Cliff City food trucks — everyone scores 0 or 3-5, nothing between¶

▶ Live on BetterVoting: vote · results ↗ (election fm8cbv · test BV2235) — an independent tabulator to check the winners below against.

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 Bao rather than STAR's Churro, but this is an artifact of score→rank conversion, not a robust method difference: 10 of 40 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 (Churro). 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	Churro
RCV-IRV	Bao
Ranked Robin (RCV-RR)	Churro
Approval	Churro
Range / Score	Bao
Condorcet	Churro

Flags: 10 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie); RR conversion-sensitive (weak=Churro, strict=Bao)

Source election: 06_Other/ballot_style_lab/cases/02_c4_b40_cliff-city.yaml · STAR tabulated mirror: 02_c4_b40_cliff-city_tabulated.txt

4 candidates, 40 ballots.

The ballots¶

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

Count	Arepa	Bao	Churro	Dumpling
3	0	5	4	0
7	0	5	0	0
4	5	0	0	0
1	5	0	5	5
1	4	0	0	4
1	0	3	4	0
4	0	0	5	0
1	1	3	4	0
3	0	5	0	4
2	0	4	4	0
1	0	0	0	4
1	0	0	4	0
2	5	0	4	0
1	0	5	5	0
1	0	0	5	5
1	3	3	3	3
1	0	0	3	5
1	0	4	0	0
1	4	0	4	0
1	5	4	5	0
1	0	5	5	5
1	0	0	4	3

STAR result (official)¶

Scoring round (sum of scores): Bao 100, Churro 99, Arepa 52, Dumpling 46

Finalists (top two): Bao and Churro

Automatic runoff: Bao 14 vs Churro 15 (11 equal/no-preference)

STAR winner: Churro

Full LH STAR engine report:

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
                 |    * Bao     |  * Churro   |
-----------------------------------------------
         * Bao > |     ---      |14 - 11 - 15 |
      * Churro > | 15 - 11 - 14 |    ---      |

[Divergence from STAR]
  STAR                   = Churro
  Choose-One (Plurality) = Bao   (differs from STAR)
  RCV-IRV                = Bao   (differs from STAR)
  Note: 10 of 40 ballots (25%) 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.

[Runoff Reversal]
 - Score Round Winner(s) = (Bao)
 - Runoff Round Winner   = (Churro)
  Candidate Bao earned the highest total score, but
  Candidate Churro 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 40 ballots.
Count × Arepa,Bao,Churro,Dumpling
    6 ×     0,  5,     0,       0
    4 ×     0,  0,     5,       0
    3 ×     0,  5,     4,       0
    3 ×     5,  0,     0,       0
    3 ×     0,  5,     0,       4
    2 ×     0,  4,     4,       0
    2 ×     5,  0,     4,       0
    1 ×     5,  -,     -,       -
    1 ×     5,  0,     5,       5
    1 ×     4,  0,     0,       4
    1 ×     0,  3,     4,       0
    1 ×     1,  3,     4,       0
    1 ×     0,  0,     0,       4
    1 ×     0,  0,     4,       0
    1 ×     -,  5,     -,       -
    1 ×     0,  5,     5,       0
    1 ×     0,  0,     5,       5
    1 ×     3,  3,     3,       3
    1 ×     0,  0,     3,       5
    1 ×     0,  4,     0,       0
    1 ×     4,  0,     4,       0
    1 ×     5,  4,     5,       0
    1 ×     -,  5,     5,       5
    1 ×     0,  0,     4,       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
Arepa       8   2   1   0   1  26    2  |    52      1.3        1.4
Bao        15   4   3   0   0  17    1  |   100      2.5        2.6
Churro      9  12   2   0   0  15    2  |    99      2.5        2.6
Dumpling    4   5   2   0   0  27    2  |    46      1.2        1.2
  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.
   Bao           -- 100 -- First place
   Churro        --  99 -- Second place
   Arepa         --  52
   Dumpling      --  46
 Bao and Churro advance.

