Runoff reversal, the jarring case — the near-consensus favorite loses a 51–49 runoff to a polarizing rival¶
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 Rye. Only Approval differs, electing Uma: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Uma's breadth of acceptability over Rye's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Rye |
| RCV-IRV | Rye |
| Ranked Robin (RCV-RR) | Rye |
| Approval | Uma |
| Range / Score | Uma |
| Condorcet | Rye |
Flags: none
Source election: 01_STAR/02_Examples/runoff_overturns_leader/cases/reversal_jarring_c3_b100.yaml · STAR tabulated mirror: reversal_jarring_c3_b100_tabulated.txt
3 candidates, 100 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Uma | Rye | Tao |
|---|---|---|---|
| 51 | 4 | 5 | 0 |
| 49 | 5 | 0 | 1 |
STAR result (official)¶
Scoring round (sum of scores): Uma 449, Rye 255, Tao 49
Finalists (top two): Uma and Rye
Automatic runoff: Uma 49 vs Rye 51
STAR winner: Rye
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Uma | * Rye |
-----------------------------------------------
* Uma > | --- |49 - 0 - 51 |
* Rye > | 51 - 0 - 49 | --- |
[Divergence from STAR]
STAR = Rye
Approval = Uma (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Uma)
- Runoff Round Winner = (Rye)
Candidate Uma earned the highest total score, but
Candidate Rye 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 100 ballots.
Count × Uma,Rye,Tao
51 × 4, 5, 0
49 × 5, 0, 1
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Uma 49 51 0 0 0 0 | 449 4.5
Rye 51 0 0 0 0 49 | 255 2.6
Tao 0 0 0 0 49 51 | 49 0.5
Scoring Round
The two highest-scoring candidates advance to the next round.
Uma -- 449 -- First place
Rye -- 255 -- Second place
Tao -- 49
Uma and Rye advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Rye -- 51 -- First place
Uma -- 49
Equal Support -- 0
Rye wins.
Voters with a preference: 100 of 100 (no Equal Support).
Rye 51 (51%) vs Uma 49 (49%); majority = 51.
Winner — STAR Voting Method (single winner)
Rye
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 100 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: Uma, Rye, Tao
51 × Rye > Uma (4, 5, 0)
49 × Uma > Tao (5, 0, 1)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Rye 51 Elected
Uma 49 Rejected
Tao 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Rye
--- 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): Rye
Outside (2): Uma, Tao
One member ⇒ Rye is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Rye 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 100 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Uma, Rye, Tao
51 × Rye > Uma > Tao (4, 5, 0)
49 × Uma > Tao > Rye (5, 0, 1)
Round-Robin — every pair, head-to-head (For – Against):
Rye beats Uma 51 – 49
Uma beats Tao 100 – 0
Rye beats Tao 51 – 49
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Uma | Rye | Tao |
-------------------------------------------------------------
Uma > | --- | 49 - 0 - 51 |100 - 0 - 0 |
Rye > | 51 - 0 - 49 | --- | 51 - 0 - 49 |
Tao > | 0 - 0 - 100 | 49 - 0 - 51 | --- |
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 Rye 2–0–0 2 +4 Uma, Tao
2 Uma 1–1–0 1 +98 Tao
3 Tao 0–2–0 0 -102 —
Winner — Ranked Robin (RCV-RR): Rye
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): Rye
Outside (2): Uma, Tao
One member ⇒ Rye is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Rye 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