Nine candidates, 25 voters — the 0–5 score ballot¶
▶ Live on BetterVoting: vote · results ↗ (election 37yf8x · test BV2280) — an independent tabulator to check the winners below against.
Bucket — APPROVAL_OR_MINOR: Only Approval differs
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
STAR, RCV-IRV and Ranked Robin all agree on Finn. Only Approval differs, electing Emma: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Emma's breadth of acceptability over Finn's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Finn |
| RCV-IRV | Finn |
| Ranked Robin (RCV-RR) | Finn |
| Approval | Emma |
| Range / Score | Finn |
| Condorcet | Finn |
Flags: 25 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie)
Source election: method_comparisons/ballot_expressiveness/cases/bv2280_37yf8x_star.yaml · STAR tabulated mirror: bv2280_37yf8x_star_tabulated.txt
9 candidates, 25 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Ada | Ben | Cleo | Dev | Emma | Finn | Gus | Hugo | Iris |
|---|---|---|---|---|---|---|---|---|---|
| 2 | 4 | 5 | 4 | 4 | 4 | 2 | 2 | 0 | 0 |
| 4 | 0 | 2 | 2 | 2 | 3 | 4 | 5 | 5 | 5 |
| 1 | 5 | 4 | 4 | 3 | 3 | 2 | 1 | 0 | 0 |
| 2 | 0 | 1 | 2 | 2 | 2 | 3 | 4 | 5 | 5 |
| 1 | 0 | 2 | 3 | 3 | 4 | 5 | 4 | 2 | 1 |
| 1 | 2 | 4 | 5 | 5 | 5 | 3 | 2 | 0 | 0 |
| 2 | 0 | 1 | 2 | 2 | 2 | 4 | 4 | 5 | 5 |
| 1 | 0 | 2 | 3 | 3 | 3 | 5 | 5 | 3 | 3 |
| 2 | 0 | 2 | 3 | 3 | 3 | 5 | 4 | 2 | 2 |
| 1 | 3 | 5 | 5 | 5 | 4 | 3 | 2 | 0 | 0 |
| 2 | 5 | 5 | 4 | 4 | 4 | 2 | 2 | 0 | 0 |
| 1 | 1 | 3 | 5 | 5 | 5 | 4 | 3 | 0 | 0 |
| 1 | 0 | 2 | 3 | 3 | 3 | 5 | 5 | 2 | 2 |
| 1 | 5 | 4 | 4 | 4 | 3 | 2 | 2 | 0 | 0 |
| 2 | 5 | 4 | 3 | 3 | 3 | 2 | 1 | 0 | 0 |
| 1 | 3 | 5 | 5 | 5 | 5 | 3 | 2 | 0 | 0 |
STAR result (official)¶
Scoring round (sum of scores): Finn 84, Emma 83, Cleo 81, Dev 80, Gus 80, Ben 75, Hugo 51, Iris 50, Ada 47
Finalists (top two): Finn and Emma
Automatic runoff: Finn 13 vs Emma 12
STAR winner: Finn
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Emma | * Finn |
-----------------------------------------------
* Emma > | --- |12 - 0 - 13 |
* Finn > | 13 - 0 - 12 | --- |
[Divergence from STAR]
STAR = Finn
Choose-One (Plurality) = Ada (differs from STAR)
Approval = Emma (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 25 ballots.
Count × Ada,Ben,Cleo,Dev,Emma,Finn,Gus,Hugo,Iris
4 × 0, 2, 2, 2, 3, 4, 5, 5, 5
2 × 4, 5, 4, 4, 4, 2, 2, 0, 0
2 × 0, 1, 2, 2, 2, 3, 4, 5, 5
2 × 0, 1, 2, 2, 2, 4, 4, 5, 5
2 × 0, 2, 3, 3, 3, 5, 4, 2, 2
2 × 5, 5, 4, 4, 4, 2, 2, 0, 0
2 × 5, 4, 3, 3, 3, 2, 1, 0, 0
1 × 5, 4, 4, 3, 3, 2, 1, 0, 0
1 × 0, 2, 3, 3, 4, 5, 4, 2, 1
1 × 2, 4, 5, 5, 5, 3, 2, 0, 0
1 × 0, 2, 3, 3, 3, 5, 5, 3, 3
1 × 3, 5, 5, 5, 4, 3, 2, 0, 0
1 × 1, 3, 5, 5, 5, 4, 3, 0, 0
1 × 0, 2, 3, 3, 3, 5, 5, 2, 2
1 × 5, 4, 4, 4, 3, 2, 2, 0, 0
1 × 3, 5, 5, 5, 5, 3, 2, 0, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Ada 6 2 2 1 1 13 | 47 1.9
Ben 6 5 1 9 4 0 | 75 3.0
Cleo 4 6 7 8 0 0 | 81 3.2
Dev 4 5 8 8 0 0 | 80 3.2
Emma 3 6 12 4 0 0 | 83 3.3
Finn 5 7 5 8 0 0 | 84 3.4
Gus 6 7 1 8 3 0 | 80 3.2
Hugo 8 0 1 4 0 12 | 51 2.0
Iris 8 0 1 3 1 12 | 50 2.0
Scoring Round
The two highest-scoring candidates advance to the next round.
