Noise Soup — weak factions, cross-winds, flat-liners and static¶

▶ Live on BetterVoting: vote · results ↗ (election 74pbyg · test BV2237) — an independent tabulator to check the winners below against.

Bucket — CYCLE_OR_THREE_WAY: Cycle / three-way split

Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.

What happens¶

There is no Condorcet winner — the head-to-head results form a cycle (X beats Y beats Z beats X). With no pairwise anchor the methods split: STAR=Caleb, RCV-IRV=Beth, Ranked Robin=Beth (RR breaks the cycle by total margin). No rule is clearly 'right'; a genuinely hard election, not an indictment of any one method.

Winners by method¶

Method	Winner
STAR	Caleb
RCV-IRV	Beth
Ranked Robin (RCV-RR)	Beth
Approval	Beth
Range / Score	Beth
Condorcet	none (cycle)

Flags: 13 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie)

Source election: 06_Other/ballot_style_lab/cases/04_c4_b47_noise-soup.yaml · STAR tabulated mirror: 04_c4_b47_noise-soup_tabulated.txt

4 candidates, 47 ballots.

The ballots¶

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

Count	Aaron	Beth	Caleb	Dana
1	5	5	5	5
1	3	3	3	3
2	5	5	0	5
1	0	4	4	3
2	2	5	3	4
1	5	0	3	1
2	5	0	0	0
1	4	5	2	3
2	0	0	1	5
2	0	2	5	2
2	4	5	0	0
1	4	0	0	5
2	1	5	0	2
2	0	0	5	0
3	0	0	0	0
1	5	3	4	2
1	2	4	5	3
1	1	0	0	5
1	3	4	5	2
1	0	5	0	5
1	5	4	2	3
1	3	0	5	4
1	5	2	2	0
1	2	5	0	0
1	0	5	5	5
1	0	0	5	3
1	5	4	2	0
1	5	3	5	0
1	0	3	4	5
1	5	0	5	0
1	5	3	2	4
1	4	2	3	5
1	0	0	4	5
1	0	5	4	0
1	0	0	1	0
1	4	5	3	2
1	0	2	2	3

STAR result (official)¶

Scoring round (sum of scores): Beth 120, Caleb 113, Dana 112, Aaron 109

Finalists (top two): Beth and Caleb

Automatic runoff: Beth 16 vs Caleb 18 (13 equal/no-preference)

STAR winner: Caleb

Full LH STAR engine report:

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
                 |    * Beth    |  * Caleb    |
-----------------------------------------------
        * Beth > |     ---      |16 - 13 - 18 |
       * Caleb > | 18 - 13 - 16 |    ---      |

[Divergence from STAR]
  STAR                   = Caleb
  Choose-One (Plurality) = Aaron   (differs from STAR)
  RCV-IRV                = Beth   (differs from STAR)
  Approval               = Beth   (differs from STAR)
  RCV-RR                 = Beth   (differs from STAR)
  Note: 13 of 47 ballots (28%) 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) sides with RCV-IRV, so STAR is the outlier
        here — STAR need not elect the Condorcet candidate.

[Runoff Reversal]
 - Score Round Winner(s) = (Beth)
 - Runoff Round Winner   = (Caleb)
  Candidate Beth earned the highest total score, but
  Candidate Caleb won the automatic runoff — not a malfunction,
  STAR working as designed: the runoff elects the finalist preferred
  by the majority (of voters with a preference).


