3 candidates / 2 seats, Bloc STAR — tie at every rung (484mbm)¶

Generated from b484mbm_tie_every_rung.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: Bloc STAR (multi-winner, majoritarian) · 2 seats · Expected winners: Blythe, Arden

▶ Live on BetterVoting: vote · results ↗ (election 484mbm).

Official tie-break (lot) order: Blythe > Arden > Corin — consulted only if every deterministic tiebreaker stays tied (how the ladder works).

Scenario¶

The smallest election that ties all the way down. Three voters, three candidates, two seats; the ballots rotate, so each voter's 3 / 4 / 5 lands on a different candidate (Arden > Blythe > Corin > Arden, rock-paper-scissors).

Every deterministic rung comes back level. Scores: 12 = 12 = 12. Pairwise: each candidate is preferred on 3 of the 9 matchup-ballots, and each wins exactly one head-to-head 2-1, so the cycle ties on either reading. Five-star: one score-5 vote each. Nothing in the ballots separates the three, so the two seats are filled entirely by whatever tie-breaking policy was published before the count.

That makes it a clean divergence probe, and the two engines take different paths to the same pair. BetterVoting SKIPS the pairwise rung whenever more than two candidates are tied (log pairwise_too_many_candidates), falls through five-star, and settles seat 1 with its seeded random draw perm = [Blythe, Arden, Corin] -> Blythe, then Arden. The LH engine DOES compute the pairwise rung, finds it tied 3-3-3, and only then reaches its own tiebreaker. Pinning lot_numbers to BV's perm reproduces BV exactly.

Also a live repro of the tieBreakType reporting gap already seen on BV130-r2: round 0 carries tieBreakType: "random" and the logs name both draws, but the top-level tieBreakType is "none" and tied is [] — so the summary a reader sees does not say a seat was decided by lot.

Backs the .starvote input-format page, which runs the same election through Larry Hastings' own CLI with the tiebreaker switched off, where it refuses to pick anyone at all: 07_Concepts/tabulation_engines/LH_starvote/starvote_file_format.md

Ballots¶

Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical ballots).

Arden,Blythe,Corin
3,4,5
5,3,4
4,5,3

What the engine says¶

The count, step by step — the rounds and how the winner is reached:

--- Bloc STAR Voting Method (2 winners) ---

[Bloc STAR]
 Tabulating 3 ballots to fill 2 seats.
Arden,Blythe,Corin
    3,     4,    5
    5,     3,    4
    4,     5,    3

[Bloc STAR: Round 1: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Arden         -- 12 -- Tied for first place
   Blythe        -- 12 -- Tied for first place
   Corin         -- 12 -- Tied for first place
 There's a three-way tie for first.

[Bloc STAR: Round 1: Scoring Round: First tiebreaker]
 The two candidates preferred in the most head-to-head matchups advance.
   Arden         -- 3 -- Tied for first place
   Blythe        -- 3 -- Tied for first place
   Corin         -- 3 -- Tied for first place
   Equal Support -- 0
 There's still a three-way tie for first.

[Bloc STAR: Round 1: Scoring Round: Second tiebreaker]
 The two candidates with the most votes of score 5 advance.
   Arden         -- 1 -- Tied for first place
   Blythe        -- 1 -- Tied for first place
   Corin         -- 1 -- Tied for first place
 There's still a three-way tie for first.

*(Ties are resolved by choosing the tied candidate with the highest-priority official lot number.)*
    Lot-number priority order: ['Blythe', 'Arden', 'Corin']

[Tiebreaker: Lot Number Priority]
  Tie among: ['Arden', 'Blythe', 'Corin']
  Resolved: ['Blythe', 'Arden'] (selected by lot-number priority).

[Lot-decided tie — rare]
  ⚠ The ballots did not break this tie: the deterministic rungs
    (pairwise / score, then five-star) all came back equal, so the
    pre-published LOT order chose among the tied candidates — the
    result here was set by lot, not by the votes. Usually the
    "dead rung": no tied candidate held a score-5 vote (five-star
    counts fives, not fours). Verify the tied candidates' 5-counts.

[Bloc STAR: Round 1: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Blythe        -- 2 -- First place
   Arden         -- 1
   Equal Support -- 0
 Blythe wins.
   Runoff math:
     3  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     3  voters with a preference  (majority = 2)
           Blythe 2 (67%)  ·  Arden 1 (33%)

──────────────────────────────────────────────────

[Bloc STAR: Round 2: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Arden         -- 12 -- First place
   Corin         -- 12 -- Second place
 Arden and Corin advance.

[Bloc STAR: Round 2: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Arden         -- 2 -- First place
   Corin         -- 1
   Equal Support -- 0
 Arden wins.
   Runoff math:
     3  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     3  voters with a preference  (majority = 2)
           Arden 2 (67%)  ·  Corin 1 (33%)

[Bloc STAR: Winners — Bloc STAR Voting Method (2 winners)]
 Blythe
 Arden

Full audit — preference matrix, Condorcet, and score distribution¶

--- Preference Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        Informational only — not part of the 2-winner count below,
        so no Top-2 finalists are marked.
               |    Arden   |   Blythe  |   Corin   |
-----------------------------------------------------
       Arden > |    ---     |1 - 0 - 2  |2 - 0 - 1  |
      Blythe > | 2 - 0 - 1  |   ---     |1 - 0 - 2  |
       Corin > | 1 - 0 - 2  |2 - 0 - 1  |   ---     |

[Condorcet Winner]
  No Condorcet winner (majority cycle: Arden > Corin > Blythe > Arden)

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Arden      1  1  1  0  0  0  |    12   4.0
Blythe     1  1  1  0  0  0  |    12   4.0
Corin      1  1  1  0  0  0  |    12   4.0

Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 02_STAR_Bloc/02_Examples/cases/b484mbm_tie_every_rung.yaml

3 candidates / 2 seats, Bloc STAR — tie at every rung (484mbm)¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