Nurmi Ex.16 sincere — STAR: elects the Condorcet winner B

▶ Live on BetterVoting: vote · results ↗ (election 4htk44 · test BV2162) — 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 B — and so do Ranked Robin and Condorcet, because B is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects A: B collects fewer top (first-choice) votes, so IRV eliminates B early, and those ballots transfer to A. 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	B
RCV-IRV	A
Ranked Robin (RCV-RR)	B
Approval	B
Range / Score	B
Condorcet	B

Flags: none

Source election: method_comparisons/felsenthal_paradoxes/cases/bv2162_4htk44_star.yaml · STAR tabulated mirror: bv2162_4htk44_star_tabulated.txt

4 candidates, 103 ballots.

The ballots

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

Count	A	B	C	D
33	5	4	2	1
29	4	5	2	1
24	2	4	5	1
17	1	2	4	5

STAR result (official)

Scoring round (sum of scores): B 407, A 346, C 312, D 171

Finalists (top two): B and A

Automatic runoff: B 70 vs A 33

STAR winner: B

Full LH STAR engine report:

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
                 |     * A      |    * B      |
-----------------------------------------------
           * A > |     ---      |33 -  0 - 70 |
           * B > | 70 -  0 - 33 |    ---      |

[Divergence from STAR]
  STAR                   = B
  Choose-One (Plurality) = A   (differs from STAR)
  RCV-IRV                = A   (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 103 ballots.
Count × A,B,C,D
   33 × 5,4,2,1
   29 × 4,5,2,1
   24 × 2,4,5,1
   17 × 1,2,4,5

[Score Distribution] (how many ballots gave each star rating)
                   Score
Candidate   5   4   3   2   1   0  | Total   Avg
A          33  29   0  24  17   0  |   346   3.4
B          29  57   0  17   0   0  |   407   4.0
C          24  17   0  62   0   0  |   312   3.0
D          17   0   0   0  86   0  |   171   1.7

Scoring Round
 The two highest-scoring candidates advance to the next round.
   B             -- 407 -- First place
   A             -- 346 -- Second place
   C             -- 312
   D             -- 171
 B and A advance.

Automatic Runoff Round
 The candidate preferred in the most head-to-head matchups wins.
   B             -- 70 -- First place
   A             -- 33
   Equal Support --  0
 B wins.
   Voters with a preference: 103 of 103 (no Equal Support).
   B 70 (68%) vs A 33 (32%); majority = 52.

Winner — STAR Voting Method (single winner)
 B

RCV-IRV — round by round

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 103 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: A, B, C, D
    33 ×   A > B > C > D      (5, 4, 2, 1)
    29 ×   B > A > C > D      (4, 5, 2, 1)
    24 ×   C > B > A > D      (2, 4, 5, 1)
    17 ×   D > C > B > A      (1, 2, 4, 5)

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
A                 33  Hopeful
B                 29  Hopeful
C                 24  Hopeful
D                 17  Rejected

ROUND 2
Candidate      Votes  Status
-----------  -------  --------
C                 41  Hopeful
A                 33  Hopeful
B                 29  Rejected
D                  0  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
A                 62  Elected
C                 41  Rejected
B                  0  Rejected
D                  0  Rejected


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

--- 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 4): B
   Outside (3):        A, C, D
   One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner A is OUTSIDE the Smith set. ✗
      Every member of the set (B) beats A head-to-head, yet
      RCV-IRV elected A 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 103 ballots (score ballots).

Ballots:
   the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: A, B, C, D
    33 × A > B > C > D      (5, 4, 2, 1)
    29 × B > A > C > D      (4, 5, 2, 1)
    24 × C > B > A > D      (2, 4, 5, 1)
    17 × D > C > B > A      (1, 2, 4, 5)

Round-Robin — every pair, head-to-head (For – Against):
   B  beats A   70 – 33
   A  beats C   62 – 41
   A  beats D   86 – 17
   B  beats C   62 – 41
   B  beats D   86 – 17
   C  beats D   86 – 17

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
      |      A       |     B       |     C       |     D       |
----------------------------------------------------------------
  A > |     ---      |33 -  0 - 70 |62 -  0 - 41 |86 -  0 - 17 |
  B > | 70 -  0 - 33 |    ---      |62 -  0 - 41 |86 -  0 - 17 |
  C > | 41 -  0 - 62 |41 -  0 - 62 |    ---      |86 -  0 - 17 |
  D > | 17 -  0 - 86 |17 -  0 - 86 |17 -  0 - 86 |    ---      |

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  B          3–0–0         3    +127  A, C, D
    2  A          2–1–0         2     +53  C, D
    3  C          1–2–0         1     +27  D
    4  D          0–3–0         0    -207  —

Winner — Ranked Robin (RCV-RR): B
   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 4): B
   Outside (3):        A, C, D
   One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner B 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