Does the squeeze survive noise? Two poles, one consensus middle¶

▶ Live on BetterVoting: vote · results ↗ (election td7jfy · test BV2238) — an independent tabulator to check the winners below against.

Bucket — IRV_DIFFERS_ARTIFACT: RCV-IRV differs — tie-break artifact

Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.

What happens¶

On these ballots RCV-IRV reports Cora rather than STAR's Ben, but this is an artifact of score→rank conversion, not a robust method difference: 2 of 38 ballots have tied non-zero scores, so their ranks are set by an arbitrary candidate-priority order. Ranked Robin and the Condorcet (pairwise) winner both agree with STAR (Ben). Do not use this case to criticize RCV-IRV — the disagreement is a coin-flip created by equal scores and would vanish under a different (equally arbitrary) tie-break.

Winners by method¶

Method	Winner
STAR	Ben
RCV-IRV	Cora
Ranked Robin (RCV-RR)	Ben
Approval	Cora
Range / Score	Cora
Condorcet	Ben

Flags: 2 tied-score ballot(s)

Source election: 06_Other/ballot_style_lab/cases/05_c3_b38_squeeze-survives.yaml · STAR tabulated mirror: 05_c3_b38_squeeze-survives_tabulated.txt

3 candidates, 38 ballots.

The ballots¶

Each row is a group of identical score ballots (0 = no support, 5 = max).

Count	Ava	Ben	Cora
1	3	5	3
1	0	2	5
3	5	4	0
2	0	5	1
6	5	4	3
2	5	2	0
4	3	4	5
10	0	1	5
1	0	0	5
1	0	4	5
1	2	1	0
1	5	3	0
1	0	5	5
3	0	5	2
1	3	0	5

STAR result (official)¶

Scoring round (sum of scores): Cora 124, Ben 111, Ava 80

Finalists (top two): Cora and Ben

Automatic runoff: Cora 18 vs Ben 19 (1 equal/no-preference)

STAR winner: Ben

Full LH STAR engine report:

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
                 |    * Ben     |   * Cora    |
-----------------------------------------------
         * Ben > |     ---      |19 -  1 - 18 |
        * Cora > | 18 -  1 - 19 |    ---      |

[Divergence from STAR]
  STAR                   = Ben
  Choose-One (Plurality) = Cora   (differs from STAR)
  RCV-IRV                = Cora   (differs from STAR)
  Approval               = Cora   (differs from STAR)
  Note: 2 of 38 ballots (5%) had equal non-zero scores, so their ranks were
        decided by candidate priority order. The RCV-IRV result may be an
        artifact of score-to-rank tie-breaking rather than a deep
        difference.
  Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
        outlier — the classic center-squeeze signature.

[Runoff Reversal]
 - Score Round Winner(s) = (Cora)
 - Runoff Round Winner   = (Ben)
  Candidate Cora earned the highest total score, but
  Candidate Ben won the automatic runoff — not a malfunction,
  STAR working as designed: the runoff elects the finalist preferred
  by the majority (of voters with a preference).


--- STAR Voting Method (single winner) ---
 Tabulating 38 ballots.
Count × Ava,Ben,Cora
    6 ×   5,  4,   3
    5 ×   0,  1,   5
    5 ×   -,  1,   5
    4 ×   3,  4,   5
    3 ×   0,  5,   2
    2 ×   5,  4,   -
    2 ×   5,  2,   0
    1 ×   3,  5,   3
    1 ×   0,  2,   5
    1 ×   0,  5,   1
    1 ×   0,  0,   5
    1 ×   0,  4,   5
    1 ×   2,  1,   0
    1 ×   -,  5,   1
    1 ×   5,  3,   0
    1 ×   0,  5,   5
    1 ×   3,  0,   5
    1 ×   5,  4,   0
  ('-' = left blank / abstained; '0' = scored zero — both count as 0 stars.)

[Score Distribution] (how many ballots gave each star rating)
                   Score
Candidate   5   4   3   2   1   0  Abs  | Total  Avg all  Avg rated
Ava        12   0   6   1   0  13    6  |    80      2.1        2.5
Ben         7  14   1   3  11   2    0  |   111      2.9        2.9
Cora       19   0   7   3   2   5    2  |   124      3.3        3.4
  Avg all   = Total / all ballots — a blank counts as 0, so this is the Total the Scoring Round ranks on, per ballot.
  Avg rated = Total / the ballots that scored this candidate (Abs excluded) — support among voters who had an opinion.

Scoring Round
 The two highest-scoring candidates advance to the next round.
   Cora          -- 124 -- First place
   Ben           -- 111 -- Second place
   Ava           --  80
 Cora and Ben advance.

