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Ice cream ladder — a STAR tie in both rounds, settled without the lot (BV2180, fp62p2)

Method: STAR (single winner) · 1 seat · Expected winner: Strawberry · full count →

▶ Live on BetterVoting: vote · results ↗ (election fp62p2).

🪜 The happy-path tiebreak. This is the worked example from the STAR tie-breaking ladder, now a live election. It ties in both rounds — a three-way tie for the second finalist, then a two-way tie in the runoff — and settles both with deterministic rungs (five-star, then score). The pre-published lot order is never consulted, so LH and BetterVoting agree and the result is fully reproducible. It's the deliberate contrast to BV555/xmyf7k, where every rung ties down to the random floor.

Level 201/301. Two voters, six ice-cream flavors. Winner: Strawberry.

The ballots (2 voters)

Chocolate, Chocolate Chip, Fudge Brownie, Vanilla, Strawberry, Mango
4,         5,              4,             1,       2,          -
1,         0,              0,             4,       5,          4

(- = left blank ≡ 0.) Source: bv2180_fp62p2_ice_cream_ladder.yaml.

How the winner is found — the ladder in action

Step What happens Rung that decides
Scoring round Strawberry 7 leads; Chocolate, Chocolate Chip, Vanilla tie at 5 for the 2nd slot — (tie)
Scoring tiebreak 1 pairwise among the three: all 2 → still tied pairwise (no-op)
Scoring tiebreak 2 five-star count: Chocolate Chip 1, Chocolate 0, Vanilla 0 → advances five-star ✓
Runoff Strawberry 1 vs Chocolate Chip 1 head-to-head → tied — (tie)
Runoff tiebreak 1 total score: Strawberry 7 > Chocolate Chip 5 → wins score ✓

Both ties resolve before the lot. The elegant part (see the ladder doc): each round breaks its tie with the other round's yardstick — a scoring-round tie (equal totals) is broken by the runoff's pairwise, then five-star; a runoff tie (equal preference) is broken by the scoring round's total score.

View 1 — BetterVoting (fp62p2)

BetterVoting runs the same protocol; because no random rung is reached, it elects Strawberry too.

📷 Paste the BetterVoting fp62p2 result screenshot here (filename suffix _fp62p2, under img/).

View 2 — the LH engine (reference)

[Divergence from STAR]
  STAR                   = Strawberry
  Choose-One (Plurality) = Chocolate Chip   (differs from STAR)
  Approval               = Chocolate   (differs from STAR)

--- STAR Voting Method (single winner) ---

[STAR Voting]
 Tabulating 2 ballots.
Chocolate,Chocolate Chip,Fudge Brownie,Vanilla,Strawberry,Mango
        4,             5,            4,      1,         2,    -
        1,             0,            0,      4,         5,    4
  ('-' = left blank / abstained; '0' = scored zero — both count as 0 stars.)

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Strawberry     -- 7 -- First place
   Chocolate      -- 5 -- Tied for second place
   Chocolate Chip -- 5 -- Tied for second place
   Vanilla        -- 5 -- Tied for second place
   Fudge Brownie  -- 4
   Mango          -- 4
 Strawberry advances, but there's a three-way tie for second.

[STAR Voting: Scoring Round: First tiebreaker]
 The candidate preferred in the most head-to-head matchups advances.
   Chocolate      -- 2 -- Tied for second place
   Chocolate Chip -- 2 -- Tied for second place
   Vanilla        -- 2 -- Tied for second place
   Equal Support  -- 0
 There's still a three-way tie for second.

[STAR Voting: Scoring Round: Second tiebreaker]
 The candidate with the most votes of score 5 advances.
   Chocolate Chip -- 1 -- Second place
   Chocolate      -- 0
   Vanilla        -- 0
 Strawberry and Chocolate Chip advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Chocolate Chip -- 1 -- Tied for first place
   Strawberry     -- 1 -- Tied for first place
   Equal Support  -- 0
 There's a two-way tie for first.

[STAR Voting: Automatic Runoff Round: First tiebreaker]
 The highest-scoring candidate wins.
   Strawberry     -- 7 -- First place
   Chocolate Chip -- 5
 Strawberry wins.

[STAR Voting: Winner — STAR Voting Method (single winner)]
 Strawberry

Full audit copy: _tabulated.

BV vs LH

Both engines elect Strawberry — confirmed against BetterVoting's frozen export (_bv_export.json), whose Results record tieBreakType: five_star for the scoring round: BV broke the three-way tie by the five-star count, exactly as LH does. Unlike the 3-way dead heat, they must agree here: every tie is broken by a deterministic rung (five-star, then score), so no random shuffle is reached. That's what makes this case freezable / BV-backable where BV555/xmyf7k is LH-only.

See also