Sincere STAR — the center wins (Beth is the Condorcet winner)¶
▶ Live on BetterVoting: vote · results ↗ (election 2kcwbw · test BV2221) — 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 Beth — and so do Ranked Robin and Condorcet, because Beth is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Ana: Beth collects fewer top (first-choice) votes, so IRV eliminates Beth early, and those ballots transfer to Ana. 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 | Beth |
| RCV-IRV | Ana |
| Ranked Robin (RCV-RR) | Beth |
| Approval | Beth |
| Range / Score | Beth |
| Condorcet | Beth |
Flags: none
Source election: method_comparisons/star_5_1_0_challenge/cases/bv2221_2kcwbw_sincere.yaml · STAR tabulated mirror: bv2221_2kcwbw_sincere_tabulated.txt
3 candidates, 100 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Ana | Beth | Cole |
|---|---|---|---|
| 48 | 5 | 3 | 0 |
| 47 | 0 | 3 | 5 |
| 5 | 2 | 5 | 0 |
STAR result (official)¶
Scoring round (sum of scores): Beth 310, Ana 250, Cole 235
Finalists (top two): Beth and Ana
Automatic runoff: Beth 52 vs Ana 48
STAR winner: Beth
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Ana | * Beth |
-----------------------------------------------
* Ana > | --- |48 - 0 - 52 |
* Beth > | 52 - 0 - 48 | --- |
[Divergence from STAR]
STAR = Beth
Choose-One (Plurality) = Ana (differs from STAR)
RCV-IRV = Ana (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 × Ana,Beth,Cole
48 × 5, 3, 0
47 × 0, 3, 5
5 × 2, 5, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Ana 48 0 0 5 0 47 | 250 2.5
Beth 5 0 95 0 0 0 | 310 3.1
Cole 47 0 0 0 0 53 | 235 2.4
Scoring Round
The two highest-scoring candidates advance to the next round.
Beth -- 310 -- First place
Ana -- 250 -- Second place
Cole -- 235
Beth and Ana advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Beth -- 52 -- First place
Ana -- 48
Equal Support -- 0
Beth wins.
Voters with a preference: 100 of 100 (no Equal Support).
Beth 52 (52%) vs Ana 48 (48%); majority = 51.
Winner — STAR Voting Method (single winner)
Beth
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: Ana, Beth, Cole
48 × Ana > Beth (5, 3, 0)
47 × Cole > Beth (0, 3, 5)
5 × Beth > Ana (2, 5, 0)
ROUND 1
Candidate Votes Status
----------- ------- --------
Ana 48 Hopeful
Cole 47 Hopeful
Beth 5 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Ana 53 Elected
Cole 47 Rejected
Beth 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Ana
--- 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): Beth
Outside (2): Ana, Cole
One member ⇒ Beth is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Ana is OUTSIDE the Smith set. ✗
Every member of the set (Beth) beats Ana head-to-head, yet
RCV-IRV elected Ana 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: Ana, Beth, Cole
48 × Ana > Beth > Cole (5, 3, 0)
47 × Cole > Beth > Ana (0, 3, 5)
5 × Beth > Ana > Cole (2, 5, 0)
Round-Robin — every pair, head-to-head (For – Against):
Beth beats Ana 52 – 48
Ana beats Cole 53 – 47
Beth beats Cole 53 – 47
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Ana | Beth | Cole |
-----------------------------------------------------
Ana > | --- |48 - 0 - 52 |53 - 0 - 47 |
Beth > | 52 - 0 - 48 | --- |53 - 0 - 47 |
Cole > | 47 - 0 - 53 |47 - 0 - 53 | --- |
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 Beth 2–0–0 2 +10 Ana, Cole
2 Ana 1–1–0 1 +2 Cole
3 Cole 0–2–0 0 -12 —
Winner — Ranked Robin (RCV-RR): Beth
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): Beth
Outside (2): Ana, Cole
One member ⇒ Beth is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Beth 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