Automatic Runoff Round
 The candidate preferred in the most head-to-head matchups wins.
   Ben           -- 19 -- First place
   Cora          -- 18
   Equal Support --  1
 Ben wins.
   Voters with a preference: 37 of 38 (1 Equal Support).
   Ben 19 (51%) vs Cora 18 (49%); majority = 19.

Winner — STAR Voting Method (single winner)
 Ben

RCV-IRV — round by round¶

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 38 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: Ava, Ben, Cora
     1 ×   Ben > Ava > Cora      (3, 5, 3)
     1 ×   Cora > Ben      (0, 2, 5)
     3 ×   Ava > Ben      (5, 4, 0)
     2 ×   Ben > Cora      (0, 5, 1)
     6 ×   Ava > Ben > Cora      (5, 4, 3)
     2 ×   Ava > Ben      (5, 2, 0)
     4 ×   Cora > Ben > Ava      (3, 4, 5)
    10 ×   Cora > Ben      (0, 1, 5)
     1 ×   Cora      (0, 0, 5)
     1 ×   Cora > Ben      (0, 4, 5)
     1 ×   Ava > Ben      (2, 1, 0)
     1 ×   Ava > Ben      (5, 3, 0)
     1 ×   Ben > Cora      (0, 5, 5)
     3 ×   Ben > Cora      (0, 5, 2)
     1 ×   Cora > Ava      (3, 0, 5)

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Cora              18  Hopeful
Ava               13  Hopeful
Ben                7  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Cora              24  Elected
Ava               14  Rejected
Ben                0  Rejected


Winner(s) — RCV / Instant-Runoff Voting (single winner)
  Cora

--- 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): Ben
   Outside (2):        Ava, Cora
   One member ⇒ Ben is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Cora is OUTSIDE the Smith set. ✗
      Every member of the set (Ben) beats Cora head-to-head, yet
      RCV-IRV elected Cora 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 38 ballots (score ballots).

Ballots:
   the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Ava, Ben, Cora
     1 × Ben > Ava=Cora      (3, 5, 3)
     1 × Cora > Ben > Ava      (0, 2, 5)
     3 × Ava > Ben > Cora      (5, 4, 0)
     2 × Ben > Cora > Ava      (0, 5, 1)
     6 × Ava > Ben > Cora      (5, 4, 3)
     2 × Ava > Ben > Cora      (5, 2, 0)
     4 × Cora > Ben > Ava      (3, 4, 5)
    10 × Cora > Ben > Ava      (0, 1, 5)
     1 × Cora > Ava=Ben      (0, 0, 5)
     1 × Cora > Ben > Ava      (0, 4, 5)
     1 × Ava > Ben > Cora      (2, 1, 0)
     1 × Ava > Ben > Cora      (5, 3, 0)
     1 × Ben=Cora > Ava      (0, 5, 5)
     3 × Ben > Cora > Ava      (0, 5, 2)
     1 × Cora > Ava > Ben      (3, 0, 5)

Round-Robin — every pair, head-to-head (For – Against):
   Ben   beats Ava    23 – 14
   Cora  beats Ava    24 – 13
   Ben   beats Cora   19 – 18

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |     Ava      |    Ben      |    Cora     |
-----------------------------------------------------
   Ava > |     ---      |14 -  1 - 23 |13 -  1 - 24 |
   Ben > | 23 -  1 - 14 |    ---      |19 -  1 - 18 |
  Cora > | 24 -  1 - 13 |18 -  1 - 19 |    ---      |

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  Ben        2–0–0         2     +10  Cora, Ava
    2  Cora       1–1–0         1     +10  Ava
    3  Ava        0–2–0         0     -20  —

Winner — Ranked Robin (RCV-RR): Ben
   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): Ben
   Outside (2):        Ava, Cora
   One member ⇒ Ben is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Ben 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

Count	Ava	Ben	Cora
1	3	5	3
1	0	2	5
3	5	4	0
2	0	5	1
6	5	4	3
2	5	2	0
4	3	4	5
10	0	1	5
1	0	0	5
1	0	4	5
1	2	1	0
1	5	3	0
1	0	5	5
3	0	5	2
1	3	0	5

Count	Ava	Ben	Cora
1	3	5	3
1	0	2	5
3	5	4	0
2	0	5	1
6	5	4	3
2	5	2	0
4	3	4	5
10	0	1	5
1	0	0	5
1	0	4	5
1	2	1	0
1	5	3	0
1	0	5	5
3	0	5	2
1	3	0	5

Count	Ava	Ben	Cora
1	3	5	3
1	0	2	5
3	5	4	0
2	0	5	1
6	5	4	3
2	5	2	0
4	3	4	5
10	0	1	5
1	0	0	5
1	0	4	5
1	2	1	0
1	5	3	0
1	0	5	5
3	0	5	2
1	3	0	5