STAR à la Approval — 0/1 & marker ballots are legal on a STAR ballot

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 A rather than STAR's D, but this is an artifact of score→rank conversion, not a robust method difference: 4 of 8 ballots have tied non-zero scores, so their ranks are set by an arbitrary candidate-priority order; the RCV-IRV winner flips when that priority order is reversed. Ranked Robin and the Condorcet (pairwise) winner both agree with STAR (D). 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	D
RCV-IRV	A
Ranked Robin (RCV-RR)	D
Approval	A
Range / Score	D
Condorcet	D

Flags: 4 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie); RR conversion-sensitive (weak=D, strict=A)

Source election: 01_STAR/02_Examples/cases/star_ala_approval.yaml · STAR tabulated mirror: star_ala_approval_tabulated.txt

4 candidates, 8 ballots.

The ballots

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

Count	A	B	C	D
1	0	0	1	1
4	0	0	0	0
1	1	0	0	1
1	1	1	0	1
1	5	5	5	5

STAR result (official)

Scoring round (sum of scores): D 8, A 7, B 6, C 6

Finalists (top two): D and A

Automatic runoff: D 1 vs A 0 (7 equal/no-preference)

STAR winner: D

Full LH STAR engine report:

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
               |    * A     |   * D     |
-----------------------------------------
         * A > |    ---     |0 - 7 - 1  |
         * D > | 1 - 7 - 0  |   ---     |

[Divergence from STAR]
  STAR                   = D
  Choose-One (Plurality) = A   (differs from STAR)
  RCV-IRV                = A   (differs from STAR)
  Approval               = A   (differs from STAR)
  Note: 4 of 8 ballots (50%) 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.

--- STAR Voting Method (single winner) ---
 Tabulating 8 ballots. Note: 2 of 8 ballots are marked as abstentions.
A,B,C,D
-,-,1,1
-,-,0,0
1,0,0,1
1,1,0,1
~,~,~,~
0,0,0,0
5,5,5,5
-,-,-,-
  ('-' = 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
A          1  0  0  0  2  1    4  |     7      0.9        1.8
B          1  0  0  0  1  2    4  |     6      0.8        1.5
C          1  0  0  0  1  4    2  |     6      0.8        1.0
D          1  0  0  0  3  2    2  |     8      1.0        1.3
  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.
   D             -- 8 -- First place
   A             -- 7 -- Second place
   B             -- 6
   C             -- 6
 D and A advance.

Automatic Runoff Round
 The candidate preferred in the most head-to-head matchups wins.
   D             -- 1 -- First place
   A             -- 0
   Equal Support -- 7
 D wins.
   Voters with a preference: 1 of 8 (7 Equal Support).
   D 1 (100%) vs A 0 (0%); majority = 1.

Winner — STAR Voting Method (single winner)
 D

RCV-IRV — round by round

⚠️ This election has a fragile IRV tie (equal scores force an arbitrary tie-break). The round table below is only one realization; a different tie-break can change the winner. See the flag above.

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 8 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
     1 ×   C > D      (0, 0, 1, 1)
     4 ×   (all unranked)      (0, 0, 0, 0)
     1 ×   A > D      (1, 0, 0, 1)
     1 ×   A > B > D      (1, 1, 0, 1)
     1 ×   A > B > C > D      (5, 5, 5, 5)

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
A                  3  Elected
C                  1  Rejected
D                  0  Rejected
B                  0  Rejected
Blank Votes        4  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): D
   Outside (3):        A, B, C
   One member ⇒ D is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner A is OUTSIDE the Smith set. ✗
      Every member of the set (D) 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 8 ballots (score ballots).

Ballots:
   the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: A, B, C, D
     1 × C=D > A=B      (0, 0, 1, 1)
     4 × A=B=C=D      (0, 0, 0, 0)
     1 × A=D > B=C      (1, 0, 0, 1)
     1 × A=B=D > C      (1, 1, 0, 1)
     1 × A=B=C=D      (5, 5, 5, 5)

Round-Robin — every pair, head-to-head (For – Against):
   A  beats B   1 – 0
   A  beats C   2 – 1
   D  beats A   1 – 0
   B  ties  C   1 – 1
   D  beats B   2 – 0
   D  beats C   2 – 0

--- 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 > |    ---    |1 - 7 - 0 |2 - 5 - 1 |0 - 7 - 1 |
  B > | 0 - 7 - 1 |   ---    |1 - 6 - 1 |0 - 6 - 2 |
  C > | 1 - 5 - 2 |1 - 6 - 1 |   ---    |0 - 6 - 2 |
  D > | 1 - 7 - 0 |2 - 6 - 0 |2 - 6 - 0 |   ---    |

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  D          3–0–0         3      +5  A, B, C
    2  A          2–1–0         2      +1  B, C
    3  B          0–2–1       0.5      -3  —
    4  C          0–2–1       0.5      -3  —

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