--- STAR Voting Method (single winner) ---
 Tabulating 47 ballots. Note: 2 of 47 ballots are marked as abstentions.
Count × Aaron,Beth,Caleb,Dana
    2 ×     5,   5,    0,   5
    2 ×     2,   5,    3,   4
    2 ×     5,   0,    0,   0
    2 ×     0,   2,    5,   2
    2 ×     1,   5,    0,   2
    2 ×     0,   0,    5,   0
    1 ×     5,   5,    5,   5
    1 ×     3,   3,    3,   3
    1 ×     0,   4,    4,   3
    1 ×     5,   0,    3,   1
    1 ×     4,   5,    2,   3
    1 ×     0,   0,    1,   5
    1 ×     4,   5,    -,   -
    1 ×     4,   0,    0,   5
    1 ×     ?,   ?,    ?,   ?
    1 ×     5,   3,    4,   2
    1 ×     2,   4,    5,   3
    1 ×     ~,   ~,    ~,   ~
    1 ×     0,   0,    0,   0
    1 ×     1,   -,    -,   5
    1 ×     3,   4,    5,   2
    1 ×     0,   5,    0,   5
    1 ×     5,   4,    2,   3
    1 ×     3,   0,    5,   4
    1 ×     -,   -,    1,   5
    1 ×     5,   2,    2,   0
    1 ×     2,   5,    0,   0
    1 ×     -,   5,    5,   5
    1 ×     0,   0,    5,   3
    1 ×     4,   5,    0,   0
    1 ×     5,   4,    2,   0
    1 ×     5,   3,    5,   0
    1 ×     0,   3,    4,   5
    1 ×     5,   0,    5,   0
    1 ×     5,   3,    2,   4
    1 ×     4,   2,    3,   5
    1 ×     0,   0,    4,   5
    1 ×     -,   5,    4,   -
    1 ×     0,   0,    1,   0
    1 ×     4,   5,    3,   2
    1 ×     0,   2,    2,   3
  ('-' = 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
Aaron      13   6   3   4   3  13    5  |   109      2.3        2.6
Beth       15   5   5   5   0  13    4  |   120      2.6        2.8
Caleb      12   5   6   6   3  11    4  |   113      2.4        2.6
Dana       12   4   7   7   1  12    4  |   112      2.4        2.6
  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.
   Beth          -- 120 -- First place
   Caleb         -- 113 -- Second place
   Dana          -- 112
   Aaron         -- 109
 Beth and Caleb advance.

Automatic Runoff Round
 The candidate preferred in the most head-to-head matchups wins.
   Caleb         -- 18 -- First place
   Beth          -- 16
   Equal Support -- 13
 Caleb wins.
   Voters with a preference: 34 of 47 (13 Equal Support).
   Caleb 18 (53%) vs Beth 16 (47%); majority = 18.

Winner — STAR Voting Method (single winner)
 Caleb

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 47 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: Aaron, Beth, Caleb, Dana
     1 ×   Aaron > Beth > Caleb > Dana      (5, 5, 5, 5)
     1 ×   Aaron > Beth > Caleb > Dana      (3, 3, 3, 3)
     2 ×   Aaron > Beth > Dana      (5, 5, 0, 5)
     1 ×   Beth > Caleb > Dana      (0, 4, 4, 3)
     2 ×   Beth > Dana > Caleb > Aaron      (2, 5, 3, 4)
     1 ×   Aaron > Caleb > Dana      (5, 0, 3, 1)
     2 ×   Aaron      (5, 0, 0, 0)
     1 ×   Beth > Aaron > Dana > Caleb      (4, 5, 2, 3)
     2 ×   Dana > Caleb      (0, 0, 1, 5)
     2 ×   Caleb > Beth > Dana      (0, 2, 5, 2)
     2 ×   Beth > Aaron      (4, 5, 0, 0)
     1 ×   Dana > Aaron      (4, 0, 0, 5)
     2 ×   Beth > Dana > Aaron      (1, 5, 0, 2)
     2 ×   Caleb      (0, 0, 5, 0)
     3 ×   (all unranked)      (0, 0, 0, 0)
     1 ×   Aaron > Caleb > Beth > Dana      (5, 3, 4, 2)
     1 ×   Caleb > Beth > Dana > Aaron      (2, 4, 5, 3)
     1 ×   Dana > Aaron      (1, 0, 0, 5)
     1 ×   Caleb > Beth > Aaron > Dana      (3, 4, 5, 2)
     1 ×   Beth > Dana      (0, 5, 0, 5)
     1 ×   Aaron > Beth > Dana > Caleb      (5, 4, 2, 3)
     1 ×   Caleb > Dana > Aaron      (3, 0, 5, 4)
     1 ×   Aaron > Beth > Caleb      (5, 2, 2, 0)
     1 ×   Beth > Aaron      (2, 5, 0, 0)
     1 ×   Beth > Caleb > Dana      (0, 5, 5, 5)
     1 ×   Caleb > Dana      (0, 0, 5, 3)
     1 ×   Aaron > Beth > Caleb      (5, 4, 2, 0)
     1 ×   Aaron > Caleb > Beth      (5, 3, 5, 0)
     1 ×   Dana > Caleb > Beth      (0, 3, 4, 5)
     1 ×   Aaron > Caleb      (5, 0, 5, 0)
     1 ×   Aaron > Dana > Beth > Caleb      (5, 3, 2, 4)
     1 ×   Dana > Aaron > Caleb > Beth      (4, 2, 3, 5)
     1 ×   Dana > Caleb      (0, 0, 4, 5)
     1 ×   Beth > Caleb      (0, 5, 4, 0)
     1 ×   Caleb      (0, 0, 1, 0)
     1 ×   Beth > Aaron > Caleb > Dana      (4, 5, 3, 2)
     1 ×   Dana > Beth > Caleb      (0, 2, 2, 3)

