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Ties in Bloc STAR

One line: Bloc STAR has no tiebreak rules of its own — it runs STAR's ladder once per seat. What is new is the consequence: because each seat is decided in the field the previous seat left behind, a tie broken at seat 1 can change who wins seat 2, not merely the order the winners are announced in.

→ The ladder itself: STAR Tie-Breaking — The Full Chain · the mechanics: Bloc STAR · the case index: 02_STAR_Bloc

Level: 301 · deep dive

The ladder, briefly

Unchanged from single-winner STAR, and worth re-reading in full rather than from memory:

SCORING ROUND  — tie for the last finalist slot?
  1. PAIRWISE   2. FIVE-STAR   3. LOT ORDER

AUTOMATIC RUNOFF  — the two finalists tied?
  1. SCORE      2. FIVE-STAR   3. LOT ORDER

Each round breaks its tie with the other round's yardstick, because the measure that tied can't be the one that separates. In a Bloc race this whole apparatus runs once per seat, independently — so a 4-seat election can break four ties, in eight different places, by two different rules.

The Bloc-specific consequence: a seat-1 tie is not confined to seat 1

Here is the part that has no single-winner analogue. Three candidates, two seats, five ballots. Nadia and Omar tie at 15 points; Priya trails at 12. The seat-1 runoff is a dead heat and every deterministic rung ties behind it:

[Divergence from STAR]
  STAR   = Omar
  RCV-RR = Nadia   (differs from STAR)
  Full round-by-round reports (generated for review):
  RCV-RR round-robin: cases_tabulated/bloc_lot_path_dependence_b_c3_b5_RCV-RR_tabulated.txt

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

[Bloc STAR]
 Tabulating 5 ballots to fill 2 seats.
Count × Nadia,Omar,Priya
    2 ×     5,   0,    1
    2 ×     0,   5,    5
    1 ×     5,   5,    0

[Bloc STAR: Round 1: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Nadia         -- 15 -- First place
   Omar          -- 15 -- Second place
   Priya         -- 12
 Nadia and Omar advance.

[Bloc STAR: Round 1: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Nadia         -- 2 -- Tied for first place
   Omar          -- 2 -- Tied for first place
   Equal Support -- 1
 There's a two-way tie for first.

[Bloc STAR: Round 1: Automatic Runoff Round: First tiebreaker]
 The highest-scoring candidate wins.
   Nadia         -- 15 -- Tied for first place
   Omar          -- 15 -- Tied for first place
 There's still a two-way tie for first.

[Bloc STAR: Round 1: Automatic Runoff Round: Second tiebreaker]
 The candidate with the most votes of score 5 wins.
   Nadia         -- 3 -- Tied for first place
   Omar          -- 3 -- Tied for first place
 There's still a two-way tie for first.

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

[Tiebreaker: Lot Number Priority]
  Tie among: ['Nadia', 'Omar']
  Resolved: ['Omar'] (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 2: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Nadia         -- 15 -- First place
   Priya         -- 12 -- Second place
 Nadia and Priya advance.

[Bloc STAR: Round 2: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Nadia         -- 3 -- First place
   Priya         -- 2
   Equal Support -- 0
 Nadia wins.
   Runoff math:
     5  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     5  voters with a preference  (majority = 3)
           Nadia 3 (60%)  ·  Priya 2 (40%)

[Bloc STAR: Winners — Bloc STAR Voting Method (2 winners)]
 Omar
 Nadia

So the lot decides seat 1. Run the same five ballots under the two possible lot orders:

Published lot Seat 1 Seat 2 Council
[Nadia, Omar, Priya] Nadia (by lot) Priya beats Omar 2–1 Nadia, Priya
[Omar, Nadia, Priya] Omar (by lot) Nadia beats Priya 3–2 Omar, Nadia

Priya sits on the council in one run and not the other, and no ballot changed. The lot did not reorder the winners; it picked a different set of them.

Why the two seat-2 runoffs go opposite ways: Omar and Priya are scored 5/5 by the two ballots that would otherwise separate them, so Omar carries only 1 of the 3 ballots that express a preference. Nadia and Priya are never tied on any ballot, and Nadia takes 3 of 5. Two near-identical candidates, opposite results against the same third one — which is exactly the kind of asymmetry the removal step exposes.

Run it: lot A (yaml) · lot B (yaml)

Contrast a top-N method — Bloc Approval, SNTV, Bloc Ranked Robin all produce one ranking and cut it at N, so a tie there can only ever swap the last seat. Bloc STAR is the one at-large method where a coin toss propagates.

The dead rung, and its opposite

The five-star rung counts votes of the scale maximum — literally score == 5. Two ways it fails to help, and this repo has a case for each:

  • Inert. If neither tied candidate holds a single 5, the rung runs, prints 0 – 0, and settles nothing — the dead rung. BV130-r2 is built for it: six candidates capped at 4, so Ada and Dan tie 15–15 with five-star counts of 0 and 0, and seat 1 goes to the lot.
  • Live and still tied. In the Nadia/Omar case above both candidates hold three 5s. The rung had plenty to weigh and weighed it to a draw. The engine's warning text guesses "usually the dead rung" and tells you to check the counts — do check them, because "the lot decided" and "the five-star rung was empty" are not the same finding.

A lot-decided seat is genuinely rare in a real election. It is not rare in a small teaching file, and it is not rare in a race where nobody uses the top of the scale.

What BetterVoting reports — read the export, not the banner

The Bloc case set is largely a set of tie probes against BetterVoting, and the recurring finding is a reporting one rather than a counting one. BV's ordering data is complete and reproducible: the export publishes perm (candidates in tiebreak order), each candidate's tieBreakOrder, and the tied[]/other[] lists, and pinning lot_numbers to BV's perm replays the draw exactly.

The summary on top of it is what misleads:

  • BV131 — seat 1 is decided by lot, the election is marked "Passed", and the top-level tieBreakType reads none. Nothing on the results page says a coin was tossed.
  • BV130-r2 — same shape: a genuine random draw settled seat 1 (perm puts Dan ahead of Ada), tieBreakType still none.

So when a Bloc result matters, read the export's perm and tieBreakOrder, not the banner. A reader who trusts tieBreakType will believe an election was decided by voters when it was decided by a shuffle.

Two adjacent BV defects the same case set turned up, worth knowing because they change the count rather than the label: flat / no-preference ballots being dropped entirely (BV132, #1073) and an all-identical-ballot election tallying nTallyVotes: 0 (BV750, #1052).

Reading a Bloc result for ties

  1. Which seat, not whether. "There was a tie" is not enough — ask which seat it was on, because a seat-1 tie is the one that can move later seats.
  2. Check the tied candidates' five-star counts before crediting or blaming the rung.
  3. Publish the lot before the ballots. That is what makes a lot-decided seat auditable instead of merely asserted: lot_numbers: in the YAML, perm in a BV export.
  4. The seat order is evidence. It tells you where in the sequence the count stopped being determined by the votes.

See also