Finn -- 84 -- First place
Emma -- 83 -- Second place
Cleo -- 81
Dev -- 80
Gus -- 80
Ben -- 75
Hugo -- 51
Iris -- 50
Ada -- 47
Finn and Emma advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Finn -- 13 -- First place
Emma -- 12
Equal Support -- 0
Finn wins.
Voters with a preference: 25 of 25 (no Equal Support).
Finn 13 (52%) vs Emma 12 (48%); majority = 13.
Winner — STAR Voting Method (single winner)
Finn
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 25 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: Ada, Ben, Cleo, Dev, Emma, Finn, Gus, Hugo, Iris
2 × Ben > Ada > Cleo > Dev > Emma > Finn > Gus (4, 5, 4, 4, 4, 2, 2, 0, 0)
4 × Gus > Hugo > Iris > Finn > Emma > Ben > Cleo > Dev (0, 2, 2, 2, 3, 4, 5, 5, 5)
1 × Ada > Ben > Cleo > Dev > Emma > Finn > Gus (5, 4, 4, 3, 3, 2, 1, 0, 0)
2 × Hugo > Iris > Gus > Finn > Cleo > Dev > Emma > Ben (0, 1, 2, 2, 2, 3, 4, 5, 5)
1 × Finn > Emma > Gus > Cleo > Dev > Ben > Hugo > Iris (0, 2, 3, 3, 4, 5, 4, 2, 1)
1 × Cleo > Dev > Emma > Ben > Finn > Ada > Gus (2, 4, 5, 5, 5, 3, 2, 0, 0)
2 × Hugo > Iris > Finn > Gus > Cleo > Dev > Emma > Ben (0, 1, 2, 2, 2, 4, 4, 5, 5)
1 × Finn > Gus > Cleo > Dev > Emma > Hugo > Iris > Ben (0, 2, 3, 3, 3, 5, 5, 3, 3)
2 × Finn > Gus > Cleo > Dev > Emma > Ben > Hugo > Iris (0, 2, 3, 3, 3, 5, 4, 2, 2)
1 × Ben > Cleo > Dev > Emma > Ada > Finn > Gus (3, 5, 5, 5, 4, 3, 2, 0, 0)
2 × Ada > Ben > Cleo > Dev > Emma > Finn > Gus (5, 5, 4, 4, 4, 2, 2, 0, 0)
1 × Cleo > Dev > Emma > Finn > Ben > Gus > Ada (1, 3, 5, 5, 5, 4, 3, 0, 0)
1 × Finn > Gus > Cleo > Dev > Emma > Ben > Hugo > Iris (0, 2, 3, 3, 3, 5, 5, 2, 2)
1 × Ada > Ben > Cleo > Dev > Emma > Finn > Gus (5, 4, 4, 4, 3, 2, 2, 0, 0)
2 × Ada > Ben > Cleo > Dev > Emma > Finn > Gus (5, 4, 3, 3, 3, 2, 1, 0, 0)
1 × Ben > Cleo > Dev > Emma > Ada > Finn > Gus (3, 5, 5, 5, 5, 3, 2, 0, 0)
ROUND 1
Candidate Votes Status
----------- ------- --------
Ada 6 Hopeful
Finn 5 Hopeful
Ben 4 Hopeful
Gus 4 Hopeful
Hugo 4 Hopeful
Cleo 2 Rejected
Iris 0 Rejected
Dev 0 Rejected
Emma 0 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Ada 6 Hopeful
Finn 6 Hopeful
Ben 5 Hopeful
Gus 4 Hopeful
Hugo 4 Rejected
Cleo 0 Rejected
Iris 0 Rejected
Dev 0 Rejected
Emma 0 Rejected
ROUND 3
Candidate Votes Status
----------- ------- --------
Finn 8 Hopeful
Gus 6 Hopeful
Ada 6 Hopeful
Ben 5 Rejected
Hugo 0 Rejected
Cleo 0 Rejected
Iris 0 Rejected
Dev 0 Rejected
Emma 0 Rejected
ROUND 4
Candidate Votes Status
----------- ------- --------
