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Dead heat — Ranked Robin runs the whole tiebreak ladder (LH-only)

Method: Ranked Robin (RCV-RR / Copeland) · 1 seat · Expected winner: Ada · full count →

Four score ballots, three candidates, engineered so every deterministic rung ties. Ada and Ben tie each other head-to-head and tie on total margin, and both beat Cara — so Ranked Robin walks its full ladder (most wins → total margin → lot order) and only the pre-published lot settles it. This is the one case in the set that exercises the Equal Support column and the +½ Copeland credit — and the one case that is LH-only on purpose, because it's exactly where the LH and BetterVoting tiebreaks diverge.

Reference: dead_heat_lot_tiebreak.yaml (expected_winners: [Ada]). No BetterVoting election — see "Why LH-only" below.

The ballots

Score ballots (0–5). Two voters are indifferent between Ada and Ben (both 5) — that indifference is Equal Support, no head-to-head preference:

Ada,Ben,Cara
5,5,0     ← Ada = Ben (Equal Support), both over Cara
5,5,0     ← Ada = Ben (Equal Support), both over Cara
4,3,1     ← Ada > Ben > Cara
3,4,1     ← Ben > Ada > Cara

The tabulation (LH native)

Full report in the _tabulated mirror:

Round-Robin — every pair, head-to-head (For – Against):
   Ada   ties  Ben    1 – 1
   Ada   beats Cara   4 – 0
   Ben   beats Cara   4 – 0

--- Pairwise (Round-Robin) Matrix ---
Legend: For - Equal Support - Against   (row vs column)
         |    Ada    |   Ben    |  Cara    |
--------------------------------------------
   Ada > |    ---    |1 - 2 - 1 |4 - 0 - 0 |
   Ben > | 1 - 2 - 1 |   ---    |4 - 0 - 0 |
  Cara > | 0 - 0 - 4 |0 - 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  Ada        1–0–1       1.5      +4  Cara
    2  Ben        1–0–1       1.5      +4  Cara
    3  Cara       0–2–0         0      -8  —

Winner — Ranked Robin (RCV-RR): Ada

Read the Ada↔Ben cell: 1 - 2 - 1 — one voter each way, and 2 Equal Support (the indifferent voters). For equals Against, so it's a tie, worth ½ to each in Copeland (1 win over Cara + ½ = 1.5). Ada and Ben are identical on wins (1) and on margin (+4), so only the pre-published lot [Ada, Ben, Cara] breaks it → Ada.

This is the only case that lights up the Equal Support column and the ½-Copeland credit, and the only one that reaches the lot rung — the full deterministic ladder in four ballots.

Why LH-only (the divergence)

The LH engine and BetterVoting resolve this differently, which is the whole reason there's no BV election here:

Tiebreak ladder
LH run_ranked_robin most wins → total margin → lot order — fully deterministic
BetterVoting RankedRobin.ts most wins → head-to-head (2-way only) → random

Here the two leaders tie each other head-to-head, so BV's 2-way rule can't resolve them and it falls through to a random pick — which can't be frozen into a reproducible _bv_export.json. So this case documents the LH ladder specifically; BetterVoting would agree that Ada and Ben are co-leaders but would not deterministically choose between them. Full write-up: rr_tiebreak_lh_vs_bv.md.

Engine wording

The winner note distinguishes a dead heat from a real cycle:

*** 2 candidates tie on the highest Copeland score (1.5): Ada, Ben — a dead heat (they draw head-to-head, not a cycle). Resolved by total margin, then lot order.

Ada and Ben both beat Cara and tie each other (no beat-around-the-loop), so the engine says dead heat, not "Condorcet cycle" — the latter is reserved for a genuine directed loop (rock-paper-scissors). See rr_tiebreak_lh_vs_bv.md.

See also