Felsenthal Ex.3 District II — STAR: also Bruno¶

▶ Live on BetterVoting: vote · results ↗ (election h87k6v · test BV2148) — an independent tabulator to check the winners below against.

Bucket — APPROVAL_OR_MINOR: Only Approval differs

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, RCV-IRV and Ranked Robin all agree on Bruno. Only Approval differs, electing Cora: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Cora's breadth of acceptability over Bruno's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.

Winners by method¶

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

Flags: none

Source election: method_comparisons/felsenthal_paradoxes/cases/bv2148_h87k6v_star.yaml · STAR tabulated mirror: bv2148_h87k6v_star_tabulated.txt

3 candidates, 15 ballots.

The ballots¶

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

Count	Alma	Bruno	Cora
6	5	1	3
8	1	5	3
1	3	1	5

STAR result (official)¶

Scoring round (sum of scores): Bruno 47, Cora 47, Alma 41

Finalists (top two): Bruno and Cora

Automatic runoff: Bruno 8 vs Cora 7

STAR winner: Bruno

Full LH STAR engine report:

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
               |  * Bruno   |  * Cora   |
-----------------------------------------
     * Bruno > |    ---     |8 - 0 - 7  |
      * Cora > | 7 - 0 - 8  |   ---     |

[Divergence from STAR]
  STAR     = Bruno
  Approval = Cora   (differs from STAR)

--- STAR Voting Method (single winner) ---
 Tabulating 15 ballots.
Count × Alma,Bruno,Cora
    8 ×    1,    5,   3
    6 ×    5,    1,   3
    1 ×    3,    1,   5

[Score Distribution] (how many ballots gave each star rating)
                   Score
Candidate   5   4   3   2   1   0  | Total   Avg
Alma        6   0   1   0   8   0  |    41   2.7
Bruno       8   0   0   0   7   0  |    47   3.1
Cora        1   0  14   0   0   0  |    47   3.1

Scoring Round
 The two highest-scoring candidates advance to the next round.
   Bruno         -- 47 -- First place
   Cora          -- 47 -- Second place
   Alma          -- 41
 Bruno and Cora advance.

Automatic Runoff Round
 The candidate preferred in the most head-to-head matchups wins.
   Bruno         -- 8 -- First place
   Cora          -- 7
   Equal Support -- 0
 Bruno wins.
   Voters with a preference: 15 of 15 (no Equal Support).
   Bruno 8 (53%) vs Cora 7 (47%); majority = 8.

Winner — STAR Voting Method (single winner)
 Bruno

RCV-IRV — round by round¶

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 15 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: Alma, Bruno, Cora
     6 ×   Alma > Cora > Bruno      (5, 1, 3)
     8 ×   Bruno > Cora > Alma      (1, 5, 3)
     1 ×   Cora > Alma > Bruno      (3, 1, 5)

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Bruno              8  Elected
Alma               6  Rejected
Cora               1  Rejected


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

--- 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): Bruno
   Outside (2):        Alma, Cora
   One member ⇒ Bruno is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Bruno is INSIDE the Smith set. ✓
      Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
   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 15 ballots (score ballots).

Ballots:
   the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Alma, Bruno, Cora
     6 × Alma > Cora > Bruno      (5, 1, 3)
     8 × Bruno > Cora > Alma      (1, 5, 3)
     1 × Cora > Alma > Bruno      (3, 1, 5)

Round-Robin — every pair, head-to-head (For – Against):
   Bruno  beats Alma    8 – 7
   Cora   beats Alma    9 – 6
   Bruno  beats Cora    8 – 7

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
          |   Alma    |  Bruno   |  Cora    |
---------------------------------------------
   Alma > |    ---    |7 - 0 - 8 |6 - 0 - 9 |
  Bruno > | 8 - 0 - 7 |   ---    |8 - 0 - 7 |
   Cora > | 9 - 0 - 6 |7 - 0 - 8 |   ---    |

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  Bruno      2–0–0         2      +2  Cora, Alma
    2  Cora       1–1–0         1      +2  Alma
    3  Alma       0–2–0         0      -4  —

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