BV1525 — 5 candidates / 4 winners, Bloc STAR (Condorcet-loser ties for seat 1)¶
Generated from bv1525_condorcet_loser_bloc.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.
Method: Bloc STAR (multi-winner, majoritarian) · 4 seats · Expected winners: First, Second, Third, Fourth
▶ Live on BetterVoting: vote · results ↗ (election dkj9dx · test BV1525).
Official tie-break (lot) order: First > Condorcet Loser > Second > Third > Fourth — consulted only if every deterministic tiebreaker stays tied (how the ladder works).
Scenario¶
The LH reference for BetterVoting test BV1525 (4 winners, 16 ballots), which reproduces Larry Hastings' own electowiki Bloc-STAR test election (test_election_bloc_star_and_electowiki). Five candidates named for their intended finish — First, Condorcet Loser, Second, Third, Fourth — 16 ballots, 4 seats.
The teaching point (electowiki): a Score co-leader can be a near-CONDORCET LOSER — a candidate who loses every head-to-head runoff. Here "Condorcet Loser" ties "First" for the top score (both 24) and so ties for seat 1's runoff (pairwise 8-8, five-star 0-0). Only the LOT can separate them. With the pre-published permutation [First, Condorcet Loser, Second, Third, Fourth], First takes seat 1; Condorcet Loser then LOSES every subsequent runoff and wins no seat. Winners: First, Second, Third, Fourth.
The lot matters: if Condorcet Loser had won the seat-1 coin toss, the outcome would be Condorcet Loser, First, Second, Third — the ONLY other valid ordering. A pre-published lot makes which of the two happens reproducible; a random draw (as in STAR Vote 2.0) does not, and picks different winners on each run.
Ballots¶
Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical ballots).
First,Condorcet Loser,Second,Third,Fourth
3,0,1,1,1
3,0,1,1,1
3,0,1,1,1
3,0,1,1,1
3,0,1,1,1
3,0,1,1,1
3,0,1,1,1
3,0,1,1,1
0,4,0,0,0
0,4,0,0,0
0,4,0,0,0
0,4,0,0,0
0,4,0,0,0
0,1,3,2,1
0,1,3,2,1
0,2,5,4,3
What the engine says¶
The count, step by step — the rounds and how the winner is reached:
--- Bloc STAR Voting Method (4 winners) ---
[Bloc STAR]
Tabulating 16 ballots to fill 4 seats.
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
[Bloc STAR: Round 1: Scoring Round]
The two highest-scoring candidates advance to the next round.
Condorcet Loser -- 24 -- First place
First -- 24 -- Second place
Second -- 19
Third -- 16
Fourth -- 13
Condorcet Loser and First advance.
[Bloc STAR: Round 1: Automatic Runoff Round]
The candidate preferred in the most head-to-head matchups wins.
Condorcet Loser -- 8 -- Tied for first place
First -- 8 -- Tied for first place
Equal Support -- 0
There's a two-way tie for first.
[Bloc STAR: Round 1: Automatic Runoff Round: First tiebreaker]
The highest-scoring candidate wins.
Condorcet Loser -- 24 -- Tied for first place
First -- 24 -- 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.
Condorcet Loser -- 0 -- Tied for first place
First -- 0 -- 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: ['First', 'Condorcet Loser', 'Second', 'Third', 'Fourth']
[Tiebreaker: Lot Number Priority]
Tie among: ['Condorcet Loser', 'First']
Resolved: ['First'] (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.
Condorcet Loser -- 24 -- First place
Second -- 19 -- Second place
Third -- 16
Fourth -- 13
Condorcet Loser and Second advance.
[Bloc STAR: Round 2: Automatic Runoff Round]
The candidate preferred in the most head-to-head matchups wins.
Second -- 11 -- First place
Condorcet Loser -- 5
Equal Support -- 0
Second wins.