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Aaron             14  Hopeful
Beth              13  Hopeful
Caleb              9  Hopeful
Dana               8  Rejected
Blank Votes        3  Rejected

ROUND 2
Candidate      Votes  Status
-----------  -------  --------
Aaron             17  Hopeful
Beth              14  Hopeful
Caleb             13  Rejected
Dana               0  Rejected
Blank Votes        3  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Beth              19  Elected
Aaron             18  Rejected
Caleb              0  Rejected
Dana               0  Rejected
Blank Votes       10  Rejected


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

--- 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 (4 of 4): Beth, Caleb, Dana, Aaron
   Outside (0):        —
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   cycle, so the strongest "candidate" is a set, not a person. Which member of
   the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
   about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
   Note: the Copeland leaders (Beth) are only part of the set — the
   win–loss table's top block understates how wide the contention is.
   RCV-IRV winner Beth is INSIDE the Smith set. ✓
      Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
   Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
   candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
   may be smaller 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 47 ballots (score ballots).

Ballots:
   the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Aaron, Beth, Caleb, Dana
     1 × Aaron=Beth=Caleb=Dana      (5, 5, 5, 5)
     1 × Aaron=Beth=Caleb=Dana      (3, 3, 3, 3)
     2 × Aaron=Beth=Dana > Caleb      (5, 5, 0, 5)
     1 × Beth=Caleb > Dana > Aaron      (0, 4, 4, 3)
     2 × Beth > Dana > Caleb > Aaron      (2, 5, 3, 4)
     1 × Aaron > Caleb > Dana > Beth      (5, 0, 3, 1)
     2 × Aaron > Beth=Caleb=Dana      (5, 0, 0, 0)
     1 × Beth > Aaron > Dana > Caleb      (4, 5, 2, 3)
     2 × Dana > Caleb > Aaron=Beth      (0, 0, 1, 5)
     2 × Caleb > Beth=Dana > Aaron      (0, 2, 5, 2)
     2 × Beth > Aaron > Caleb=Dana      (4, 5, 0, 0)
     1 × Dana > Aaron > Beth=Caleb      (4, 0, 0, 5)
     2 × Beth > Dana > Aaron > Caleb      (1, 5, 0, 2)
     2 × Caleb > Aaron=Beth=Dana      (0, 0, 5, 0)
     3 × Aaron=Beth=Caleb=Dana      (0, 0, 0, 0)
     1 × Aaron > Caleb > Beth > Dana      (5, 3, 4, 2)
     1 × Caleb > Beth > Dana > Aaron      (2, 4, 5, 3)
     1 × Dana > Aaron > Beth=Caleb      (1, 0, 0, 5)
     1 × Caleb > Beth > Aaron > Dana      (3, 4, 5, 2)
     1 × Beth=Dana > Aaron=Caleb      (0, 5, 0, 5)
     1 × Aaron > Beth > Dana > Caleb      (5, 4, 2, 3)
     1 × Caleb > Dana > Aaron > Beth      (3, 0, 5, 4)
     1 × Aaron > Beth=Caleb > Dana      (5, 2, 2, 0)
     1 × Beth > Aaron > Caleb=Dana      (2, 5, 0, 0)
     1 × Beth=Caleb=Dana > Aaron      (0, 5, 5, 5)
     1 × Caleb > Dana > Aaron=Beth      (0, 0, 5, 3)
     1 × Aaron > Beth > Caleb > Dana      (5, 4, 2, 0)
     1 × Aaron=Caleb > Beth > Dana      (5, 3, 5, 0)
     1 × Dana > Caleb > Beth > Aaron      (0, 3, 4, 5)
     1 × Aaron=Caleb > Beth=Dana      (5, 0, 5, 0)
     1 × Aaron > Dana > Beth > Caleb      (5, 3, 2, 4)
     1 × Dana > Aaron > Caleb > Beth      (4, 2, 3, 5)
     1 × Dana > Caleb > Aaron=Beth      (0, 0, 4, 5)
     1 × Beth > Caleb > Aaron=Dana      (0, 5, 4, 0)
     1 × Caleb > Aaron=Beth=Dana      (0, 0, 1, 0)
     1 × Beth > Aaron > Caleb > Dana      (4, 5, 3, 2)
     1 × Dana > Beth=Caleb > Aaron      (0, 2, 2, 3)

