Exercise 3 — One electorate, five verdicts (the snack vote)¶
▶ Live on BetterVoting: vote · results ↗ (election ywqhq4 · test BV2191) — 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 Cherry — and so do Ranked Robin and Condorcet, because Cherry is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Banana: Cherry collects fewer top (first-choice) votes, so IRV eliminates Cherry early, and those ballots transfer to Banana. 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 | Cherry |
| RCV-IRV | Banana |
| Ranked Robin (RCV-RR) | Cherry |
| Approval | Cherry |
| Range / Score | Cherry |
| Condorcet | Cherry |
Flags: none
Source election: 01_STAR/05_Practice/cases/ex03_five_verdicts.yaml · STAR tabulated mirror: ex03_five_verdicts_tabulated.txt
3 candidates, 9 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Apple | Banana | Cherry |
|---|---|---|---|
| 4 | 5 | 0 | 3 |
| 3 | 0 | 5 | 4 |
| 2 | 0 | 1 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Cherry 34, Apple 20, Banana 17
Finalists (top two): Cherry and Apple
Automatic runoff: Cherry 5 vs Apple 4
STAR winner: Cherry
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Apple | * Cherry |
-----------------------------------------
* Apple > | --- |4 - 0 - 5 |
* Cherry > | 5 - 0 - 4 | --- |
[Divergence from STAR]
STAR = Cherry
Choose-One (Plurality) = Apple (differs from STAR)
RCV-IRV = Banana (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 × Apple,Banana,Cherry
4 × 5, 0, 3
3 × 0, 5, 4
2 × 0, 1, 5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Apple 4 0 0 0 0 5 | 20 2.2
Banana 3 0 0 0 2 4 | 17 1.9
Cherry 2 3 4 0 0 0 | 34 3.8
Scoring Round
The two highest-scoring candidates advance to the next round.
Cherry -- 34 -- First place
Apple -- 20 -- Second place
Banana -- 17
Cherry and Apple advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Cherry -- 5 -- First place
Apple -- 4
Equal Support -- 0
Cherry wins.
Voters with a preference: 9 of 9 (no Equal Support).
Cherry 5 (56%) vs Apple 4 (44%); majority = 5.
Winner — STAR Voting Method (single winner)
Cherry
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: Apple, Banana, Cherry
4 × Apple > Cherry (5, 0, 3)
3 × Banana > Cherry (0, 5, 4)
2 × Cherry > Banana (0, 1, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Apple 4 Hopeful
Banana 3 Hopeful
Cherry 2 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Banana 5 Elected
Apple 4 Rejected
Cherry 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Banana
--- 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): Cherry
Outside (2): Apple, Banana
One member ⇒ Cherry is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Banana is OUTSIDE the Smith set. ✗
Every member of the set (Cherry) beats Banana head-to-head, yet
RCV-IRV elected Banana 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: Apple, Banana, Cherry
4 × Apple > Cherry > Banana (5, 0, 3)
3 × Banana > Cherry > Apple (0, 5, 4)
2 × Cherry > Banana > Apple (0, 1, 5)
Round-Robin — every pair, head-to-head (For – Against):
Banana beats Apple 5 – 4
Cherry beats Apple 5 – 4
Cherry beats Banana 6 – 3
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Apple | Banana | Cherry |
----------------------------------------------
Apple > | --- |4 - 0 - 5 |4 - 0 - 5 |
Banana > | 5 - 0 - 4 | --- |3 - 0 - 6 |
Cherry > | 5 - 0 - 4 |6 - 0 - 3 | --- |
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 Cherry 2–0–0 2 +4 Banana, Apple
2 Banana 1–1–0 1 -2 Apple
3 Apple 0–2–0 0 -2 —
Winner — Ranked Robin (RCV-RR): Cherry
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): Cherry
Outside (2): Apple, Banana
One member ⇒ Cherry is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Cherry 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