Condorcet centrist, full form (100 voters, 47/47/3/3) — STAR elects Casey¶
▶ Live on BetterVoting: vote · results ↗ (election bkwfjr · test BV2172) — an independent tabulator to check the winners below against.
Bucket — IRV_OUTLIER_RR_WITH_STAR: RCV-IRV is the outlier (center squeeze)
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
STAR elects Casey — and so do Ranked Robin and Condorcet, because Casey is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Avery: Casey collects fewer top (first-choice) votes, so IRV eliminates Casey early, and those ballots transfer to Avery. This is the classic center squeeze — the broadly acceptable candidate is knocked out by round-by-round elimination even though a majority prefers them in a direct matchup. Two methods (STAR + RR) against one (RCV-IRV): IRV is the outlier.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Casey |
| RCV-IRV | Avery |
| Ranked Robin (RCV-RR) | Casey |
| Approval | Casey |
| Range / Score | Casey |
| Condorcet | Casey |
Flags: none
Source election: method_comparisons/symmetric_centrist_all_methods/cases/bv2172_bkwfjr_star.yaml · STAR tabulated mirror: bv2172_bkwfjr_star_tabulated.txt
Also present (identical ballots) at: method_comparisons/symmetric_centrist_bv2170/cases/bv2170_pp2q4q_star.yaml.
3 candidates, 100 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Avery | Blake | Casey |
|---|---|---|---|
| 47 | 5 | 1 | 3 |
| 47 | 1 | 5 | 3 |
| 3 | 3 | 1 | 5 |
| 3 | 1 | 3 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Casey 312, Avery 294, Blake 294
Finalists (top two): Casey and Avery
Automatic runoff: Casey 53 vs Avery 47
STAR winner: Casey
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
Note: Avery and Blake tied at 294 in the Scoring Round, and the lot
rung (the ballots could not separate them) advanced Avery. The *
marks who advanced, not who scored highest. Blake is filtered
out of this grid — see the Scoring Round for how the tie was
settled.
| * Avery | * Casey |
-----------------------------------------------
* Avery > | --- |47 - 0 - 53 |
* Casey > | 53 - 0 - 47 | --- |
[Divergence from STAR]
STAR = Casey
Choose-One (Plurality) = Avery (differs from STAR)
RCV-IRV = Avery (differs from STAR)
Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
method difference, not a tie-breaking artifact.
Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
outlier — the classic center-squeeze signature.
--- STAR Voting Method (single winner) ---
Tabulating 100 ballots.
Count × Avery,Blake,Casey
47 × 5, 1, 3
47 × 1, 5, 3
3 × 3, 1, 5
3 × 1, 3, 5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Avery 47 0 3 0 50 0 | 294 2.9
Blake 47 0 3 0 50 0 | 294 2.9
Casey 6 0 94 0 0 0 | 312 3.1
Scoring Round
The two highest-scoring candidates advance to the next round.
Casey -- 312 -- First place
Avery -- 294 -- Tied for second place
Blake -- 294 -- Tied for second place
Casey advances, but there's a two-way tie for second.
Scoring Round: First tiebreaker
The candidate preferred in the most head-to-head matchups advances.
Avery -- 50 -- Tied for second place
Blake -- 50 -- Tied for second place
Equal Support -- 0
There's still a two-way tie for second.
Scoring Round: Second tiebreaker
The candidate with the most votes of score 5 advances.
Avery -- 47 -- Tied for second place
Blake -- 47 -- Tied for second place
There's still a two-way tie for second.
*(Ties are resolved by choosing the tied candidate with the highest-priority official lot number.)*
Lot-number priority order: ['Avery', 'Blake', 'Casey']
[Tiebreaker: Lot Number Priority]
Tie among: ['Avery', 'Blake']
Resolved: ['Avery'] (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.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Casey -- 53 -- First place
Avery -- 47
Equal Support -- 0
Casey wins.
Voters with a preference: 100 of 100 (no Equal Support).
Casey 53 (53%) vs Avery 47 (47%); majority = 51.
Winner — STAR Voting Method (single winner)
Casey
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 100 ballots (converted from score ballots; 0 = unranked, equal scores broken by candidate priority).
Ballots:
the ranking RCV-IRV reads (0 = unranked, equal scores broken by priority);
the source score ballot follows in () per column: Avery, Blake, Casey
47 × Avery > Casey > Blake (5, 1, 3)
47 × Blake > Casey > Avery (1, 5, 3)
3 × Casey > Avery > Blake (3, 1, 5)
3 × Casey > Blake > Avery (1, 3, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Avery 47 Hopeful
Blake 47 Hopeful
Casey 6 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Avery 50 Elected
Blake 50 Rejected
Casey 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Avery
--- Smith Set (the generalized Condorcet winner) ---
The smallest group whose every member beats every candidate outside it —
the honest answer to "who is even in contention?".
Smith set (1 of 3): Casey
Outside (2): Avery, Blake
One member ⇒ Casey is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Avery is OUTSIDE the Smith set. ✗
Every member of the set (Casey) beats Avery head-to-head, yet
RCV-IRV elected Avery anyway. RCV-IRV is not Smith-efficient (nor
Condorcet-efficient) — this is the shape a center squeeze leaves behind.
More: 07_Concepts/topics/smith_set.md
NOTE: a generated cross-method view of the STAR ballots, for comparison only — not the official STAR result.
Ranked Robin (RCV-RR) — every pair, head-to-head¶
--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
Tabulating 100 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Avery, Blake, Casey
47 × Avery > Casey > Blake (5, 1, 3)
47 × Blake > Casey > Avery (1, 5, 3)
3 × Casey > Avery > Blake (3, 1, 5)
3 × Casey > Blake > Avery (1, 3, 5)
Round-Robin — every pair, head-to-head (For – Against):
Avery ties Blake 50 – 50
Casey beats Avery 53 – 47
Casey beats Blake 53 – 47
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Avery | Blake | Casey |
------------------------------------------------------
Avery > | --- |50 - 0 - 50 |47 - 0 - 53 |
Blake > | 50 - 0 - 50 | --- |47 - 0 - 53 |
Casey > | 53 - 0 - 47 |53 - 0 - 47 | --- |
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 Casey 2–0–0 2 +12 Avery, Blake
2 Avery 0–1–1 0.5 -6 —
3 Blake 0–1–1 0.5 -6 —
Winner — Ranked Robin (RCV-RR): Casey
beats every opponent head-to-head — the Condorcet winner.
--- Smith Set (the generalized Condorcet winner) ---
The smallest group whose every member beats every candidate outside it —
the honest answer to "who is even in contention?".
Smith set (1 of 3): Casey
Outside (2): Avery, Blake
One member ⇒ Casey is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Casey is INSIDE the Smith set. ✓
Guaranteed: Ranked Robin (Copeland) is Smith-efficient — every member of
the set outscores every outsider, so the top of the win–loss table is
always inside the set, however the tie among them is then broken.
More: 07_Concepts/topics/smith_set.md