Round-Robin — every pair, head-to-head (For – Against):
   Beth   beats Aaron   19 – 14
   Aaron  beats Caleb   20 – 19
   Dana   beats Aaron   20 – 16
   Caleb  beats Beth    18 – 16
   Beth   beats Dana    18 – 12
   Caleb  ties  Dana    18 – 18

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
          |    Aaron     |    Beth     |   Caleb     |    Dana     |
--------------------------------------------------------------------
  Aaron > |     ---      |14 - 14 - 19 |20 -  8 - 19 |16 - 11 - 20 |
   Beth > | 19 - 14 - 14 |    ---      |16 - 13 - 18 |18 - 17 - 12 |
  Caleb > | 19 -  8 - 20 |18 - 13 - 16 |    ---      |18 - 11 - 18 |
   Dana > | 20 - 11 - 16 |12 - 17 - 18 |18 - 11 - 18 |    ---      |

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       2–1–0         2      +9  Dana, Aaron
    2  Caleb      1–1–1       1.5      +1  Beth
    3  Dana       1–1–1       1.5      -2  Aaron
    4  Aaron      1–2–0         1      -8  Caleb

Winner — Ranked Robin (RCV-RR): Beth
   the most head-to-head wins (2).

--- 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 (4 of 4): Beth, Caleb, Dana, Aaron
   Outside (0):        —
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   cycle, so the strongest "candidate" is a set, not a person. Which member of
   the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
   about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
   Note: the Copeland leaders (Beth) are only part of the set — the
   win–loss table's top block understates how wide the contention is.
   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.
   Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
   candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
   may be smaller here.
   More: 07_Concepts/topics/smith_set.md

Count	Aaron	Beth	Caleb	Dana
1	5	5	5	5
1	3	3	3	3
2	5	5	0	5
1	0	4	4	3
2	2	5	3	4
1	5	0	3	1
2	5	0	0	0
1	4	5	2	3
2	0	0	1	5
2	0	2	5	2
2	4	5	0	0
1	4	0	0	5
2	1	5	0	2
2	0	0	5	0
3	0	0	0	0
1	5	3	4	2
1	2	4	5	3
1	1	0	0	5
1	3	4	5	2
1	0	5	0	5
1	5	4	2	3
1	3	0	5	4
1	5	2	2	0
1	2	5	0	0
1	0	5	5	5
1	0	0	5	3
1	5	4	2	0
1	5	3	5	0
1	0	3	4	5
1	5	0	5	0
1	5	3	2	4
1	4	2	3	5
1	0	0	4	5
1	0	5	4	0
1	0	0	1	0
1	4	5	3	2
1	0	2	2	3

Count	Aaron	Beth	Caleb	Dana
1	5	5	5	5
1	3	3	3	3
2	5	5	0	5
1	0	4	4	3
2	2	5	3	4
1	5	0	3	1
2	5	0	0	0
1	4	5	2	3
2	0	0	1	5
2	0	2	5	2
2	4	5	0	0
1	4	0	0	5
2	1	5	0	2
2	0	0	5	0
3	0	0	0	0
1	5	3	4	2
1	2	4	5	3
1	1	0	0	5
1	3	4	5	2
1	0	5	0	5
1	5	4	2	3
1	3	0	5	4
1	5	2	2	0
1	2	5	0	0
1	0	5	5	5
1	0	0	5	3
1	5	4	2	0
1	5	3	5	0
1	0	3	4	5
1	5	0	5	0
1	5	3	2	4
1	4	2	3	5
1	0	0	4	5
1	0	5	4	0
1	0	0	1	0
1	4	5	3	2
1	0	2	2	3

Count	Aaron	Beth	Caleb	Dana
1	5	5	5	5
1	3	3	3	3
2	5	5	0	5
1	0	4	4	3
2	2	5	3	4
1	5	0	3	1
2	5	0	0	0
1	4	5	2	3
2	0	0	1	5
2	0	2	5	2
2	4	5	0	0
1	4	0	0	5
2	1	5	0	2
2	0	0	5	0
3	0	0	0	0
1	5	3	4	2
1	2	4	5	3
1	1	0	0	5
1	3	4	5	2
1	0	5	0	5
1	5	4	2	3
1	3	0	5	4
1	5	2	2	0
1	2	5	0	0
1	0	5	5	5
1	0	0	5	3
1	5	4	2	0
1	5	3	5	0
1	0	3	4	5
1	5	0	5	0
1	5	3	2	4
1	4	2	3	5
1	0	0	4	5
1	0	5	4	0
1	0	0	1	0
1	4	5	3	2
1	0	2	2	3