Automatic Runoff Round
 The candidate preferred in the most head-to-head matchups wins.
   Churro        -- 15 -- First place
   Bao           -- 14
   Equal Support -- 11
 Churro wins.
   Voters with a preference: 29 of 40 (11 Equal Support).
   Churro 15 (52%) vs Bao 14 (48%); majority = 15.

Winner — STAR Voting Method (single winner)
 Churro

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 40 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: Arepa, Bao, Churro, Dumpling
     3 ×   Bao > Churro      (0, 5, 4, 0)
     7 ×   Bao      (0, 5, 0, 0)
     4 ×   Arepa      (5, 0, 0, 0)
     1 ×   Arepa > Churro > Dumpling      (5, 0, 5, 5)
     1 ×   Arepa > Dumpling      (4, 0, 0, 4)
     1 ×   Churro > Bao      (0, 3, 4, 0)
     4 ×   Churro      (0, 0, 5, 0)
     1 ×   Churro > Bao > Arepa      (1, 3, 4, 0)
     3 ×   Bao > Dumpling      (0, 5, 0, 4)
     2 ×   Bao > Churro      (0, 4, 4, 0)
     1 ×   Dumpling      (0, 0, 0, 4)
     1 ×   Churro      (0, 0, 4, 0)
     2 ×   Arepa > Churro      (5, 0, 4, 0)
     1 ×   Bao > Churro      (0, 5, 5, 0)
     1 ×   Churro > Dumpling      (0, 0, 5, 5)
     1 ×   Arepa > Bao > Churro > Dumpling      (3, 3, 3, 3)
     1 ×   Dumpling > Churro      (0, 0, 3, 5)
     1 ×   Bao      (0, 4, 0, 0)
     1 ×   Arepa > Churro      (4, 0, 4, 0)
     1 ×   Arepa > Churro > Bao      (5, 4, 5, 0)
     1 ×   Bao > Churro > Dumpling      (0, 5, 5, 5)
     1 ×   Churro > Dumpling      (0, 0, 4, 3)

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Bao               18  Hopeful
Arepa             11  Hopeful
Churro             9  Rejected
Dumpling           2  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Bao               20  Elected
Arepa             11  Rejected
Churro             0  Rejected
Dumpling           0  Rejected
Blank Votes        9  Rejected


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

--- 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): Churro
   Outside (3):        Arepa, Bao, Dumpling
   One member ⇒ Churro is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Bao is OUTSIDE the Smith set. ✗
      Every member of the set (Churro) beats Bao head-to-head, yet
      RCV-IRV elected Bao 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 40 ballots (score ballots).

Ballots:
   the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Arepa, Bao, Churro, Dumpling
     3 × Bao > Churro > Arepa=Dumpling      (0, 5, 4, 0)
     7 × Bao > Arepa=Churro=Dumpling      (0, 5, 0, 0)
     4 × Arepa > Bao=Churro=Dumpling      (5, 0, 0, 0)
     1 × Arepa=Churro=Dumpling > Bao      (5, 0, 5, 5)
     1 × Arepa=Dumpling > Bao=Churro      (4, 0, 0, 4)
     1 × Churro > Bao > Arepa=Dumpling      (0, 3, 4, 0)
     4 × Churro > Arepa=Bao=Dumpling      (0, 0, 5, 0)
     1 × Churro > Bao > Arepa > Dumpling      (1, 3, 4, 0)
     3 × Bao > Dumpling > Arepa=Churro      (0, 5, 0, 4)
     2 × Bao=Churro > Arepa=Dumpling      (0, 4, 4, 0)
     1 × Dumpling > Arepa=Bao=Churro      (0, 0, 0, 4)
     1 × Churro > Arepa=Bao=Dumpling      (0, 0, 4, 0)
     2 × Arepa > Churro > Bao=Dumpling      (5, 0, 4, 0)
     1 × Bao=Churro > Arepa=Dumpling      (0, 5, 5, 0)
     1 × Churro=Dumpling > Arepa=Bao      (0, 0, 5, 5)
     1 × Arepa=Bao=Churro=Dumpling      (3, 3, 3, 3)
     1 × Dumpling > Churro > Arepa=Bao      (0, 0, 3, 5)
     1 × Bao > Arepa=Churro=Dumpling      (0, 4, 0, 0)
     1 × Arepa=Churro > Bao=Dumpling      (4, 0, 4, 0)
     1 × Arepa=Churro > Bao > Dumpling      (5, 4, 5, 0)
     1 × Bao=Churro=Dumpling > Arepa      (0, 5, 5, 5)
     1 × Churro > Dumpling > Arepa=Bao      (0, 0, 4, 3)

