Exercise 6 — Bullet voting backfires: the honest ballots¶
▶ Live on BetterVoting: vote · results ↗ (election x4dkfd · test BV2193) — 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 Bree — and so do Ranked Robin and Condorcet, because Bree is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Cash: Bree collects fewer top (first-choice) votes, so IRV eliminates Bree early, and those ballots transfer to Cash. 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 | Bree |
| RCV-IRV | Cash |
| Ranked Robin (RCV-RR) | Bree |
| Approval | Bree |
| Range / Score | Bree |
| Condorcet | Bree |
Flags: none
Source election: 01_STAR/05_Practice/cases/ex06_bullet_honest.yaml · STAR tabulated mirror: ex06_bullet_honest_tabulated.txt
3 candidates, 9 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Ari | Bree | Cash |
|---|---|---|---|
| 4 | 5 | 3 | 0 |
| 4 | 0 | 2 | 5 |
| 1 | 0 | 5 | 1 |
STAR result (official)¶
Scoring round (sum of scores): Bree 25, Cash 21, Ari 20
Finalists (top two): Bree and Cash
Automatic runoff: Bree 5 vs Cash 4
STAR winner: Bree
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Bree | * Cash |
-----------------------------------------
* Bree > | --- |5 - 0 - 4 |
* Cash > | 4 - 0 - 5 | --- |
[Divergence from STAR]
STAR = Bree
Choose-One (Plurality) = Ari (differs from STAR)
RCV-IRV = Cash (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 × Ari,Bree,Cash
4 × 5, 3, 0
4 × 0, 2, 5
1 × 0, 5, 1
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Ari 4 0 0 0 0 5 | 20 2.2
Bree 1 0 4 4 0 0 | 25 2.8
Cash 4 0 0 0 1 4 | 21 2.3
Scoring Round
The two highest-scoring candidates advance to the next round.
Bree -- 25 -- First place
Cash -- 21 -- Second place
Ari -- 20
Bree and Cash advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Bree -- 5 -- First place
Cash -- 4
Equal Support -- 0
Bree wins.
Voters with a preference: 9 of 9 (no Equal Support).
Bree 5 (56%) vs Cash 4 (44%); majority = 5.
Winner — STAR Voting Method (single winner)
Bree
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: Ari, Bree, Cash
4 × Ari > Bree (5, 3, 0)
4 × Cash > Bree (0, 2, 5)
1 × Bree > Cash (0, 5, 1)
ROUND 1
Candidate Votes Status
----------- ------- --------
Cash 4 Hopeful
Ari 4 Hopeful
Bree 1 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Cash 5 Elected
Ari 4 Rejected
Bree 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Cash
--- 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): Bree
Outside (2): Ari, Cash
One member ⇒ Bree is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Cash is OUTSIDE the Smith set. ✗
Every member of the set (Bree) beats Cash head-to-head, yet
RCV-IRV elected Cash 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: Ari, Bree, Cash
4 × Ari > Bree > Cash (5, 3, 0)
4 × Cash > Bree > Ari (0, 2, 5)
1 × Bree > Cash > Ari (0, 5, 1)
Round-Robin — every pair, head-to-head (For – Against):
Bree beats Ari 5 – 4
Cash beats Ari 5 – 4
Bree beats Cash 5 – 4
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Ari | Bree | Cash |
--------------------------------------------
Ari > | --- |4 - 0 - 5 |4 - 0 - 5 |
Bree > | 5 - 0 - 4 | --- |5 - 0 - 4 |
Cash > | 5 - 0 - 4 |4 - 0 - 5 | --- |
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 Bree 2–0–0 2 +2 Cash, Ari
2 Cash 1–1–0 1 +0 Ari
3 Ari 0–2–0 0 -2 —
Winner — Ranked Robin (RCV-RR): Bree
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): Bree
Outside (2): Ari, Cash
One member ⇒ Bree is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Bree 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