Runoff math:
16 ballots cast
− 0 Equal Support (no preference between the two finalists)
──
16 voters with a preference (majority = 9)
Second 11 (69%) · Condorcet Loser 5 (31%)
──────────────────────────────────────────────────
[Bloc STAR: Round 3: Scoring Round]
The two highest-scoring candidates advance to the next round.
Condorcet Loser -- 24 -- First place
Third -- 16 -- Second place
Fourth -- 13
Condorcet Loser and Third advance.
[Bloc STAR: Round 3: Automatic Runoff Round]
The candidate preferred in the most head-to-head matchups wins.
Third -- 11 -- First place
Condorcet Loser -- 5
Equal Support -- 0
Third wins.
Runoff math:
16 ballots cast
− 0 Equal Support (no preference between the two finalists)
──
16 voters with a preference (majority = 9)
Third 11 (69%) · Condorcet Loser 5 (31%)
──────────────────────────────────────────────────
[Bloc STAR: Round 4: Scoring Round]
The two highest-scoring candidates advance to the next round.
Condorcet Loser -- 24 -- First place
Fourth -- 13 -- Second place
Condorcet Loser and Fourth advance.
[Bloc STAR: Round 4: Automatic Runoff Round]
The candidate preferred in the most head-to-head matchups wins.
Fourth -- 9 -- First place
Condorcet Loser -- 5
Equal Support -- 2
Fourth wins.
Runoff math:
16 ballots cast
− 2 Equal Support (no preference between the two finalists)
──
14 voters with a preference (majority = 8)
Fourth 9 (64%) · Condorcet Loser 5 (36%)
[Bloc STAR: Winners — Bloc STAR Voting Method (4 winners)]
First
Second
Third
Fourth
Full audit — preference matrix, Condorcet, and score distribution¶
--- Preference Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
Informational only — not part of the 4-winner count below,
so no Top-2 finalists are marked.
| First | Condorcet Loser | Second | Third | Fourth |
-----------------------------------------------------------------------------------------------------------------------------------
First > | --- | 8 - 0 - 8 | 8 - 5 - 3 | 8 - 5 - 3 | 8 - 5 - 3 |
Condorcet Loser > | 8 - 0 - 8 | --- | 5 - 0 - 11 | 5 - 0 - 11 | 5 - 2 - 9 |
Second > | 3 - 5 - 8 | 11 - 0 - 5 | --- | 3 - 13 - 0 | 3 - 13 - 0 |
Third > | 3 - 5 - 8 | 11 - 0 - 5 | 0 - 13 - 3 | --- | 3 - 13 - 0 |
Fourth > | 3 - 5 - 8 | 9 - 2 - 5 | 0 - 13 - 3 | 0 - 13 - 3 | --- |
[Condorcet Winner]
No strict Condorcet winner; weak Condorcet winner: First — matches the STAR winner
[Condorcet Loser]
No strict Condorcet loser; weak Condorcet loser: Condorcet Loser (never wins a matchup)
[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
Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).
Run it yourself:
python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 02_STAR_Bloc/02_Examples/cases/bv1525_condorcet_loser_bloc.yaml
See also¶
- Condorcet efficiency (topic hub)
- Ties & tie-breaking (topic hub)
- Runoff reversal (worked set)
- Glossary · all cases by method
More cases in this set: 00_c3_b3_bloc-baseline-2-seats · 01_c4_b2_bloc-star-2-seats · b484mbm_tie_every_rung · bloc_lot_path_dependence_a_c3_b5 · bloc_lot_path_dependence_b_c3_b5 · bv129_score_tiebreak_bloc · bv130_bloc_pagination_731 · bv130r2_dead_rung_bloc · bv131_guido_bloc · bv132_verify_votes_bloc · bv1815_bloc_3c2s_basic · bv1835_8h3yrx_score_leader_no_seat · bv2105_r4dqvd_ice_cream_bloc · bv2105r2_w3vvff_ice_cream_recheck · bv2269_t488h9_race_nobody_can_lose · bv750_tie_breaking_bloc · lackner_skowron_shadow_bloc_star_c7_b12 · race_nobody_can_lose_two_seat_control