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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