Center Squeeze — STAR (ranks→scores): agrees with Condorcet, not IRV¶
▶ Live on BetterVoting: vote · results ↗ (election ywckmg · test BV2137) — 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 Anderson — and so do Ranked Robin and Condorcet, because Anderson is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Carter: Anderson collects fewer top (first-choice) votes, so IRV eliminates Anderson early, and those ballots transfer to Carter. 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 | Anderson |
| RCV-IRV | Carter |
| Ranked Robin (RCV-RR) | Anderson |
| Approval | Anderson |
| Range / Score | Anderson |
| Condorcet | Anderson |
Flags: none
Source election: method_comparisons/center_squeeze_bv2137/cases/bv2137_ywckmg_star.yaml · STAR tabulated mirror: bv2137_ywckmg_star_tabulated.txt
3 candidates, 100 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Reagan | Anderson | Carter |
|---|---|---|---|
| 45 | 5 | 3 | 1 |
| 20 | 1 | 5 | 3 |
| 35 | 1 | 3 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Anderson 340, Reagan 280, Carter 280
Finalists (top two): Anderson and Reagan
Automatic runoff: Anderson 55 vs Reagan 45
STAR winner: Anderson
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
Note: Carter and Reagan tied at 280 in the Scoring Round, and the
head-to-head rung advanced Carter. The * marks who advanced, not
who scored highest. Reagan is filtered out of this grid, so the
head-to-head that settled it is not shown — see the Scoring
Round.
| * Anderson | * Carter |
-----------------------------------------------
* Anderson > | --- |65 - 0 - 35 |
* Carter > | 35 - 0 - 65 | --- |
[Divergence from STAR]
STAR = Anderson
Choose-One (Plurality) = Reagan (differs from STAR)
RCV-IRV = Carter (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 100 ballots.
Count × Reagan,Anderson,Carter
45 × 5, 3, 1
35 × 1, 3, 5
20 × 1, 5, 3
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Reagan 45 0 0 0 55 0 | 280 2.8
Anderson 20 0 80 0 0 0 | 340 3.4
Carter 35 0 20 0 45 0 | 280 2.8
Scoring Round
The two highest-scoring candidates advance to the next round.
Anderson -- 340 -- First place
Carter -- 280 -- Tied for second place
Reagan -- 280 -- Tied for second place
Anderson advances, but there's a two-way tie for second.
Scoring Round: First tiebreaker
The candidate preferred in the most head-to-head matchups advances.
Carter -- 55 -- Second place
Reagan -- 45
Equal Support -- 0
Anderson and Carter advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Anderson -- 65 -- First place
Carter -- 35
Equal Support -- 0
Anderson wins.
Voters with a preference: 100 of 100 (no Equal Support).
Anderson 65 (65%) vs Carter 35 (35%); majority = 51.
Winner — STAR Voting Method (single winner)
Anderson
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: Reagan, Anderson, Carter
45 × Reagan > Anderson > Carter (5, 3, 1)
20 × Anderson > Carter > Reagan (1, 5, 3)
35 × Carter > Anderson > Reagan (1, 3, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Reagan 45 Hopeful
Carter 35 Hopeful
Anderson 20 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Carter 55 Elected
Reagan 45 Rejected
Anderson 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Carter
--- 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): Anderson
Outside (2): Reagan, Carter
One member ⇒ Anderson is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Carter is OUTSIDE the Smith set. ✗
Every member of the set (Anderson) beats Carter head-to-head, yet
RCV-IRV elected Carter 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 100 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Reagan, Anderson, Carter
45 × Reagan > Anderson > Carter (5, 3, 1)
20 × Anderson > Carter > Reagan (1, 5, 3)
35 × Carter > Anderson > Reagan (1, 3, 5)
Round-Robin — every pair, head-to-head (For – Against):
Anderson beats Reagan 55 – 45
Carter beats Reagan 55 – 45
Anderson beats Carter 65 – 35
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Reagan | Anderson | Carter |
---------------------------------------------------------
Reagan > | --- |45 - 0 - 55 |45 - 0 - 55 |
Anderson > | 55 - 0 - 45 | --- |65 - 0 - 35 |
Carter > | 55 - 0 - 45 |35 - 0 - 65 | --- |
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 Anderson 2–0–0 2 +40 Carter, Reagan
2 Carter 1–1–0 1 -20 Reagan
3 Reagan 0–2–0 0 -20 —
Winner — Ranked Robin (RCV-RR): Anderson
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): Anderson
Outside (2): Reagan, Carter
One member ⇒ Anderson is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Anderson 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