Exercise 10 — Later-no-harm: the generous ballots¶
▶ Live on BetterVoting: vote · results ↗ (election yyhj9x · test BV2196) — an independent tabulator to check the winners below against.
Bucket — IRV_OUTLIER_RR_WITH_STAR: RCV-IRV is the outlier (center squeeze)
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 elects Bess — and so do Ranked Robin and Condorcet, because Bess is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Amir: Bess collects fewer top (first-choice) votes, so IRV eliminates Bess early, and those ballots transfer to Amir. This is the classic center squeeze — the broadly acceptable candidate is knocked out by round-by-round elimination even though a majority prefers them in a direct matchup. Two methods (STAR + RR) against one (RCV-IRV): IRV is the outlier.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Bess |
| RCV-IRV | Amir |
| Ranked Robin (RCV-RR) | Bess |
| Approval | Bess |
| Range / Score | Bess |
| Condorcet | Bess |
Flags: none
Source election: 01_STAR/05_Practice/cases/ex10_generous.yaml · STAR tabulated mirror: ex10_generous_tabulated.txt
3 candidates, 9 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Amir | Bess | Cato |
|---|---|---|---|
| 4 | 5 | 3 | 0 |
| 2 | 2 | 5 | 0 |
| 3 | 0 | 1 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Bess 25, Amir 24, Cato 15
Finalists (top two): Bess and Amir
Automatic runoff: Bess 5 vs Amir 4
STAR winner: Bess
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Amir | * Bess |
-----------------------------------------
* Amir > | --- |4 - 0 - 5 |
* Bess > | 5 - 0 - 4 | --- |
[Divergence from STAR]
STAR = Bess
Choose-One (Plurality) = Amir (differs from STAR)
RCV-IRV = Amir (differs from STAR)
Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
method difference, not a tie-breaking artifact.
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 9 ballots.
Count × Amir,Bess,Cato
4 × 5, 3, 0
3 × 0, 1, 5
2 × 2, 5, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Amir 4 0 0 2 0 3 | 24 2.7
Bess 2 0 4 0 3 0 | 25 2.8
Cato 3 0 0 0 0 6 | 15 1.7
Scoring Round
The two highest-scoring candidates advance to the next round.
Bess -- 25 -- First place
Amir -- 24 -- Second place
Cato -- 15
Bess and Amir advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Bess -- 5 -- First place
Amir -- 4
Equal Support -- 0
Bess wins.
Voters with a preference: 9 of 9 (no Equal Support).
Bess 5 (56%) vs Amir 4 (44%); majority = 5.
Winner — STAR Voting Method (single winner)
Bess
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: Amir, Bess, Cato
4 × Amir > Bess (5, 3, 0)
2 × Bess > Amir (2, 5, 0)
3 × Cato > Bess (0, 1, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Amir 4 Hopeful
Cato 3 Hopeful
Bess 2 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Amir 6 Elected
Cato 3 Rejected
Bess 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Amir
--- 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): Bess
Outside (2): Amir, Cato
One member ⇒ Bess is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Amir is OUTSIDE the Smith set. ✗
Every member of the set (Bess) beats Amir head-to-head, yet
RCV-IRV elected Amir 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 9 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Amir, Bess, Cato
4 × Amir > Bess > Cato (5, 3, 0)
2 × Bess > Amir > Cato (2, 5, 0)
3 × Cato > Bess > Amir (0, 1, 5)
Round-Robin — every pair, head-to-head (For – Against):
Bess beats Amir 5 – 4
Amir beats Cato 6 – 3
Bess beats Cato 6 – 3
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Amir | Bess | Cato |
--------------------------------------------
Amir > | --- |4 - 0 - 5 |6 - 0 - 3 |
Bess > | 5 - 0 - 4 | --- |6 - 0 - 3 |
Cato > | 3 - 0 - 6 |3 - 0 - 6 | --- |
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 Bess 2–0–0 2 +4 Amir, Cato
2 Amir 1–1–0 1 +2 Cato
3 Cato 0–2–0 0 -6 —
Winner — Ranked Robin (RCV-RR): Bess
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): Bess
Outside (2): Amir, Cato
One member ⇒ Bess is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Bess 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