The Post-it switch, made real — STAR: Blue, now also the score co-leader¶

▶ Live on BetterVoting: vote · results ↗ (election 8kg698 · test BV2178) — 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 Blue. Only Approval differs, electing Pink: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Pink's breadth of acceptability over Blue's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.

Winners by method¶

Method	Winner
STAR	Blue
RCV-IRV	Blue
Ranked Robin (RCV-RR)	Blue
Approval	Pink
Range / Score	Purple
Condorcet	Blue

Flags: none

Source election: method_comparisons/postit_rcv_example/cases/bv2178_8kg698_star.yaml · STAR tabulated mirror: bv2178_8kg698_star_tabulated.txt

4 candidates, 20 ballots.

The ballots¶

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

Count	Purple	Green	Blue	Pink
7	5	0	0	0
4	0	5	4	3
3	0	4	5	3
2	0	0	5	4
1	4	0	5	0
1	3	4	0	5
1	4	0	0	5
1	0	0	0	5

STAR result (official)¶

Scoring round (sum of scores): Purple 46, Blue 46, Pink 44, Green 36

Finalists (top two): Purple and Blue

Automatic runoff: Purple 9 vs Blue 10 (1 equal/no-preference)

STAR winner: Blue

Full LH STAR engine report:

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
                 |   * Purple   |   * Blue    |
-----------------------------------------------
      * Purple > |     ---      | 9 -  1 - 10 |
        * Blue > | 10 -  1 -  9 |    ---      |

[Divergence from STAR]
  STAR                   = Blue
  Choose-One (Plurality) = Purple   (differs from STAR)
  Approval               = Pink   (differs from STAR)

--- STAR Voting Method (single winner) ---
 Tabulating 20 ballots.
Count × Purple,Green,Blue,Pink
    7 ×      5,    0,   0,   0
    4 ×      0,    5,   4,   3
    3 ×      0,    4,   5,   3
    2 ×      0,    0,   5,   4
    1 ×      4,    0,   5,   0
    1 ×      3,    4,   0,   5
    1 ×      4,    0,   0,   5
    1 ×      0,    0,   0,   5

[Score Distribution] (how many ballots gave each star rating)
                   Score
Candidate   5   4   3   2   1   0  | Total   Avg
Purple      7   2   1   0   0  10  |    46   2.3
Green       4   4   0   0   0  12  |    36   1.8
Blue        6   4   0   0   0  10  |    46   2.3
Pink        3   2   7   0   0   8  |    44   2.2

Scoring Round
 The two highest-scoring candidates advance to the next round.
   Blue          -- 46 -- First place
   Purple        -- 46 -- Second place
   Pink          -- 44
   Green         -- 36
 Blue and Purple advance.

Automatic Runoff Round
 The candidate preferred in the most head-to-head matchups wins.
   Blue          -- 10 -- First place
   Purple        --  9
   Equal Support --  1
 Blue wins.
   Voters with a preference: 19 of 20 (1 Equal Support).
   Blue 10 (53%) vs Purple 9 (47%); majority = 10.

Winner — STAR Voting Method (single winner)
 Blue

RCV-IRV — round by round¶

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 20 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: Purple, Green, Blue, Pink
     7 ×   Purple      (5, 0, 0, 0)
     4 ×   Green > Blue > Pink      (0, 5, 4, 3)
     3 ×   Blue > Green > Pink      (0, 4, 5, 3)
     2 ×   Blue > Pink      (0, 0, 5, 4)
     1 ×   Blue > Purple      (4, 0, 5, 0)
     1 ×   Pink > Green > Purple      (3, 4, 0, 5)
     1 ×   Pink > Purple      (4, 0, 0, 5)
     1 ×   Pink      (0, 0, 0, 5)

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Purple             7  Hopeful
Blue               6  Hopeful
Green              4  Hopeful
Pink               3  Rejected

ROUND 2
Candidate      Votes  Status
-----------  -------  --------
Purple             8  Hopeful
Blue               6  Hopeful
Green              5  Rejected
Pink               0  Rejected
Blank Votes        1  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Blue              10  Elected
Purple             9  Rejected
Green              0  Rejected
Pink               0  Rejected
Blank Votes        1  Rejected


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

--- 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): Blue
   Outside (3):        Purple, Green, Pink
   One member ⇒ Blue is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Blue 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 20 ballots (score ballots).

Ballots:
   the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Purple, Green, Blue, Pink
     7 × Purple > Green=Blue=Pink      (5, 0, 0, 0)
     4 × Green > Blue > Pink > Purple      (0, 5, 4, 3)
     3 × Blue > Green > Pink > Purple      (0, 4, 5, 3)
     2 × Blue > Pink > Purple=Green      (0, 0, 5, 4)
     1 × Blue > Purple > Green=Pink      (4, 0, 5, 0)
     1 × Pink > Green > Purple > Blue      (3, 4, 0, 5)
     1 × Pink > Purple > Green=Blue      (4, 0, 0, 5)
     1 × Pink > Purple=Green=Blue      (0, 0, 0, 5)

Round-Robin — every pair, head-to-head (For – Against):
   Purple  beats Green     9 –  8
   Blue    beats Purple   10 –  9
   Pink    beats Purple   12 –  8
   Blue    beats Green     6 –  5
   Green   beats Pink      7 –  5
   Blue    beats Pink     10 –  3

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
           |    Purple    |   Green     |    Blue     |    Pink     |
---------------------------------------------------------------------
  Purple > |     ---      | 9 -  3 -  8 | 9 -  1 - 10 | 8 -  0 - 12 |
   Green > |  8 -  3 -  9 |    ---      | 5 -  9 -  6 | 7 -  8 -  5 |
    Blue > | 10 -  1 -  9 | 6 -  9 -  5 |    ---      |10 -  7 -  3 |
    Pink > | 12 -  0 -  8 | 5 -  8 -  7 | 3 -  7 - 10 |    ---      |

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  Blue       3–0–0         3      +9  Green, Purple, Pink
    2  Green      1–2–0         1      +0  Pink
    3  Purple     1–2–0         1      -4  Green
    4  Pink       1–2–0         1      -5  Purple

Winner — Ranked Robin (RCV-RR): Blue
   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): Blue
   Outside (3):        Purple, Green, Pink
   One member ⇒ Blue is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Blue 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