗
Every member of the set (Diego) beats Elsa head-to-head, yet
RCV-IRV elected Elsa 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, Diego, Elsa, Greta
6 × Ana > Bruno > Diego > Elsa > Greta (5, 4, 3, 2, 0)
10 × Ana=Bruno > Diego > Elsa > Greta (5, 5, 3, 2, 0)
13 × Bruno=Diego > Ana=Elsa > Greta (3, 5, 5, 3, 0)
9 × Diego > Elsa > Bruno > Ana=Greta (0, 2, 5, 4, 0)
12 × Elsa > Diego > Greta > Bruno > Ana (0, 2, 4, 5, 3)
8 × Greta > Elsa > Diego > Bruno > Ana (0, 1, 3, 4, 5)
7 × Greta > Elsa > Diego > Bruno > Ana (0, 1, 2, 3, 5)
Round-Robin — every pair, head-to-head (For – Against):
Bruno beats Ana 49 – 6
Diego beats Ana 49 – 16
Elsa beats Ana 36 – 16
Ana beats Greta 29 – 27
Diego beats Bruno 36 – 16
Elsa beats Bruno 36 – 29
Bruno beats Greta 38 – 27
Diego beats Elsa 38 – 27
Diego beats Greta 50 – 15
Elsa 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 | Diego | Elsa | Greta |
----------------------------------------------------------------------------------
Ana > | --- | 6 - 10 - 49 |16 - 0 - 49 |16 - 13 - 36 |29 - 9 - 27 |
Bruno > | 49 - 10 - 6 | --- |16 - 13 - 36 |29 - 0 - 36 |38 - 0 - 27 |
Diego > | 49 - 0 - 16 |36 - 13 - 16 | --- |38 - 0 - 27 |50 - 0 - 15 |
Elsa > | 36 - 13 - 16 |36 - 0 - 29 |27 - 0 - 38 | --- |50 - 0 - 15 |
Greta > | 27 - 9 - 29 |27 - 0 - 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 Diego 4–0–0 4 +99 Elsa, Bruno, Ana, Greta
2 Elsa 3–1–0 3 +51 Bruno, Ana, Greta
3 Bruno 2–2–0 2 +27 Ana, Greta
4 Ana 1–3–0 1 -94 Greta
5 Greta 0–4–0 0 -83 —
Winner — Ranked Robin (RCV-RR): Diego
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 5): Diego
Outside (4): Ana, Bruno, Elsa, Greta
One member ⇒ Diego is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Diego 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