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BV1525 — 5 candidates / 4 winners, Bloc STAR: a Condorcet loser ties for seat 1

Method: Bloc STAR (multi-winner, majoritarian) · 4 seats · Expected winners: First, Second, Third, Fourth · full count →

Larry Hastings' electowiki Bloc-STAR test election, reproduced as the LH reference for BetterVoting test BV1525 (4 winners, 16 ballots). The candidates are named for their intended finish — First, Condorcet Loser, Second, Third, Fourth. The twist: a Score co-leader can be a near-Condorcet loser (loses every head-to-head). Here "Condorcet Loser" ties "First" for the top score and so ties for the seat-1 runoff; the lot alone separates them. Winners: First, Second, Third, Fourth.

▶ Live on BetterVoting: vote · results ↗ (election dkj9dx). On this run BetterVoting drew First for seat 1 — matching this file's published-lot outcome. Note the reporting quirk: BV flags the seat-1 round tieBreakType: random (correct — its logs walk runoff_tied → runoff_score_tie → runoff_five_star_tie → runoff_random), but the top-level summary still reads tieBreakType: none, the same under-report seen in BV130-r2 and BV131.

Reference file: bv1525_condorcet_loser_bloc.yaml (expected_winners: [First, Second, Third, Fourth]). Backs sheet row BV1525. Source: Larry's test_election_bloc_star_and_electowiki.starvote.

The election

Bloc STAR, 5 candidates, 4 seats, 16 ballots (four distinct ballots, weighted 8 / 5 / 2 / 1):

Count × First,Condorcet Loser,Second,Third,Fourth
    8 × 3,0,1,1,1
    5 × 0,4,0,0,0
    2 × 0,1,3,2,1
    1 × 0,2,5,4,3

[Score Distribution] (how many ballots gave each star rating)
                         Score
Candidate         5   4   3   2   1   0  | Total   Avg
First             0   0   8   0   0   8  |    24   1.5
Condorcet Loser   0   5   0   1   2   8  |    24   1.5
Second            1   0   2   0   8   5  |    19   1.2
Third             0   1   0   2   8   5  |    16   1.0
Fourth            0   0   1   0  10   5  |    13   0.8

First and Condorcet Loser tie at 24 for the top score; nothing reaches 5, so the five-star rung is dead.

Seat 1 — the tie, and why the lot matters

The two top scorers advance, tie 8–8 in the runoff, tie again on score (24–24) and five-star (0–0), and the pre-published permutation [First, Condorcet Loser, Second, Third, Fourth] breaks it for First:

Abridged for the lesson — not verbatim engine output
Round 1: Scoring Round — Condorcet Loser (24) and First (24) advance.
Round 1: Automatic Runoff — Condorcet Loser 8 ; First 8   ← tied
Round 1: First tiebreaker (score)   — 24 ; 24             ← tied
Round 1: Second tiebreaker (most 5s) — 0 ; 0              ← dead rung
[Tiebreaker: Lot Number Priority]  Resolved: ['First']    (permutation [First, Condorcet Loser, ...])
[Lot-decided tie — rare]

Round 2: Condorcet Loser (24) & Second (19) advance → Second wins the runoff (11 vs 5).
Round 3: Condorcet Loser (24) & Third  (16) advance → Third  wins the runoff (11 vs 5).
Round 4: Condorcet Loser (24) & Fourth (13) advance → Fourth wins the runoff ( 9 vs 5).

Winners — Bloc STAR Voting Method (4 winners)
 First
 Second
 Third
 Fourth
Full audit copy: _main_tabulated/bv1525_condorcet_loser_bloc_tabulated.txt.

The finding

Condorcet Loser tops the score in every round yet wins no seat. Because they lose every head-to-head runoff, they only ever have a shot at seat 1 — and only by winning the coin toss. That is exactly the electowiki caution: the Score winner can be a Condorcet loser, so handing a seat to both candidates who tie in the first runoff (an option electowiki mentions) would wrongly seat Condorcet Loser. STAR's runoff, plus a tiebreak, prevents it.

Only two orderings are valid, decided entirely by the seat-1 lot:

  • lot favors First → First, Second, Third, Fourth (this file)
  • lot favors Condorcet Loser → Condorcet Loser, First, Second, Third

A pre-published permutation makes which one occurs reproducible. A random draw (BetterVoting) does not — it "picks a different list of winners with each run," which is why comparing engines on this ballot set is hard until the tiebreak order is pinned (cf. #1063 / #1417; #358).