Same winner, very different counts — STAR adds, IRV eliminates¶
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 Carmen. Only Approval differs, electing Andre: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Andre's breadth of acceptability over Carmen's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Carmen |
| RCV-IRV | Carmen |
| Ranked Robin (RCV-RR) | Carmen |
| Approval | Andre |
| Range / Score | Carmen |
| Condorcet | Carmen |
Flags: none
Source election: method_comparisons/_main/cases/count_simplicity_star_vs_irv.yaml · STAR tabulated mirror: count_simplicity_star_vs_irv_tabulated.txt
5 candidates, 40 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Andre | Blake | Carmen | Dana | Evan |
|---|---|---|---|---|---|
| 10 | 4 | 3 | 5 | 2 | 1 |
| 9 | 5 | 3 | 4 | 2 | 1 |
| 8 | 3 | 5 | 4 | 2 | 1 |
| 7 | 3 | 2 | 4 | 5 | 1 |
| 6 | 3 | 2 | 4 | 1 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Carmen 170, Andre 148, Blake 123, Dana 95, Evan 64
Finalists (top two): Carmen and Andre
Automatic runoff: Carmen 31 vs Andre 9
STAR winner: Carmen
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Andre | * Carmen |
-----------------------------------------------
* Andre > | --- | 9 - 0 - 31 |
* Carmen > | 31 - 0 - 9 | --- |
[Divergence from STAR]
STAR = Carmen
Approval = Andre (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 40 ballots.
Count × Andre,Blake,Carmen,Dana,Evan
10 × 4, 3, 5, 2, 1
9 × 5, 3, 4, 2, 1
8 × 3, 5, 4, 2, 1
7 × 3, 2, 4, 5, 1
6 × 3, 2, 4, 1, 5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Andre 9 10 21 0 0 0 | 148 3.7
Blake 8 0 19 13 0 0 | 123 3.1
Carmen 10 30 0 0 0 0 | 170 4.3
Dana 7 0 0 27 6 0 | 95 2.4
Evan 6 0 0 0 34 0 | 64 1.6
Scoring Round
The two highest-scoring candidates advance to the next round.
Carmen -- 170 -- First place
Andre -- 148 -- Second place
Blake -- 123
Dana -- 95
Evan -- 64
Carmen and Andre advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Carmen -- 31 -- First place
Andre -- 9
Equal Support -- 0
Carmen wins.
Voters with a preference: 40 of 40 (no Equal Support).
Carmen 31 (78%) vs Andre 9 (22%); majority = 21.
Winner — STAR Voting Method (single winner)
Carmen
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 40 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: Andre, Blake, Carmen, Dana, Evan
10 × Carmen > Andre > Blake > Dana > Evan (4, 3, 5, 2, 1)
9 × Andre > Carmen > Blake > Dana > Evan (5, 3, 4, 2, 1)
8 × Blake > Carmen > Andre > Dana > Evan (3, 5, 4, 2, 1)
7 × Dana > Carmen > Andre > Blake > Evan (3, 2, 4, 5, 1)
6 × Evan > Carmen > Andre > Blake > Dana (3, 2, 4, 1, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Carmen 10 Hopeful
Andre 9 Hopeful
Blake 8 Hopeful
Dana 7 Hopeful
Evan 6 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Carmen 16 Hopeful
Andre 9 Hopeful
Blake 8 Hopeful
Dana 7 Rejected
Evan 0 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Carmen 23 Elected
Andre 9 Rejected
Blake 8 Rejected
Dana 0 Rejected
Evan 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Carmen
--- 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): Carmen
Outside (4): Andre, Blake, Dana, Evan
One member ⇒ Carmen is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Carmen 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 40 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Andre, Blake, Carmen, Dana, Evan
10 × Carmen > Andre > Blake > Dana > Evan (4, 3, 5, 2, 1)
9 × Andre > Carmen > Blake > Dana > Evan (5, 3, 4, 2, 1)
8 × Blake > Carmen > Andre > Dana > Evan (3, 5, 4, 2, 1)
7 × Dana > Carmen > Andre > Blake > Evan (3, 2, 4, 5, 1)
6 × Evan > Carmen > Andre > Blake > Dana (3, 2, 4, 1, 5)
Round-Robin — every pair, head-to-head (For – Against):
Andre beats Blake 32 – 8
Carmen beats Andre 31 – 9
Andre beats Dana 33 – 7
Andre beats Evan 34 – 6
Carmen beats Blake 32 – 8
Blake beats Dana 33 – 7
Blake beats Evan 34 – 6
Carmen beats Dana 33 – 7
Carmen beats Evan 34 – 6
Dana beats Evan 34 – 6
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Andre | Blake | Carmen | Dana | Evan |
-----------------------------------------------------------------------------------
Andre > | --- |32 - 0 - 8 | 9 - 0 - 31 |33 - 0 - 7 |34 - 0 - 6 |
Blake > | 8 - 0 - 32 | --- | 8 - 0 - 32 |33 - 0 - 7 |34 - 0 - 6 |
Carmen > | 31 - 0 - 9 |32 - 0 - 8 | --- |33 - 0 - 7 |34 - 0 - 6 |
Dana > | 7 - 0 - 33 | 7 - 0 - 33 | 7 - 0 - 33 | --- |34 - 0 - 6 |
Evan > | 6 - 0 - 34 | 6 - 0 - 34 | 6 - 0 - 34 | 6 - 0 - 34 | --- |
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 Carmen 4–0–0 4 +100 Andre, Blake, Dana, Evan
2 Andre 3–1–0 3 +56 Blake, Dana, Evan
3 Blake 2–2–0 2 +6 Dana, Evan
4 Dana 1–3–0 1 -50 Evan
5 Evan 0–4–0 0 -112 —
Winner — Ranked Robin (RCV-RR): Carmen
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): Carmen
Outside (4): Andre, Blake, Dana, Evan
One member ⇒ Carmen is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Carmen 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