Exercise 4 — Lillehammer 1994: nine judges, three skaters, two winners¶
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 Baiul. Only Approval differs, electing Kerrigan: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Kerrigan's breadth of acceptability over Baiul's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Baiul |
| RCV-IRV | Baiul |
| Ranked Robin (RCV-RR) | Baiul |
| Approval | Kerrigan |
| Range / Score | Kerrigan |
| Condorcet | Baiul |
Flags: none
Source election: 01_STAR/05_Practice/cases/ex04_olympics_1994.yaml · STAR tabulated mirror: ex04_olympics_1994_tabulated.txt
3 candidates, 9 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Baiul | Kerrigan | Lu |
|---|---|---|---|
| 5 | 5 | 3 | 1 |
| 2 | 3 | 5 | 1 |
| 2 | 1 | 5 | 3 |
STAR result (official)¶
Scoring round (sum of scores): Kerrigan 35, Baiul 33, Lu 13
Finalists (top two): Kerrigan and Baiul
Automatic runoff: Kerrigan 4 vs Baiul 5
STAR winner: Baiul
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Baiul | * Kerrigan |
-----------------------------------------------
* Baiul > | --- | 5 - 0 - 4 |
* Kerrigan > | 4 - 0 - 5 | --- |
[Divergence from STAR]
STAR = Baiul
Approval = Kerrigan (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Kerrigan)
- Runoff Round Winner = (Baiul)
Candidate Kerrigan earned the highest total score, but
Candidate Baiul won the automatic runoff — not a malfunction,
STAR working as designed: the runoff elects the finalist preferred
by the majority (of voters with a preference).
--- STAR Voting Method (single winner) ---
Tabulating 9 ballots.
Count × Baiul,Kerrigan,Lu
5 × 5, 3, 1
2 × 3, 5, 1
2 × 1, 5, 3
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Baiul 5 0 2 0 2 0 | 33 3.7
Kerrigan 4 0 5 0 0 0 | 35 3.9
Lu 0 0 2 0 7 0 | 13 1.4
Scoring Round
The two highest-scoring candidates advance to the next round.
Kerrigan -- 35 -- First place
Baiul -- 33 -- Second place
Lu -- 13
Kerrigan and Baiul advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Baiul -- 5 -- First place
Kerrigan -- 4
Equal Support -- 0
Baiul wins.
Voters with a preference: 9 of 9 (no Equal Support).
Baiul 5 (56%) vs Kerrigan 4 (44%); majority = 5.
Winner — STAR Voting Method (single winner)
Baiul
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 9 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: Baiul, Kerrigan, Lu
5 × Baiul > Kerrigan > Lu (5, 3, 1)
2 × Kerrigan > Baiul > Lu (3, 5, 1)
2 × Kerrigan > Lu > Baiul (1, 5, 3)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Baiul 5 Elected
Kerrigan 4 Rejected
Lu 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Baiul
--- 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 3): Baiul
Outside (2): Kerrigan, Lu
One member ⇒ Baiul is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Baiul 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 9 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Baiul, Kerrigan, Lu
5 × Baiul > Kerrigan > Lu (5, 3, 1)
2 × Kerrigan > Baiul > Lu (3, 5, 1)
2 × Kerrigan > Lu > Baiul (1, 5, 3)
Round-Robin — every pair, head-to-head (For – Against):
Baiul beats Kerrigan 5 – 4
Baiul beats Lu 7 – 2
Kerrigan beats Lu 9 – 0
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Baiul | Kerrigan | Lu |
---------------------------------------------------
Baiul > | --- |5 - 0 - 4 |7 - 0 - 2 |
Kerrigan > | 4 - 0 - 5 | --- |9 - 0 - 0 |
Lu > | 2 - 0 - 7 |0 - 0 - 9 | --- |
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 Baiul 2–0–0 2 +6 Kerrigan, Lu
2 Kerrigan 1–1–0 1 +8 Lu
3 Lu 0–2–0 0 -14 —
Winner — Ranked Robin (RCV-RR): Baiul
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 3): Baiul
Outside (2): Kerrigan, Lu
One member ⇒ Baiul is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Baiul 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