Felsenthal Ex.4 full electorate — STAR: elects the Condorcet winner Beth¶

▶ Live on BetterVoting: vote · results ↗ (election dxg8pb · test BV2150) — 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 Beth — and so do Ranked Robin and Condorcet, because Beth is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Carl: Beth collects fewer top (first-choice) votes, so IRV eliminates Beth early, and those ballots transfer to Carl. 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	Beth
RCV-IRV	Carl
Ranked Robin (RCV-RR)	Beth
Approval	Beth
Range / Score	Beth
Condorcet	Beth

Flags: none

Source election: method_comparisons/felsenthal_paradoxes/cases/bv2150_dxg8pb_star.yaml · STAR tabulated mirror: bv2150_dxg8pb_star_tabulated.txt

3 candidates, 11 ballots.

The ballots¶

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

Count	Andy	Beth	Carl
4	5	3	1
3	1	5	3
1	3	1	5
3	1	3	5

STAR result (official)¶

Scoring round (sum of scores): Beth 37, Carl 33, Andy 29

Finalists (top two): Beth and Carl

Automatic runoff: Beth 7 vs Carl 4

STAR winner: Beth

Full LH STAR engine report:

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
               |   * Beth   |  * Carl   |
-----------------------------------------
      * Beth > |    ---     |7 - 0 - 4  |
      * Carl > | 4 - 0 - 7  |   ---     |

[Divergence from STAR]
  STAR                   = Beth
  Choose-One (Plurality) = Andy   (differs from STAR)
  RCV-IRV                = Carl   (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 11 ballots.
Count × Andy,Beth,Carl
    4 ×    5,   3,   1
    3 ×    1,   5,   3
    3 ×    1,   3,   5
    1 ×    3,   1,   5

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Andy       4  0  1  0  6  0  |    29   2.6
Beth       3  0  7  0  1  0  |    37   3.4
Carl       4  0  3  0  4  0  |    33   3.0

Scoring Round
 The two highest-scoring candidates advance to the next round.
   Beth          -- 37 -- First place
   Carl          -- 33 -- Second place
   Andy          -- 29
 Beth and Carl advance.

Automatic Runoff Round
 The candidate preferred in the most head-to-head matchups wins.
   Beth          -- 7 -- First place
   Carl          -- 4
   Equal Support -- 0
 Beth wins.
   Voters with a preference: 11 of 11 (no Equal Support).
   Beth 7 (64%) vs Carl 4 (36%); majority = 6.

Winner — STAR Voting Method (single winner)
 Beth

RCV-IRV — round by round¶

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 11 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: Andy, Beth, Carl
     4 ×   Andy > Beth > Carl      (5, 3, 1)
     3 ×   Beth > Carl > Andy      (1, 5, 3)
     1 ×   Carl > Andy > Beth      (3, 1, 5)
     3 ×   Carl > Beth > Andy      (1, 3, 5)

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Carl               4  Hopeful
Andy               4  Hopeful
Beth               3  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Carl               7  Elected
Andy               4  Rejected
Beth               0  Rejected


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

--- 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): Beth
   Outside (2):        Andy, Carl
   One member ⇒ Beth is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Carl is OUTSIDE the Smith set. ✗
      Every member of the set (Beth) beats Carl head-to-head, yet
      RCV-IRV elected Carl 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 11 ballots (score ballots).

Ballots:
   the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Andy, Beth, Carl
     4 × Andy > Beth > Carl      (5, 3, 1)
     3 × Beth > Carl > Andy      (1, 5, 3)
     1 × Carl > Andy > Beth      (3, 1, 5)
     3 × Carl > Beth > Andy      (1, 3, 5)

Round-Robin — every pair, head-to-head (For – Against):
   Beth  beats Andy   6 – 5
   Carl  beats Andy   7 – 4
   Beth  beats Carl   7 – 4

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |   Andy    |  Beth    |  Carl    |
--------------------------------------------
  Andy > |    ---    |5 - 0 - 6 |4 - 0 - 7 |
  Beth > | 6 - 0 - 5 |   ---    |7 - 0 - 4 |
  Carl > | 7 - 0 - 4 |4 - 0 - 7 |   ---    |

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  Beth       2–0–0         2      +4  Carl, Andy
    2  Carl       1–1–0         1      +0  Andy
    3  Andy       0–2–0         0      -4  —

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