Round-Robin — every pair, head-to-head (For – Against):
   Bao       beats Arepa      20 – 10
   Churro    beats Arepa      17 –  7
   Arepa     beats Dumpling    9 –  8
   Churro    beats Bao        15 – 14
   Bao       beats Dumpling   20 –  6
   Churro    beats Dumpling   18 –  6

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
             |    Arepa     |    Bao      |   Churro    |  Dumpling   |
-----------------------------------------------------------------------
     Arepa > |     ---      |10 - 10 - 20 | 7 - 16 - 17 | 9 - 23 -  8 |
       Bao > | 20 - 10 - 10 |    ---      |14 - 11 - 15 |20 - 14 -  6 |
    Churro > | 17 - 16 -  7 |15 - 11 - 14 |    ---      |18 - 16 -  6 |
  Dumpling > |  8 - 23 -  9 | 6 - 14 - 20 | 6 - 16 - 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  Churro     3–0–0         3     +23  Bao, Arepa, Dumpling
    2  Bao        2–1–0         2     +23  Arepa, Dumpling
    3  Arepa      1–2–0         1     -19  Dumpling
    4  Dumpling   0–3–0         0     -27  —

Winner — Ranked Robin (RCV-RR): Churro
   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): Churro
   Outside (3):        Arepa, Bao, Dumpling
   One member ⇒ Churro is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Churro 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

Count	Arepa	Bao	Churro	Dumpling
3	0	5	4	0
7	0	5	0	0
4	5	0	0	0
1	5	0	5	5
1	4	0	0	4
1	0	3	4	0
4	0	0	5	0
1	1	3	4	0
3	0	5	0	4
2	0	4	4	0
1	0	0	0	4
1	0	0	4	0
2	5	0	4	0
1	0	5	5	0
1	0	0	5	5
1	3	3	3	3
1	0	0	3	5
1	0	4	0	0
1	4	0	4	0
1	5	4	5	0
1	0	5	5	5
1	0	0	4	3

Count	Arepa	Bao	Churro	Dumpling
3	0	5	4	0
7	0	5	0	0
4	5	0	0	0
1	5	0	5	5
1	4	0	0	4
1	0	3	4	0
4	0	0	5	0
1	1	3	4	0
3	0	5	0	4
2	0	4	4	0
1	0	0	0	4
1	0	0	4	0
2	5	0	4	0
1	0	5	5	0
1	0	0	5	5
1	3	3	3	3
1	0	0	3	5
1	0	4	0	0
1	4	0	4	0
1	5	4	5	0
1	0	5	5	5
1	0	0	4	3

Count	Arepa	Bao	Churro	Dumpling
3	0	5	4	0
7	0	5	0	0
4	5	0	0	0
1	5	0	5	5
1	4	0	0	4
1	0	3	4	0
4	0	0	5	0
1	1	3	4	0
3	0	5	0	4
2	0	4	4	0
1	0	0	0	4
1	0	0	4	0
2	5	0	4	0
1	0	5	5	0
1	0	0	5	5
1	3	3	3	3
1	0	0	3	5
1	0	4	0	0
1	4	0	4	0
1	5	4	5	0
1	0	5	5	5
1	0	0	4	3