Ada 10 Hopeful
Finn 9 Hopeful
Gus 6 Rejected
Ben 0 Rejected
Hugo 0 Rejected
Cleo 0 Rejected
Iris 0 Rejected
Dev 0 Rejected
Emma 0 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Finn 15 Elected
Ada 10 Rejected
Gus 0 Rejected
Ben 0 Rejected
Hugo 0 Rejected
Cleo 0 Rejected
Iris 0 Rejected
Dev 0 Rejected
Emma 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Finn
--- 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 9): Finn
Outside (8): Ada, Ben, Cleo, Dev, Emma, Gus, Hugo, Iris
One member ⇒ Finn is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Finn 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 25 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Ada, Ben, Cleo, Dev, Emma, Finn, Gus, Hugo, Iris
2 × Ben > Ada=Cleo=Dev=Emma > Finn=Gus > Hugo=Iris (4, 5, 4, 4, 4, 2, 2, 0, 0)
4 × Gus=Hugo=Iris > Finn > Emma > Ben=Cleo=Dev > Ada (0, 2, 2, 2, 3, 4, 5, 5, 5)
1 × Ada > Ben=Cleo > Dev=Emma > Finn > Gus > Hugo=Iris (5, 4, 4, 3, 3, 2, 1, 0, 0)
2 × Hugo=Iris > Gus > Finn > Cleo=Dev=Emma > Ben > Ada (0, 1, 2, 2, 2, 3, 4, 5, 5)
1 × Finn > Emma=Gus > Cleo=Dev > Ben=Hugo > Iris > Ada (0, 2, 3, 3, 4, 5, 4, 2, 1)
1 × Cleo=Dev=Emma > Ben > Finn > Ada=Gus > Hugo=Iris (2, 4, 5, 5, 5, 3, 2, 0, 0)
2 × Hugo=Iris > Finn=Gus > Cleo=Dev=Emma > Ben > Ada (0, 1, 2, 2, 2, 4, 4, 5, 5)
1 × Finn=Gus > Cleo=Dev=Emma=Hugo=Iris > Ben > Ada (0, 2, 3, 3, 3, 5, 5, 3, 3)
2 × Finn > Gus > Cleo=Dev=Emma > Ben=Hugo=Iris > Ada (0, 2, 3, 3, 3, 5, 4, 2, 2)
1 × Ben=Cleo=Dev > Emma > Ada=Finn > Gus > Hugo=Iris (3, 5, 5, 5, 4, 3, 2, 0, 0)
2 × Ada=Ben > Cleo=Dev=Emma > Finn=Gus > Hugo=Iris (5, 5, 4, 4, 4, 2, 2, 0, 0)
1 × Cleo=Dev=Emma > Finn > Ben=Gus > Ada > Hugo=Iris (1, 3, 5, 5, 5, 4, 3, 0, 0)
1 × Finn=Gus > Cleo=Dev=Emma > Ben=Hugo=Iris > Ada (0, 2, 3, 3, 3, 5, 5, 2, 2)
1 × Ada > Ben=Cleo=Dev > Emma > Finn=Gus > Hugo=Iris (5, 4, 4, 4, 3, 2, 2, 0, 0)
2 × Ada > Ben > Cleo=Dev=Emma > Finn > Gus > Hugo=Iris (5, 4, 3, 3, 3, 2, 1, 0, 0)
1 × Ben=Cleo=Dev=Emma > Ada=Finn > Gus > Hugo=Iris (3, 5, 5, 5, 5, 3, 2, 0, 0)
Round-Robin — every pair, head-to-head (For – Against):
Ben beats Ada 19 – 4
Cleo beats Ada 17 – 6
Dev beats Ada 17 – 6
Emma beats Ada 17 – 6
Finn beats Ada 15 – 8
Gus beats Ada 14 – 10
Hugo beats Ada 13 – 12
Iris beats Ada 13 – 12
Cleo beats Ben 11 – 6
Dev beats Ben 11 – 7
Emma beats Ben 15 – 9
Finn beats Ben 14 – 11
Gus beats Ben 13 – 11
Ben beats Hugo 12 – 9
Ben beats Iris 13 – 9
Cleo beats Dev 1 – 0
Emma beats Cleo 5 – 3
