Center squeeze — STAR elects the consensus (Center)¶
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 Center — and so do Ranked Robin and Condorcet, because Center is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Left: Center collects fewer top (first-choice) votes, so IRV eliminates Center early, and those ballots transfer to Left. 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 | Center |
| RCV-IRV | Left |
| Ranked Robin (RCV-RR) | Center |
| Approval | Left |
| Range / Score | Center |
| Condorcet | Center |
Flags: none
Source election: method_comparisons/center_squeeze/cases/center_squeeze_star.yaml · STAR tabulated mirror: center_squeeze_star_tabulated.txt
3 candidates, 27 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Left | Center | Right |
|---|---|---|---|
| 12 | 5 | 4 | 3 |
| 9 | 3 | 4 | 5 |
| 6 | 4 | 5 | 3 |
STAR result (official)¶
Scoring round (sum of scores): Center 114, Left 111, Right 99
Finalists (top two): Center and Left
Automatic runoff: Center 15 vs Left 12
STAR winner: Center
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Left | * Center |
-----------------------------------------------
* Left > | --- |12 - 0 - 15 |
* Center > | 15 - 0 - 12 | --- |
[Divergence from STAR]
STAR = Center
Choose-One (Plurality) = Left (differs from STAR)
RCV-IRV = Left (differs from STAR)
Approval = Left (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 27 ballots.
Count × Left,Center,Right
12 × 5, 4, 3
9 × 3, 4, 5
6 × 4, 5, 3
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Left 12 6 9 0 0 0 | 111 4.1
Center 6 21 0 0 0 0 | 114 4.2
Right 9 0 18 0 0 0 | 99 3.7
Scoring Round
The two highest-scoring candidates advance to the next round.
Center -- 114 -- First place
Left -- 111 -- Second place
Right -- 99
Center and Left advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Center -- 15 -- First place
Left -- 12
Equal Support -- 0
Center wins.
Voters with a preference: 27 of 27 (no Equal Support).
Center 15 (56%) vs Left 12 (44%); majority = 14.
Winner — STAR Voting Method (single winner)
Center
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 27 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: Left, Center, Right
12 × Left > Center > Right (5, 4, 3)
9 × Right > Center > Left (3, 4, 5)
6 × Center > Left > Right (4, 5, 3)
ROUND 1
Candidate Votes Status
----------- ------- --------
Left 12 Hopeful
Right 9 Hopeful
Center 6 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Left 18 Elected
Right 9 Rejected
Center 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Left
--- 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): Center
Outside (2): Left, Right
One member ⇒ Center is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Left is OUTSIDE the Smith set. ✗
Every member of the set (Center) beats Left head-to-head, yet
RCV-IRV elected Left 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 27 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Left, Center, Right
12 × Left > Center > Right (5, 4, 3)
9 × Right > Center > Left (3, 4, 5)
6 × Center > Left > Right (4, 5, 3)
Round-Robin — every pair, head-to-head (For – Against):
Center beats Left 15 – 12
Left beats Right 18 – 9
Center beats Right 18 – 9
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Left | Center | Right |
-------------------------------------------------------
Left > | --- |12 - 0 - 15 |18 - 0 - 9 |
Center > | 15 - 0 - 12 | --- |18 - 0 - 9 |
Right > | 9 - 0 - 18 | 9 - 0 - 18 | --- |
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 Center 2–0–0 2 +12 Left, Right
2 Left 1–1–0 1 +6 Right
3 Right 0–2–0 0 -18 —
Winner — Ranked Robin (RCV-RR): Center
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): Center
Outside (2): Left, Right
One member ⇒ Center is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Center 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