BV2141 — a Copeland tie that needs all four Equal-Vote tiebreak degrees¶

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

▶ Live on BetterVoting: vote · results ↗ (election 3r3yf7).

The electowiki Ranked Robin "all four tie-breaking degrees" example — the hardest tie the method defines a rule for. Ava and Bianca tie so thoroughly that the first three degrees of the Equal Vote Coalition's tiebreak protocol all fail to separate them; only the 4th-degree beatpath does. It's the perfect stress test of what each engine actually does when Ranked Robin ties, and the answer is: they disagree, and BetterVoting admits it isn't finished.

Three engines, three tiebreaks, potentially three winners¶

Ava and Bianca each win 3 of 5 matchups (Copeland 3.5), each with total margin +55, each with 149 votes against. Everything a simple tiebreak looks at is equal. What each engine does next:

Engine	Tiebreak ladder	Winner here
Equal Vote 4-degree protocol (electowiki)	wins → margin-over-finalists → margin-over-all → least-polarizing → beatpath	Bianca (beatpath 14 vs 7)
BetterVoting `RankedRobin.ts`	wins → 2-way head-to-head → random	random — this draw: Ava
LH `run_ranked_robin`	wins → total margin → lot (pre-published)	Ava (lot pinned to BV's draw)

The tie runs so deep that BetterVoting gives up and rolls dice. Its own results log says so verbatim:

"Ava picked in random tie-breaker, more robust tiebreaker not yet implemented."

So BetterVoting does not implement the Equal Vote 4-degree protocol this example was written to demonstrate — it detects the Copeland tie (tieBreakType: random) and picks at random. This run landed on Ava; a re-tally could elect Bianca. That non-determinism is exactly why a tie-deciding Ranked Robin result can't be frozen as a stable BV outcome — see rr_tiebreak_lh_vs_bv.md.

The ballots¶

81 voters, six candidates. = ties a rank level; > separates levels; unranked candidates are tied for last.

10:Eli>Deegan>Ava=Cedric>Fabio
 9:Bianca=Deegan>Eli>Cedric
 8:Deegan>Eli>Ava=Bianca=Cedric
 8:Bianca>Ava>Fabio>Cedric
 8:Fabio>Cedric>Ava>Deegan>Bianca
 7:Ava>Eli>Bianca>Fabio
 6:Fabio>Bianca=Cedric>Ava
 6:Cedric>Deegan=Eli>Ava=Bianca>Fabio
 5:Deegan>Ava=Bianca>Eli>Cedric
 4:Cedric>Bianca>Ava
 4:Ava>Bianca=Fabio
 4:Ava=Bianca>Fabio
 2:Bianca=Fabio>Ava=Eli

View 1 — BetterVoting¶

BetterVoting's results confirm the tie and break it at random:

tied: [Ava, Bianca] — both copelandScore: 3.5
tieBreakType: random
elected: [Ava] (this draw); log: "Ava picked in random tie-breaker, more robust tiebreaker not yet implemented."

BetterVoting result page for 3r3yf7: headline 'Tied! — Ava won after tiebreaker', 81 voters, Voting Method: Ranked Robin. Head-to-head wins bars — Ava 70%, Bianca 70%, Cedric 50%, Deegan 50%, Eli 40%, Fabio 20%.

The frozen export (bv2141_3r3yf7_four_degree_tie_bv_export.json) records BV's random perm order [Fabio, Eli, Cedric, Deegan, Ava, Bianca] — Ava precedes Bianca, so Ava won this draw.

View 2 — the LH tabulation engine¶

LH agrees on every Copeland score (Ava/Bianca 3.5, Cedric/Deegan 2.5, Eli 2, Fabio 1) and, with lot_numbers pinned to BV's perm, reproduces BV's frozen instance (Ava) — but deterministically, via its wins → margin → lot ladder:

--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 81 ballots (ranked ballots).