Finn beats Cleo 13 – 12
Gus beats Cleo 13 – 12
Cleo beats Hugo 16 – 8
Cleo beats Iris 16 – 8
Emma beats Dev 5 – 2
Finn beats Dev 13 – 12
Gus beats Dev 13 – 12
Dev beats Hugo 16 – 8
Dev beats Iris 16 – 8
Finn beats Emma 13 – 12
Emma ties Gus 12 – 12
Emma beats Hugo 16 – 8
Emma beats Iris 16 – 8
Finn beats Gus 10 – 6
Finn beats Hugo 17 – 8
Finn beats Iris 17 – 8
Gus beats Hugo 17 – 4
Gus beats Iris 17 – 4
Hugo beats Iris 1 – 0
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Ada | Ben | Cleo | Dev | Emma | Finn | Gus | Hugo | Iris |
-----------------------------------------------------------------------------------------------------------------------------------------
Ada > | --- | 4 - 2 - 19 | 6 - 2 - 17 | 6 - 2 - 17 | 6 - 2 - 17 | 8 - 2 - 15 |10 - 1 - 14 |12 - 0 - 13 |12 - 0 - 13 |
Ben > | 19 - 2 - 4 | --- | 6 - 8 - 11 | 7 - 7 - 11 | 9 - 1 - 15 |11 - 0 - 14 |11 - 1 - 13 |12 - 4 - 9 |13 - 3 - 9 |
Cleo > | 17 - 2 - 6 |11 - 8 - 6 | --- | 1 - 24 - 0 | 3 - 17 - 5 |12 - 0 - 13 |12 - 0 - 13 |16 - 1 - 8 |16 - 1 - 8 |
Dev > | 17 - 2 - 6 |11 - 7 - 7 | 0 - 24 - 1 | --- | 2 - 18 - 5 |12 - 0 - 13 |12 - 0 - 13 |16 - 1 - 8 |16 - 1 - 8 |
Emma > | 17 - 2 - 6 |15 - 1 - 9 | 5 - 17 - 3 | 5 - 18 - 2 | --- |12 - 0 - 13 |12 - 1 - 12 |16 - 1 - 8 |16 - 1 - 8 |
Finn > | 15 - 2 - 8 |14 - 0 - 11 |13 - 0 - 12 |13 - 0 - 12 |13 - 0 - 12 | --- |10 - 9 - 6 |17 - 0 - 8 |17 - 0 - 8 |
Gus > | 14 - 1 - 10 |13 - 1 - 11 |13 - 0 - 12 |13 - 0 - 12 |12 - 1 - 12 | 6 - 9 - 10 | --- |17 - 4 - 4 |17 - 4 - 4 |
Hugo > | 13 - 0 - 12 | 9 - 4 - 12 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 0 - 17 | 4 - 4 - 17 | --- | 1 - 24 - 0 |
Iris > | 13 - 0 - 12 | 9 - 3 - 13 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 0 - 17 | 4 - 4 - 17 | 0 - 24 - 1 | --- |
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 Finn 8–0–0 8 +35 Emma, Gus, Cleo, Dev, Ben, Hugo, Iris, Ada
2 Emma 6–1–1 6.5 +37 Cleo, Dev, Ben, Hugo, Iris, Ada
3 Gus 6–1–1 6.5 +30 Cleo, Dev, Ben, Hugo, Iris, Ada
4 Cleo 5–3–0 5 +29 Dev, Ben, Hugo, Iris, Ada
5 Dev 4–4–0 4 +25 Ben, Hugo, Iris, Ada
6 Ben 3–5–0 3 +2 Hugo, Iris, Ada
7 Hugo 2–6–0 2 -47 Iris, Ada
8 Iris 1–7–0 1 -50 Ada
9 Ada 0–8–0 0 -61 —
Winner — Ranked Robin (RCV-RR): Finn
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 9): Finn
Outside (8): Ada, Ben, Cleo, Dev, Emma, Gus, Hugo, Iris
One member ⇒ Finn is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Finn 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