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Exercise 1 — Two districts, one mayor: EAST district

▶ Live on BetterVoting: vote · results ↗ (election rhbfj7 · test BV2189) — an independent tabulator to check the winners below against.

Bucket — STAR_OUTLIER_RR_WITH_IRV: STAR is the outlier

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

What happens

RCV-IRV and Ranked Robin both elect Elena, the Condorcet (pairwise) winner. STAR instead elects Avery, because its score-then-automatic-runoff can reward a candidate with broad, intense scored support even when a different candidate wins every head-to-head. Here STAR is the outlier — an honest reminder that STAR does not always elect the Condorcet candidate.

Winners by method

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

Flags: 9 tied-score ballot(s)

Source election: 01_STAR/05_Practice/cases/ex01_district_east.yaml · STAR tabulated mirror: ex01_district_east_tabulated.txt

5 candidates, 9 ballots.

The ballots

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

Count Avery Blake Carmen Diego Elena
5 3 0 4 3 5
3 5 0 3 5 0
1 5 0 3 3 0

STAR result (official)

Scoring round (sum of scores): Avery 35, Diego 33, Carmen 32, Elena 25, Blake 0

Finalists (top two): Avery and Diego

Automatic runoff: Avery 1 vs Diego 0 (8 equal/no-preference)

STAR winner: Avery

Full LH STAR engine report:

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
               |  * Avery   | * Diego   |
-----------------------------------------
     * Avery > |    ---     |1 - 8 - 0  |
     * Diego > | 0 - 8 - 1  |   ---     |

[Divergence from STAR]
  STAR                   = Avery
  Choose-One (Plurality) = Elena   (differs from STAR)
  RCV-IRV                = Elena   (differs from STAR)
  RCV-RR (Condorcet)     = Elena   (differs from STAR)
  Note: 9 of 9 ballots (100%) 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.

--- STAR Voting Method (single winner) ---
 Tabulating 9 ballots.
Count × Avery,Blake,Carmen,Diego,Elena
    5 ×     3,    0,     4,    3,    5
    3 ×     5,    0,     3,    5,    0
    1 ×     5,    0,     3,    3,    0

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Avery      4  0  5  0  0  0  |    35   3.9
Blake      0  0  0  0  0  9  |     0   0.0
Carmen     0  5  4  0  0  0  |    32   3.6
Diego      3  0  6  0  0  0  |    33   3.7
Elena      5  0  0  0  0  4  |    25   2.8

Scoring Round
 The two highest-scoring candidates advance to the next round.
   Avery         -- 35 -- First place
   Diego         -- 33 -- Second place
   Carmen        -- 32
   Elena         -- 25
   Blake         --  0
 Avery and Diego advance.

Automatic Runoff Round
 The candidate preferred in the most head-to-head matchups wins.
   Avery         -- 1 -- First place
   Diego         -- 0
   Equal Support -- 8
 Avery wins.
   Voters with a preference: 1 of 9 (8 Equal Support).
   Avery 1 (100%) vs Diego 0 (0%); majority = 1.

Winner — STAR Voting Method (single winner)
 Avery

RCV-IRV — round by round

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 9 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: Avery, Blake, Carmen, Diego, Elena
     5 ×   Elena > Carmen > Avery > Diego      (3, 0, 4, 3, 5)
     3 ×   Avery > Diego > Carmen      (5, 0, 3, 5, 0)
     1 ×   Avery > Carmen > Diego      (5, 0, 3, 3, 0)

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Elena              5  Elected
Avery              4  Rejected
Carmen             0  Rejected
Diego              0  Rejected
Blake              0  Rejected


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

--- 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 5): Elena
   Outside (4):        Avery, Blake, Carmen, Diego
   One member ⇒ Elena is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Elena 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 9 ballots (score ballots).

Ballots:
   the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Avery, Blake, Carmen, Diego, Elena
     5 × Elena > Carmen > Avery=Diego > Blake      (3, 0, 4, 3, 5)
     3 × Avery=Diego > Carmen > Blake=Elena      (5, 0, 3, 5, 0)
     1 × Avery > Carmen=Diego > Blake=Elena      (5, 0, 3, 3, 0)

Round-Robin — every pair, head-to-head (For – Against):
   Avery   beats Blake    9 – 0
   Carmen  beats Avery    5 – 4
   Avery   beats Diego    1 – 0
   Elena   beats Avery    5 – 4
   Carmen  beats Blake    9 – 0
   Diego   beats Blake    9 – 0
   Elena   beats Blake    5 – 0
   Carmen  beats Diego    5 – 3
   Elena   beats Carmen   5 – 4
   Elena   beats Diego    5 – 4

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
           |   Avery   |  Blake   | Carmen   |  Diego   |  Elena   |
--------------------------------------------------------------------
   Avery > |    ---    |9 - 0 - 0 |4 - 0 - 5 |1 - 8 - 0 |4 - 0 - 5 |
   Blake > | 0 - 0 - 9 |   ---    |0 - 0 - 9 |0 - 0 - 9 |0 - 4 - 5 |
  Carmen > | 5 - 0 - 4 |9 - 0 - 0 |   ---    |5 - 1 - 3 |4 - 0 - 5 |
   Diego > | 0 - 8 - 1 |9 - 0 - 0 |3 - 1 - 5 |   ---    |4 - 0 - 5 |
   Elena > | 5 - 0 - 4 |5 - 4 - 0 |5 - 0 - 4 |5 - 0 - 4 |   ---    |

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  Elena      4–0–0         4      +8  Carmen, Avery, Diego, Blake
    2  Carmen     3–1–0         3     +11  Avery, Diego, Blake
    3  Avery      2–2–0         2      +8  Diego, Blake
    4  Diego      1–3–0         1      +5  Blake
    5  Blake      0–4–0         0     -32  —

Winner — Ranked Robin (RCV-RR): Elena
   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 5): Elena
   Outside (4):        Avery, Blake, Carmen, Diego
   One member ⇒ Elena is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Elena 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