Ballots:
    10 × Eli > Deegan > Ava=Cedric > Fabio
     9 × Bianca=Deegan > Eli > Cedric
     8 × Deegan > Eli > Ava=Bianca=Cedric
     8 × Bianca > Ava > Fabio > Cedric
     8 × Fabio > Cedric > Ava > Deegan > Bianca
     7 × Ava > Eli > Bianca > Fabio
     6 × Fabio > Bianca=Cedric > Ava
     6 × Cedric > Deegan=Eli > Ava=Bianca > Fabio
     5 × Deegan > Ava=Bianca > Eli > Cedric
     4 × Cedric > Bianca > Ava
     4 × Ava > Bianca=Fabio
     4 × Ava=Bianca > Fabio
     2 × Bianca=Fabio > Ava=Eli

Round-Robin — every pair, head-to-head (For – Against):
   Deegan  beats Eli      30 – 19
   Ava     beats Eli      46 – 33
   Eli     beats Cedric   41 – 32
   Eli     beats Fabio    45 – 32
   Bianca  beats Eli      50 – 31
   Ava     beats Deegan   43 – 38
   Deegan  ties  Cedric   32 – 32
   Fabio   beats Deegan   39 – 38
   Deegan  beats Bianca   37 – 35
   Cedric  beats Ava      33 – 30
   Ava     beats Fabio    56 – 16
   Ava     ties  Bianca   29 – 29
   Cedric  beats Fabio    42 – 39
   Bianca  beats Cedric   39 – 28
   Bianca  beats Fabio    51 – 24

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
           |     Eli      |   Deegan    |    Ava      |   Cedric    |   Fabio     |   Bianca    |
-------------------------------------------------------------------------------------------------
     Eli > |     ---      |19 - 32 - 30 |33 -  2 - 46 |41 -  8 - 32 |45 -  4 - 32 |31 -  0 - 50 |
  Deegan > | 30 - 32 - 19 |    ---      |38 -  0 - 43 |32 - 17 - 32 |38 -  4 - 39 |37 -  9 - 35 |
     Ava > | 46 -  2 - 33 |43 -  0 - 38 |    ---      |30 - 18 - 33 |56 -  9 - 16 |29 - 23 - 29 |
  Cedric > | 32 -  8 - 41 |32 - 17 - 32 |33 - 18 - 30 |    ---      |42 -  0 - 39 |28 - 14 - 39 |
   Fabio > | 32 -  4 - 45 |39 -  4 - 38 |16 -  9 - 56 |39 -  0 - 42 |    ---      |24 -  6 - 51 |
  Bianca > | 50 -  0 - 31 |35 -  9 - 37 |29 - 23 - 29 |39 - 14 - 28 |51 -  6 - 24 |    ---      |

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  Ava        3–1–1       3.5     +55  Deegan, Eli, Fabio
    2  Bianca     3–1–1       3.5     +55  Cedric, Eli, Fabio
    3  Deegan     2–2–1       2.5      +7  Bianca, Eli
    4  Cedric     2–2–1       2.5     -14  Ava, Fabio
    5  Eli        2–3–0         2     -21  Cedric, Fabio
    6  Fabio      1–4–0         1     -82  Deegan

Winner — Ranked Robin (RCV-RR): Ava
   *** 2 candidates tie on the highest Copeland score (3.5): Ava, Bianca — a dead heat (they draw head-to-head, not a cycle). Resolved by total margin, then lot order.

Full detail: bv2141_3r3yf7_four_degree_tie_tabulated.txt.

The Ava–Bianca head-to-head is itself a tie¶

The matrix shows why no simple rule works: Ava vs Bianca is 29 – 29 (with 23 Equal Support). So BetterVoting's "break a 2-way tie by head-to-head" rung is also tied, and it falls through to random. LH's "break by total margin" rung is tied too (+55 = +55), so LH falls through to lot. Only the Equal Vote beatpath (4th degree) separates them — and it favors Bianca (14 vs 7), the answer neither engine here computes.

A note on electowiki's published matrix¶

electowiki's outcome is correct (Ava/Bianca tie → Bianca by 4th degree), and its row totals (204/204/167/175/169/150) match this tabulation exactly. But its printed cell values for Ava-over and Bianca-over {Cedric, Deegan, Eli} are each 4 too low — those rows' cells sum to 192, not the 204 total electowiki itself prints. A display slip; it changes none of the records, margins, or the winner.

Cross-checks¶

LH native run_ranked_robin — Ava/Bianca tie 3.5; lot (pinned to BV perm) → Ava.
BetterVoting RankedRobin.ts — Ava/Bianca tie 3.5; tieBreakType: random → Ava (this draw); records identical to LH.
Equal Vote 4-degree protocol (electowiki) — → Bianca (beatpath 14 vs 7); implemented by neither engine.